Download Molecular Gas in the Large Magellanic Cloud

Molecular Gas in the Large Magellanic
Cloud
Annie Hughes
Presented in fulfillment of the requirements
of the degree of Doctor of Philosophy
December 2010
Faculty of Information and Communication Technology
Swinburne University
Abstract
This thesis presents new observations and analysis of the molecular gas in the Large
Magellanic Cloud (LMC). The observations were conducted at the Mopra Telescope
as part of the Magellanic Mopra Assessment (MAGMA) project, which has obtained
high resolution (45′′ ) maps of the
12 CO(J
= 1 → 0) emission from 70% by mass of
the LMC’s molecular cloud population. We show that CO emission in the LMC arises
predominantly in spatially compact structures with high surface brightness, and that
the total CO luminosity of the LMC is two orders of magnitude lower than would be
predicted by the correlations between CO luminosity, stellar mass and 1.4 GHz radio
continuum that are observed for nearby late-type galaxies.
We present a catalogue of giant molecular clouds (GMCs) in the LMC using the
MAGMA CO data, and investigate whether the catalogued clouds are similar to GMCs
in the Milky Way and other nearby galaxies. We find that GMCs in the LMC roughly
follow the scaling relations between radius, velocity dispersion, mass and CO luminosity that have been determined for Galactic GMCs, but that LMC clouds have narrow
linewidths and faint CO luminosities relative to their size. The physical properties of
the observed GMCs are mostly insensitive to variations in the local interstellar conditions, but there are significant positive correlations between the atomic gas column
density and the GMC velocity dispersion, and the stellar mass surface density and
both the peak CO brightness and CO surface brightness of the GMCs. Our results are
difficult to reconcile with models that posit molecular clouds as equilibrium structures
that are regulated by either the interstellar radiation field or the ambient interstellar
pressure.
Finally, we consider whether molecular gas is relevant for the correlation between the
1.4 GHz radio continuum and far-infrared (FIR) emission within the LMC. We find
robust correlations between the non-thermal radio continuum and the gas and dust
emission in regions covering half the LMC’s gas disk, and we identify star formation
and the neutral gas surface density as the key parameters that determine the strength
of these correlations. In regions where the star-formation activity is low relative to the
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availability of dense gas, the non-thermal radio continuum is more tightly correlated
with the gas and dust emission. We demonstrate that coupling between the magnetic
field strength and the gas volume density can account for the exponent of the local
radio-FIR correlation that we observe in the LMC, adopting plausible assumptions for
the LMC’s UV opacity, dust-to-gas ratio and cosmic ray distribution.
Acknowledgments
This thesis took longer to arrive at its destination than most, and it is a pleasure to thank the
many people that have offered me support and inspiration along the way.
Foremost, I would like to thank my supervisors. Sarah Maddison was always positive, encouraging, generous with her time, and much too tolerant of my meandering away from her primary
astronomical interests. I thank Tony Wong and Juergen Ott for trusting me with the MAGMA
survey, and for enduring the barrage of plots and half-baked ideas that I offered in return.
Through his critical acumen and bias for theory that yields empirically testable predictions,
Tony taught me the value of approaching new ideas with a thoughtful skepticism. Juergen’s
voracious pursuit of more photons and his readiness to yarn about the big picture reminded me
that doing science is a joy, even when the experiments don’t work out. I thank Lister StaveleySmith for accepting me as an ATNF co-supervised student and for having high expectations.
Lister instilled me with dread, determination and confidence by turns. That this thesis is finished is due largely to an alchemic reaction between those three psychological states.
At the Centre for Astrophysics and Supercomputing, I am especially grateful to Matthew Bailes,
who convinced me to move to Melbourne and introduced me to astronomy research while I was
still a first-year undergraduate. The Centre will be hard-pressed to find a Director who promotes and advocates for students as strongly as Matthew does. I would also like to thank all
the observatory staff at the Australia Telescope Compact Array and the Mopra Telescope for
their help and forbearance. Mopra’s renaissance was pivotal to MAGMA, so I am especially indebted to the ATNF Engineering & Operations group. Every winter I would arrive at telescope
expecting the observing system to work, and without fail it did. My sole complaint is that the
world still appears to have problems, despite Robin and I solving them several times over on our
walks around the heliograph track. I thank Mark Calabretta, Sean Amy and Vince McIntyre at
ATNF, and Jarrod Hurley, Gin Tan and Simon Forsayeth at Swinburne for promptly appeasing
the computer gods whenever I offended them, and Amr Hassan for his generous assistance with
a figure that never quite worked out.
I was fortunate to spend time at a number of excellent institutions during the course of my
PhD. Bill Reach hosted my visit to the Spitzer Science Centre in Pasadena. If I am at all
proficient at back-of-the-envelope calculations, it is because Bill goaded me into paying more
attention to equations. Jean-Philippe Bernard invited me to the Centre d’Etude Spatiale des
Rayonnements in Toulouse. J-P’s knowledge of interstellar dust is formidable and his passion
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for research would be hazardous in someone less energetic, but above all I have appreciated
his sense of humour and friendship. You-Hua Chu and Professor Fukui made me feel welcome
during my short visits to their departments, and I thank them for the stimulating and challenging discussions about topics that I thought I understood. On a more personal level, I am
grateful to Louise Shi, Helen Zhang and Selene Wong. I doubt that they bargained on a vagrant
student as a house guest, but their hospitality made my trips to Perth and Champaign-Urbana
a genuine pleasure. Steve Ord, Andrew Campbell and Alex Cameron are good friends, but I
must nonetheless thank them here for the countless times that they put me up during short
stays in Sydney.
On several occasions, I had the privilege of spending time at the Observatio Astrónomico Nacional de Colombia. I am indebted to Benjamı́n Calvo Mozo, David Ardila, Mario Armando
Higuera Garzón, Jaime Forero Romero and Juan Manuel Tejeiro Sarmiento for making those
visits possible (and productive). My parallel life at La Nacho was made easier by the warmth
and friendliness of Doña Teresa, Giovanni Pinzón Estrada, Hernán Garrido Vertel, Juan Camilo
Buitrago, Juan Camilo Ibañez, Jean-Paul Picón and Oscar Ramirez.
I would like to thank the two other members of the MAGMA core team, Erik Muller and Jorge
Pineda, with whom I shared the wee hours, long walks and Mopra madness. Erik and Jorge
taught me everything about millimetre observing that my supervisors forgot to mention, but
should not be held responsible for the errors in my understanding that remain. Thanks also to
my fellow students at Swinburne and the ATNF, many of whom are now pursuing illustrious careers around the globe. Chris Thom has been a good friend and sounding board over the years,
as well as my first port of call for troubles with latex, IDL, and everything computer-related.
My friendship with Chris Brook predates both our PhDs; I’m glad that it has lasted in spite of
common academic interests. At the ATNF, I enjoyed working with Ann Mao, Urvashi Rau and
Deanna Matthews. Amongst the current cohort of Swinburne students, postdocs and staff, the
friendship of Juan Madrid, Francesco Pignatale, Catarina Ubach, Lee Spitler, Virginia Kilborn
and Carlos Contreras Velasquez has helped me to survive the final months of thesis write-up.
In the larger field of astronomy, I am especially thankful to Adam Leroy and Erik Rosolowsky,
whose only crime was to work on similar astronomical problems as I do. Over the years, I have
punished them with naive questions and they have invariably responded with patience, clarity
and insight. Andrew Melatos, Chris Power and Christophe Pichon proved to me that science
achieves its fullest potential when combined with a fine moral sense. I appreciate the interest
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in my work expressed by Kate Brooks, Baerbel Koribalski, Naomi McClure-Griffiths, Akiko
Kawamura, Tim Cornwall, Robert Braun, Alberto Bolatto and Ron Ekers, and am grateful for
the wisdom and advice that they offered.
Outside of astronomy, Liz Hobday, Amy Atkinson, Sarah McCusker, Chusa Eito, Anthony Rodriguez, Ariana Callejas Capra, Juan Manuel Viatela, the entire Beeson family, Ron and Roz
Goodwin, and my sister Ali have contributed enormously to my well-being and sanity while this
thesis was in progress. My family in Colombia have given me a second home and the latitude
to be myself. The first part of this thesis is dedicated to my parents, Chris and Millicent.
They brought me up to believe that learning is its own reward, and have been living with the
consequences ever since. It is too easy to take the constant things in one’s life for granted, but
I am profoundly grateful for their love and support, and appreciative that I never once heard
them say the words “real job”. The second part is dedicated to my son, Martin. You arrived
at the right time, and put everything in perspective.
Finally, I would like to thank my husband Luis, who lived through it.
Financial support for this research was provided by an Australian Postgraduate Award, with
additional funding provided by the Australia Telescope National Facility, the Faculty of Information and Communication Technologies at Swinburne University of Technology, the Australian
Federation of University Women, and the Australia Research Council via the Australia-France
Cooperation Fund in Astronomy. Much of the analysis in this thesis was enabled by tools produced by the yorick, R, and IDL programming communities. This thesis also made extensive
use of the NASA Astrophysics Data System (ADS), the NASA/IPAC Extragalactic Database
(NED), the SIMBAD database and the Vizier catalogue access tool. I am indebted to the people that support these projects, and to researchers who make their data and/or code available
online. The Australia Telescope Compact Array and Mopra Telescope are part of the Australia
Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The University of New South Wales Digital Filter Bank used for
the observations with the Mopra Telescope was provided with support from the Australian
Research Council.
Declaration
This thesis contains no material which has been accepted for the award of any other
degree or diploma. To the best of my knowledge and belief, it contains no material
previously published or written by another person, except where due reference is made
in the text of the thesis. All work presented is primarily that of the author.
Much of the material in Chapters 2 to 6 was drawn from the publications Hughes et al.
(2006), Hughes et al. (2007) and Hughes et al. (2010). I acknowledge helpful discussions and critical feedback that were provided by my co-authors and three anonymous
referees during the preparation of these publications. In addition, Tony Wong wrote
an initial version of the script that was used to calculate the wavelet cross spectra presented in Chapter 6, and co-authored the original discussion of Hughes et al. (2006).
He therefore contributed significantly to the ideas in Sections 5.6.1 and 6.4.2, although
the current text has been revised by the author to reflect the more recent analysis.
Annie Hughes
December 2010
vii
Contents
Abstract
i
Acknowledgments
v
Declaration
vii
List of Figures
xiii
List of Tables
xx
1 Introduction
1
1.1
Overview of Molecular Cloud Properties . . . . . . . . . . . . . . . . . .
5
1.2
Molecular Gas in Dwarf Galaxies . . . . . . . . . . . . . . . . . . . . . .
9
1.3
Observing Molecular Gas . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.4
The Dynamical Properties of Molecular Clouds . . . . . . . . . . . . . .
15
1.4.1
The Size-linewidth Relationship . . . . . . . . . . . . . . . . . . .
15
1.4.2
Molecular Clouds are Self-Gravitating . . . . . . . . . . . . . . .
17
1.4.3
Molecular Clouds Have Constant Column Density . . . . . . . .
21
1.5
Star Formation on Galactic Scales . . . . . . . . . . . . . . . . . . . . .
21
1.6
The Large Magellanic Cloud: A Laboratory for Extragalactic Star For-
1.7
2 A
mation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
12 CO(J
2.1
= 1 → 0) Survey of the LMC with Mopra
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1
12 CO(J
32
= 1 → 0) Surveys of the LMC . . . . . . . . . .
35
The MAGMA LMC Survey . . . . . . . . . . . . . . . . . . . . . . . . .
39
2.2.1
Observing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2.2.2
Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.3
Flux Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
2.4
Data Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.5
Ancillary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
2.2
Previous
31
ix
x
Contents
2.5.1
H I Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
2.5.2
Far-infrared Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
2.5.3
1.4 GHz Radio Continuum Data . . . . . . . . . . . . . . . . . .
65
2.5.4
NANTEN CO Data . . . . . . . . . . . . . . . . . . . . . . . . .
65
2.5.5
Stellar Mass Surface Density . . . . . . . . . . . . . . . . . . . .
67
2.5.6
H α Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
2.5.7
Interstellar Radiation Field . . . . . . . . . . . . . . . . . . . . .
68
2.5.8
Star Formation Rate Surface Density . . . . . . . . . . . . . . . .
70
2.5.9
Interstellar Pressure . . . . . . . . . . . . . . . . . . . . . . . . .
71
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
2.6.1
Qualitative Comparison with Gas and Dust Tracers . . . . . . .
72
2.6.2
Separation of H I and CO Peaks . . . . . . . . . . . . . . . . . . .
73
2.6.3
CO Emission and Global Properties of the LMC . . . . . . . . .
81
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
2.A Subregion Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
2.6
2.7
2.B Angular Separation Formulae . . . . . . . . . . . . . . . . . . . . . . . . 105
3 Properties of MAGMA GMCs: I. Overview
107
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.2
The GMC Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.3
3.2.1
Identifying GMCs . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.2.2
Selection Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Properties of GMCs in the LMC . . . . . . . . . . . . . . . . . . . . . . 132
3.3.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.3.2
Spatial Distribution and Cloud Geometry . . . . . . . . . . . . . 132
3.3.3
Physical Properties of GMCs . . . . . . . . . . . . . . . . . . . . 137
3.4
Comparison with NANTEN GMCs . . . . . . . . . . . . . . . . . . . . . 145
3.5
Physical properties of GMCs without Star Formation . . . . . . . . . . . 150
3.6
Velocity Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
3.7
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
3.7.1
The CO-to-N (H2 ) Conversion Factor . . . . . . . . . . . . . . . . 166
Contents
3.8
xi
3.7.2
Comparison with Previous Results . . . . . . . . . . . . . . . . . 171
3.7.3
Properties of non-star-forming GMCs . . . . . . . . . . . . . . . 178
3.7.4
Rotation and MAGMA GMCs . . . . . . . . . . . . . . . . . . . 179
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
3.A Data for Excluded Emission Regions . . . . . . . . . . . . . . . . . . . . 187
3.B The MAGMA GMC catalogue
. . . . . . . . . . . . . . . . . . . . . . . 189
3.C Velocity Gradients of MAGMA GMCs . . . . . . . . . . . . . . . . . . . 193
4 Properties of MAGMA GMCs: II. Scaling Relations and Environmental Trends
197
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
4.2
The Larson Scaling Relations . . . . . . . . . . . . . . . . . . . . . . . . 201
4.3
4.4
4.5
4.2.1
The Size-Linewidth Relation . . . . . . . . . . . . . . . . . . . . 202
4.2.2
The Size-Luminosity Relation . . . . . . . . . . . . . . . . . . . . 205
4.2.3
The Calibration between Virial Mass and CO Luminosity . . . . 205
GMC Properties and Environment . . . . . . . . . . . . . . . . . . . . . 207
4.3.1
Comparison with Galactocentric Radius . . . . . . . . . . . . . . 210
4.3.2
Comparison with G0 . . . . . . . . . . . . . . . . . . . . . . . . . 210
4.3.3
Comparison with the Interstellar Pressure . . . . . . . . . . . . . 212
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
4.4.1
The Origin of Larson’s Laws . . . . . . . . . . . . . . . . . . . . 217
4.4.2
GMC Properties: Trends with Environment . . . . . . . . . . . . 226
4.4.3
The Kennicutt-Schmidt Law at Cloud Scales in the LMC . . . . 230
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
5 An ATCA 20cm Radio Continuum Study of the LMC
243
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
5.2
Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
5.3
Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
5.3.1
Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
5.3.2
Deconvolution
5.3.3
Peeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
xii
Contents
5.4
5.3.4
Combination of Inteferometer and Single Dish Data . . . . . . . 256
5.3.5
Sensitivity of the ATCA+Parkes 1.4 GHz Image . . . . . . . . . 258
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
5.4.1
Total 1.4 GHz flux density of the LMC . . . . . . . . . . . . . . . 258
5.4.2
Contribution from Background Sources . . . . . . . . . . . . . . 259
5.4.3
Morphology of the LMC’s 1.4 GHz Continuum Emission . . . . . 261
5.4.4
The Radio Spectral Index . . . . . . . . . . . . . . . . . . . . . . 264
5.5
Thermal and Non-Thermal Components of the 1.4 GHz Emission . . . . 267
5.6
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
5.6.1
The Connection between Radio Continuum and CO Emission in
the LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
5.6.2
The Star Formation Rate in the LMC . . . . . . . . . . . . . . . 279
5.6.3
Variations of the Radio Spectral Index and Cosmic Ray Losses
in the LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
5.7
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
6 The Radio-FIR Correlation in the LMC
293
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
6.2
Observational Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
6.3
6.4
6.2.1
Neutral Gas Column Density Map . . . . . . . . . . . . . . . . . 298
6.2.2
Total Infrared Map . . . . . . . . . . . . . . . . . . . . . . . . . . 299
6.2.3
FIR/radio Ratio Map . . . . . . . . . . . . . . . . . . . . . . . . 301
6.2.4
1.◦ 35 × 1.◦ 35 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
6.3.1
Pixel-by-pixel Analysis . . . . . . . . . . . . . . . . . . . . . . . . 304
6.3.2
Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
6.3.3
Wavelet Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
6.3.4
Wavelet Cross-correlations . . . . . . . . . . . . . . . . . . . . . . 336
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
6.4.1
The Local Radio-FIR Correlation . . . . . . . . . . . . . . . . . . 344
6.4.2
The Global Radio-FIR Correlation . . . . . . . . . . . . . . . . . 356
Contents
6.5
xiii
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
7 Concluding Remarks
363
7.1
CO as a Tracer of H2 in Dwarf Galaxies . . . . . . . . . . . . . . . . . . 363
7.2
GMC Properties and Galactic Environment . . . . . . . . . . . . . . . . 365
7.3
Molecular Gas and the Radio-FIR Correlation . . . . . . . . . . . . . . . 367
7.4
Future Outlook: Cosmic Star Formation and the LMC . . . . . . . . . . 369
Bibliography
371
Thesis Publications
406
List of Figures
2.1
Correlation between peak brightness of Orion KL and centre frequency
of MOPS observing band . . . . . . . . . . . . . . . . . . . . . . . . . .
12 CO(J
42
2.2
MAGMA map of
= 1 → 0) integrated intensity in the LMC . .
49
2.3
Map of integrated intensity H I emission in the LMC . . . . . . . . . . .
50
2.4
Velocity channel maps of CO emission in the LMC . . . . . . . . . . . .
52
2.5
Velocity centroids of CO and H I emission in the LMC . . . . . . . . . .
53
2.6
Distribution of noise fluctuations in the MAGMA survey region . . . . .
55
2.7
Distributions of CO peak brightness and CO integrated intensity in the
MAGMA survey region . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
2.8
Map of H I peak brightness in the LMC . . . . . . . . . . . . . . . . . .
60
2.9
Maps of far-infrared emission in the LMC . . . . . . . . . . . . . . . . .
61
2.10 Global infrared-to-radio spectrum of the LMC . . . . . . . . . . . . . . .
64
2.11 Map of CO integrated intensity in the LMC by NANTEN . . . . . . . .
66
2.12 Map of H α emission in the LMC. . . . . . . . . . . . . . . . . . . . . . .
68
2.13 Maps of H I emission associated with molecular clouds in the MAGMA
survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
2.14 Locations of local CO maxima in the LMC . . . . . . . . . . . . . . . .
75
2.15 Probability distribution for angular offset between CO and H I peaks . .
77
2.16 Spatial separation of I(CO) and I(H I) peaks versus properties of CO
and H I emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
2.17 H I column density decrement versus decrement in H I properties at CO
peaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.18 MAGMA maps of
12 CO(J
= 1 → 0) integrated intensity for LMC sub-
regions and example spectra . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
80
89
Velocity channel maps of a MAGMA GMC indicating the CO emission
identified by CPROPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.2
Measured versus input radius of model clouds . . . . . . . . . . . . . . . 122
3.3
Measured versus input velocity dispersion for model clouds . . . . . . . 123
3.4
Measured versus input peak CO brightness for model clouds . . . . . . . 124
xv
xvi
List of Figures
3.5
Measured versus input major-to-minor axis ratio of model clouds . . . . 125
3.6
Measured versus input CO luminosity of model clouds . . . . . . . . . . 126
3.7
Measured versus input virial mass of model clouds . . . . . . . . . . . . 127
3.8
Measured versus input CO surface brightness of model clouds . . . . . . 128
3.9
Measured versus input mass surface density of model clouds . . . . . . . 129
3.10 Measured versus input CO-to-H2 conversion factor of model clouds . . . 130
3.11 Positional Data of GMCs in the LMC . . . . . . . . . . . . . . . . . . . 134
3.12 Spatial distribution of molecular mass in the LMC . . . . . . . . . . . . 135
3.13 Geometry of MAGMA GMCs . . . . . . . . . . . . . . . . . . . . . . . . 136
3.14 Axis ratio of MAGMA GMCs versus their radius . . . . . . . . . . . . . 136
3.15 Distribution of θ values for MAGMA GMCs . . . . . . . . . . . . . . . . 137
3.16 CO luminosity distribution of MAGMA GMCs . . . . . . . . . . . . . . 139
3.17 Size distribution of MAGMA GMCs . . . . . . . . . . . . . . . . . . . . 142
3.18 Velocity dispersion distribution of MAGMA GMCs . . . . . . . . . . . . 144
3.19 Peak CO brightness of GMCs in the MAGMA catalogue . . . . . . . . . 146
3.20 Comparison between MAGMA and NANTEN cloud property measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.21 Correlation between the virial parameter of MAGMA GMCs and their
star formation activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.22 Velocity structure in MAGMA GMCs . . . . . . . . . . . . . . . . . . . 158
3.23 Derived velocity gradients of MAGMA GMCs . . . . . . . . . . . . . . . 162
3.24 Correlation between the velocity gradient and geometry of MAGMA GMCs164
3.25 Orientation of cloud velocity gradients in the LMC . . . . . . . . . . . . 165
3.26 Velocity gradients in the atomic gas surrounding MAGMA GMCs
. . . 167
3.27 Alignment between the GMC and local H I velocity gradients versus cloud
radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
3.28 Correlation between CO luminosity and virial mass of 100 model clouds
with randomly generated radii and velocity dispersions . . . . . . . . . . 170
3.29 Radiation field and stellar mass surface density at location of MAGMA
GMCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
List of Figures
xvii
3.30 Predicted and measured values of the specific angular momenta for MAGMA
GMCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
4.1
Larson’s Laws for MAGMA GMCs . . . . . . . . . . . . . . . . . . . . . 203
4.2
GMC properties versus dKC . . . . . . . . . . . . . . . . . . . . . . . . . 211
4.3
GMC properties versus G0 . . . . . . . . . . . . . . . . . . . . . . . . . . 213
4.4
GMC properties versus Σ∗ . . . . . . . . . . . . . . . . . . . . . . . . . . 215
4.5
GMC properties versus ΣH I . . . . . . . . . . . . . . . . . . . . . . . . . 216
4.6
GMC properties versus Ph . . . . . . . . . . . . . . . . . . . . . . . . . . 218
4.7
Values of ΣH2 predicted by Elmegreen (1989) versus values observed for
MAGMA GMCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
4.8
Correlations between the surface densities of stars, gas and star formation in the LMC at the scale of individual GMCs . . . . . . . . . . . . . 232
4.9
H I column density map of a region within the LMC disk at different
angular resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
4.10 The effect of resolution on the ΣH I saturation threshold . . . . . . . . . 235
4.11 Correlation between ΣSF R and Σgas in the LMC at 80, 150, 250 and
500 pc resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
4.12 Radial profiles of H α, H I and
12 CO(J
= 1 → 0) emission in the LMC . 239
5.1
The scanning strategy and pointing centres of the ATCA LMC mosaic . 249
5.2
u − v coverage of a single pointing within the ATCA LMC mosaic . . . 250
5.3
Example of peeling for a single pointing in the ATCA mosaic . . . . . . 253
5.4
The ATCA 1.4 GHz mosaic of the LMC . . . . . . . . . . . . . . . . . . 255
5.5
Survey image of the 1.4 GHz emission in the 30 Doradus region, with and
without peeling corrections to the ATCA visibility data . . . . . . . . . 256
5.6
The combined ATCA+Parkes map of 1.4 GHz continuum emission in the
LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
5.7
The median-filtered combined ATCA+Parkes map of 1.4 GHz continuum
emission in the LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
5.8
1.4 and 4.8 GHz intensity profiles through 30 Doradus . . . . . . . . . . 264
5.9
Map of the 1.4-4.8 GHz spectral index in the LMC . . . . . . . . . . . . 268
xviii
List of Figures
5.10 Relationship between dust temperature, 160 µm surface brightness and
optical depth at 160 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
5.11 Maps of the thermal and non-thermal 1.4 GHz emission in the LMC . . 272
5.12 Model results for the non-thermal radio emission in the LMC at 1.4 GHz 275
5.13 Comparison between the 1.4 GHz and I(CO) emission in the LMC . . . 277
5.14 Map of the 1.4-to-4.8 GHz non-thermal spectral index in the LMC . . . 284
5.15 Radial profiles of the radio spectral index and thermal fraction at 1.4 GHz285
6.1
Correlation between integrated 1.4 GHz and 60 µm luminosities of 1809
galaxies in the IRAS 2 Jy Redshift Survey and NRAO VLA Sky Survey 295
6.2
Map of the total hydrogen nucleon column density in the LMC . . . . . 299
6.3
Map of the total far-infrared emission in the LMC . . . . . . . . . . . . 300
6.4
Map of the logarithmic FIR/radio ratio in the LMC . . . . . . . . . . . 302
6.5
Correlation between 70 µm and 1.4 GHz continuum emission in the LMC 307
6.6
Correlation between 70 µm and 1.4 GHz continuum emission for the
1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
6.7
Properties that influence the strength and slope of the local 70 µm1.4 GHz correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
6.8
Correlation between 70 µm and the thermal and non-thermal components of the 1.4 GHz continuum emission in the LMC . . . . . . . . . . . 313
6.9
Correlation between 70 µm and thermal 1.4 GHz emission for the 1.◦ 35 ×
1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
6.10 Correlation between 70 µm and non-thermal 1.4 GHz emission for the
1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
6.11 Properties that influence the strength of the local non-thermal 1.4 GHz70 µm correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
6.12 Relationship between neutral gas column density, 1.4 GHz continuum
and radio spectral index in the LMC . . . . . . . . . . . . . . . . . . . . 318
6.13 Correlation between N (H) and the 1.4 GHz continuum emission in the
LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
List of Figures
xix
6.14 Correlation between N (H) and 1.4 GHz continuum for the 1.◦ 35 × 1.◦ 35
fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
6.15 Correlation between N (H) and the thermal and non-thermal components
of the 1.4 GHz continuum emission in the LMC . . . . . . . . . . . . . . 321
6.16 Correlation between N (H) and thermal 1.4 GHz radio continuum for the
1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
6.17 Correlation between N (H) and non-thermal 1.4 GHz radio continuum for
the 1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
6.18 Properties that influence the strength of the local non-thermal 1.4 GHzN (H) correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
6.19 Correlation between N (H) and 70 µm flux density for the whole LMC . 325
6.20 Correlation between N (H) and 70 µm flux density for the 1.◦ 35 × 1.◦ 35 fields326
6.21 Properties that influence the slope of the local 70 µm-N (H) correlation . 327
6.22 Correlation between the FIR/radio ratio and N (H) in the LMC . . . . . 328
6.23 Correlation between the FIR/radio ratio and N (H) for the 1.◦ 35 × 1.◦ 35
fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
6.24 Properties that influence the slope and strength of the correlation between the FIR/radio ratio and the neutral gas column density . . . . . . 330
6.25 Wavelet spectra for various continuum and spectral line maps of the LMC334
6.26 Wavelet cross-correlation spectra for comparisons between maps of the
1.4 GHz radio, 70 µm and 160 µm images and the neutral gas column
density map of the LMC . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
6.27 Wavelet cross-correlation spectra between the 1.4 GHz and 70 µm images
of the 1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
6.28 Wavelet cross-correlation spectra between the neutral gas column density, 70 µm and 1.4 GHz continuum maps of the 1.◦ 35 × 1.◦ 35 fields . . . . 340
6.29 Properties that influence the breakdown scale of the 70 µm-1.4 GHz wavelet
cross-correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
6.30 Properties that influence the breakdown scale of the N (H)-1.4 GHz crosscorrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
xx
List of Figures
6.31 Correlation between non-thermal 1.4 GHz emission and stellar mass for
the 1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
6.32 Observed versus predicted slopes for the non-thermal 1.4 GHz-N (H) correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
6.33 Observed slopes of the local non-thermal 1.4 GHz-70 µm correlations versus the slope predicted by B − ρ coupling model . . . . . . . . . . . . . 353
6.34 Observed slopes of the local non-thermal 1.4 GHz-160 µm correlations
versus the slope predicted by B − ρ coupling model . . . . . . . . . . . . 355
List of Tables
1.1
Physical properties of ISM gas phases . . . . . . . . . . . . . . . . . . .
6
1.2
Positional and geometric data for the LMC . . . . . . . . . . . . . . . .
26
1.3
Global Properties of the LMC . . . . . . . . . . . . . . . . . . . . . . . .
28
2.1
Average peak brightness of Orion KL for different epochs of the MAGMA
survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Comparison between MAGMA and SEST measurements of
12 CO(J
43
=
1 → 0) emission in the LMC . . . . . . . . . . . . . . . . . . . . . . . . .
47
2.3
Characteristics of ancillary datasets used in this work . . . . . . . . . .
58
2.4
Spearman rank correlation test results for CO-H I peak separation . . .
79
2.5
Grid of H I brightness temperature solutions for plausible values of Tb,warm ,
Tk,cold , τcold and f
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
3.1
Parameters used to generate the model cloud dataset . . . . . . . . . . . 119
3.2
Model fit results for the mass distribution of GMCs in the LMC
3.3
Comparison between NANTEN and MAGMA cloud property measure-
. . . . 141
ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3.4
Average physical properties of MAGMA GMCs . . . . . . . . . . . . . . 153
3.5
Average properties of resolved GMCs in the LMC and nearby galaxies . 173
3.6
Survey parameters and general properties of galaxies in Table 3.5 . . . . 174
3.7
Data for Excluded Emission Regions . . . . . . . . . . . . . . . . . . . . 187
3.8
The MAGMA GMC catalogue
3.9
Velocity gradient fit results for MAGMA GMCs . . . . . . . . . . . . . . 193
4.1
Results of Spearman correlation tests between intrinsic and environmen-
. . . . . . . . . . . . . . . . . . . . . . . 189
tal properties of MAGMA GMCs . . . . . . . . . . . . . . . . . . . . . . 209
4.2
Results of Spearman correlation tests corresponding to Larson’s scaling
relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
4.3
Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
5.1
Observing log for the ATCA LMC 1.4 GHz survey . . . . . . . . . . . . 248
xxi
xxii
List of Tables
5.2
Characteristics of the 1.4 GHz and 4.8 GHz emission in the LMC . . . . 263
5.3
Mean H α extinction and thermal/non-thermal 1.4 GHz flux densities
derived for trial combinations of the dust screening factor and electron
temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.4
Summary of global SFR estimates for the LMC . . . . . . . . . . . . . . 281
5.5
Definitions of symbols used in Equations 5.8 to 5.12 . . . . . . . . . . . 286
5.6
Timescales for competing cosmic ray loss mechanisms in the LMC . . . 288
6.1
Characteristics of 1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . 305
6.2
Summary of the pixel-by-pixel and wavelet cross-correlation results for
the LMC and 1.◦ 35 × 1.◦ 35 fields . . . . . . . . . . . . . . . . . . . . . . . 308
6.3
Summary of properties that were investigated for their influence on the
correlations between dust, gas and radio continuum emission in the LMC 312
6.4
Summary of image pairs and wavelet cross-correlation coefficients . . . . 336
1
Introduction
The space between stars is not empty, but instead contains a tenuous, inhomogeneous
mixture of gas and dust, collectively known as the interstellar medium (ISM). Though
it represents a minor fraction of the baryonic matter in most galaxies, the ISM plays an
important role in their evolution, providing the raw fuel for star formation, receiving
then redistributing the heavy elements that are created in stellar interiors, and mediating the exchange of matter and energy between galaxies and the intergalactic medium
(IGM). Unlike stars, the ISM is neither isolated nor analytically tractable. The gaseous
component of the ISM occurs in multiple phases, with temperatures, densities and spatial structure spanning five orders of magnitude or more. Interstellar dust grains reach
a maximum dimension of several microns, yet they are the catalyst for the formation
of molecular hydrogen, and they modify the spectral energy distribution of galaxies
through the absorption and re-emission of stellar radiation. Energy is deposited into
the ISM by processes occurring on different timescales and at disparate spatial scales,
such as accretion of primordial IGM material, protostellar jets and outflows, spiral
shocks, supernovae, and thermal instability in the diffuse atomic gas. The ISM is, in
short, a complex, dynamic and beautiful system.
A complete physical description of the ISM remains an outstanding challenge for computational astrophysics. In recent years, however, both theoretical and observational
studies of the ISM have been experiencing a quiet revolution. On the theoretical front,
1
2
Chapter 1. Introduction
modern computers have enabled researchers to construct ISM models that can follow non-linear, time-dependent and out-of-equilibrium processes across an increasingly
wide range of spatial scales. Though quasi-static models remain crucial for improving
our understanding of radiative and dynamical processes in the ISM, numerical investigations into the origin and consequences of astrophysical turbulence have radically
transformed our conception of the ISM. On the observational side, advances in the resolution and sensitivity of instruments operating across the electromagnetic spectrum
have shifted the focus from global measurements of the integrated dust and gas emission
in relatively luminous galaxies, to resolved studies of ISM components within galaxies
of heterogeneous Hubble types. In the field of star formation, observations by the latest
generation of space telescopes – such as Spitzer, GALEX, and the refurbished HST –
have tended to confirm long-standing correlations between global galaxy properties,
but the new data have challenged us to decipher what these empirical scaling relations
reveal about the underlying ISM physics.
Among the ISM’s different phases, the dense molecular hydrogen gas is especially deserving of study. It is the primary component by mass of the ISM in the central regions
of spiral galaxies, and the site of all star formation (Young & Scoville, 1991). The
bulk of the molecular gas resides in giant molecular clouds (GMCs). GMCs occupy
a negligible fraction of the ISM volume, but the young stars that they form are responsible for roughly half the energy density of the ISM, which they supply through
radiative and mechanical feedback, and (in the later stages of their evolution) via the
acceleration of cosmic rays (Lequeux, 2005). Despite its importance, our knowledge of
molecular gas in other galaxies remains poor. A typical size of a Milky Way GMC is
40 pc (Blitz, 1993), so the study of individual clouds with existing millimetre interferometers is limited to galaxies within 8 Mpc. Even for surveys that aim to trace the
overall molecular gas distribution without resolving GMCs, extragalactic observations
are usually restricted to bright emission in the inner disks of luminous galaxies, as
the integration time required to achieve high sensitivity with current instrumentation
is prohibitive. The parameter space that remains sparsely sampled by current surveys
includes dwarf galaxies, as well as the interarm regions and outer disks of spiral galaxies.
3
Although it is difficult to detect, the molecular gas in these poorly studied environments may hold the key to understanding star formation and its scaling laws. Two
broad arguments support this claim. First, there can be no doubt that dwarf galaxies
form stars – some, such as NGC 253, do so vigorously! Yet the properties of the ISM
in dwarfs and spiral galaxies are quite distinct, with physical and chemical differences
that should influence the formation of molecular gas, and the subsequent potential for
molecular gas to collapse and form stars. We elaborate on some of these differences in
Section 1.2. Second, the relationship between the column density of molecular hydrogen and emission from the carbon monoxide (CO) molecule may depend on interstellar
conditions. Obtaining unequivocal evidence for such variations, and identifying the
environmental factors that regulate them, are important endeavours since CO emission remains the most practical tracer of extragalactic molecular gas. The imminent
commissioning of the Atacama Large Millimeter Array (ALMA), which will image the
molecular gas distribution in normal galaxies out to z ∼ 1, only intensifies the need for
a secure physical interpretation of the relationship between CO and H2 .
In this thesis, we present new observations and analysis of the molecular gas in the
nearby dwarf galaxy, the Large Magellanic Cloud (LMC). Our overarching aim is to
improve our understanding of molecular cloud properties and the relationship between
molecular gas and star formation. More specifically, we aim to answer the following
questions:
• Does the LMC conform to the correlations between molecular gas content, galaxy
mass and star formation rate that have been inferred from previous surveys of
star-forming galaxies?
• Do GMCs have homogeneous physical properties, regardless of their evolutionary
state and interstellar environment?
• Can existing models explain the dynamical properties of GMCs in the LMC?
Although these questions are simple, they lack definitive answers. A fourth topic has
4
Chapter 1. Introduction
broader scope, and shifts our attention to the interaction between molecular gas and
other components of the ISM. This is:
• What is the role of dense gas in maintaining a tight correlation between the
far-infrared and radio continuum emission in galaxies?
In all cases, our approach involves a detailed analysis of the molecular gas in the LMC.
While results obtained for a single galaxy lack the universality of comparative studies,
the present investigation benefits from the LMC’s iconic status across diverse areas of
astronomy, which entails a vast body of literature and a rich archive of multi-wavelength
observations.1 Empirical estimates and/or tight theoretical constraints are available for
many of the LMC’s global and ISM properties, making it one of the few galaxies where
quantitative tests of complex physical models are feasible. The second advantage of
our approach is completeness. Existing extragalactic observations of molecular gas are
strongly affected by sensitivity bias, which restricts them to studying the brightest
emission regions and most massive objects. From the survey presented in this thesis,
we construct a statistically significant sample of GMCs that not only accounts for the
bulk of the host galaxy’s CO luminosity, but also includes clouds that are unremarkable
in terms of their mass, environment and star-forming activity. Focussing solely on the
LMC thus offers a complementary perspective to the insights gained by studying large
galaxy samples, as well as a foretaste of the detailed investigations that ALMA will
enable throughout the Local Volume and beyond.
In the rest of this chapter, we present background material that pertains to the scientific
motivations of this work. We briefly review the observed properties of molecular clouds
(Section 1.1), and highlight some of the potential differences between the molecular gas
in spiral and dwarf galaxies (Section 1.2). We summarise the theoretical and empirical
rationale for using CO emission as a tracer of H2 in Section 1.3. Our current understanding of the dynamical properties of molecular clouds is reviewed in Section 1.4.
Section 1.5 introduces two powerful empirical “laws” of galactic scale star formation,
1
The extent of previous scholarship can be gauged from the NASA/IPAC Extragalactic Database,
which lists 4320 references for the LMC. For comparison, 3160 references are listed for M31, usually
regarded as the best-studied galaxy besides the Milky Way.
1.1. Overview of Molecular Cloud Properties
5
both of which lack a firm theoretical foundation. The key characteristics of the LMC
are summarised in Section 1.6, and an outline of the remaining chapters in this thesis
is presented in Section 1.7.
1.1 Overview of Molecular Cloud Properties
Interstellar gas is 70% hydrogen by mass. The hydrogen is present in three main phases,
which are used to designate the major components of the ISM (for a review, see Cox,
2005; Ferrière, 2001). The ionized ISM includes warm diffuse gas that is heated by
stellar UV radiation, dense photoionized gas in H II regions, and hot ionized gas which
is shock-heated by supernovae. Together, the warm and hot ionized gas comprise a
large fraction of the gas in the Galactic halo. The atomic ISM consists of a warm phase
with similar temperature and density as the warm ionized gas, and a higher density
cold phase that occurs in filamentary and sheet-like structures on spatial scales of a
few parsecs. Atomic gas fills most of the volume within the Galactic disk, and also
dominates the mass of the ISM in the outer regions of spiral galaxes. The molecular
gas is colder and denser, and is strongly confined to the Galactic plane. The properties
of the different gaseous ISM components are summarised in Table 1.1. One important
aspect of our conception of the ISM is that the cold atomic clouds are thought to be
in pressure equilibrium with the warm component, with P/kB = nT ≈ 2 × 104 K cm−3
in the solar neighbourhood (Field, 1965; Cox, 2005). The recent detection of thermally
unstable atomic gas with intermediate temperatures and densities does not invalidate
the pressure equilibrium model (Heiles & Troland, 2003), but it emphasises that the
ISM is affected by time-dependent phenomena that induce the gas to cycle between the
different ISM phases.
The Galaxy contains ∼ 2 × 109 M⊙ of molecular gas (Ferrière, 2001), most of which is
arranged in discrete cloud structures. Typically, these molecular clouds have masses
between 103 and 107 M⊙ , sizes between 10 and 100 pc, and mean (volume-averaged)
densities of n ∼ 100 cm−3 (Blitz, 1993). Though precise definitions in the literature
vary, the term ‘giant molecular clouds’ (GMCs) is usually reserved for clouds with
6
Chapter 1. Introduction
Table 1.1 The average density and temperature of the different gaseous components in the
ISM. The total mass of each component in the Milky Way is listed in column 5. The density is
quoted as the number density of hydrogen nuclei per cubic centimetre. Parameter values were
sourced from Ferrière (2001) and Lequeux (2005). The mass estimates assume that the ISM is
composed of 70.4% hydrogen, 28.1% helium and 1.5% heavier elements by mass.
Component
Molecular
Atomic
Ionized
Cold
Warm
Warm
Hot
H II regions
Density
[ cm−3 ]
102 − 106
20 − 50
0.2 − 0.5
0.2 − 0.5
∼ 0.0065
1 − 104
Temperature
[K]
10 − 20
50 − 100
6000 − 10000
∼ 8000
∼ 106
∼ 10000
Total Mass
[109 M⊙ ]
∼2
}&6
& 1.6
···
∼ 0.05
masses greater than 104 M⊙ , while giant molecular associations (GMAs) have masses
greater than 107 M⊙ . GMAs are only detected in the spiral arms of massive galaxies,
and it remains unclear whether they are coherent single structures or, as their name
suggests, aggregates of GMCs (e.g. Koda et al., 2009). Smaller molecular clouds with
M < 103 M⊙ are also observed, both at high galactic latitude (e.g. Magnani et al.,
1985), and in the inner and outer disk of the Milky Way (e.g. Clemens & Barvainis,
1988; Heyer et al., 2001). Regardless of their mass, the internal structure of molecular
clouds is very inhomogeneous, such that the majority of the cloud’s mass is contained
within high density substructure that occupies a small fraction of the cloud volume.
Substructure on parsec scales with densities of n ∼ 103 cm−3 is often referred to as
‘clumps’, while the term ‘cores’ typically denotes structure on sub-parsec scales with
even higher densities n > 104 cm−3 (e.g. Williams et al., 2000). The bulk of the cloud’s
volume is occupied by the intracloud medium, which possibly contains a significant
fraction of atomic gas, as well as lower density molecular gas (Blitz, 1991, 1993).
An important property of molecular clouds is that their internal motions are supersonically turbulent. This is inferred from their observed linewidths of a few km s−1 ,
which are inconsistent with thermal line broadening. The thermal velocity dispersion
of molecular gas with kinetic temperature Tk is σv,th [ km s−1 ] ≈ 0.19(Tk /[10K])1/2 (e.g.
√
McKee, 1999), indicating turbulent Mach numbers M ≡ 3(σv,nth /σv,th ) (e.g. Heiles,
2004) between 10 and 25 for clouds with Tk = 30 K and line-of-sight velocity disper-
1.1. Overview of Molecular Cloud Properties
7
sions between 2 and 5 km s−1 . Turbulence was originally regarded as a mechanism to
support molecular clouds against gravitational collapse (e.g. Fleck, 1980), but its influence may be far more profound. Recent numerical investigations have drawn attention
to transonic turbulent flows in the warm atomic gas as a potential formation pathway
for molecular clouds (e.g. Ballesteros-Paredes et al., 1999; Vázquez-Semadeni et al.,
2007), and to turbulent fragmentation within molecular gas as a mechanism that could
regulate the formation of stars (e.g. Klessen, 2001).
A long-standing puzzle about molecular cloud turbulence is why it appears to persist
for so long. Unless it is continuously replenished, supersonic turbulence should decay
q
3π
, where ρ is the gas volume density (e.g.
roughly within a free-fall time, tf f = 32Gρ
Goldreich & Kwan, 1974; Stone et al., 1998). If the lifetime of molecular clouds is
significantly longer than the dynamical timescale, then there must be a process (or
processes) that sustains the turbulence by injecting energy into the cloud on frequent
intervals. Potential turbulent driving mechanisms include small-scale processes within
molecular clouds such as protostellar outflows and expanding H II regions, and external
drivers such as galactic shear, supernovae and mass accretion from the ISM. A critical
review of potential turbulent driving mechanisms is presented by McKee & Ostriker
(2007). Evidence that supports a large-scale driving mechanism includes observations
showing that the turbulent energy spectrum in molecular clouds is almost universal,
regardless of a cloud’s location or star-forming activity (e.g. Heyer & Brunt, 2004), and
the self-similarity of clouds on scales above a few 0.1 pc (e.g. Elmegreen & Falgarone,
1996; Blitz & Williams, 1997). An alternative resolution to the problem of molecular
cloud turbulence is provided by short molecular cloud lifetimes. If star formation is
initiated within a single crossing time, and nascent stars promptly disrupt their natal
cloud, then turbulence may be ubiquitous because it is generated during the cloud formation process and does not have time to decay. Most recently, Ballesteros-Paredes
et al. (2010) have proposed that interstellar clouds and their substructure experience
hierarchical gravitational contraction, the onset of which is roughly simultaneous with
the formation of H2 molecules and the cloud becoming magnetically supercritical. In
this model, the superposition of collapse motions on large and small scales dominates
8
Chapter 1. Introduction
the non-thermal component of their global velocity dispersion. This is a significant
re-interpretation of molecular cloud linewidths, suggesting that supersonic turbulence
might be an observable consequence of gravitational collapse, rather than a process
that supports molecular clouds against self-gravity.
The physical structure of molecular clouds is primarily the result from the combined
effects of self-gravity and turbulence, which appear to act similarly across different
galactic environments. The chemical composition and thermal properties of molecular
clouds are more diverse, since they depend on a combination of gas density, column
density, metallicity, dust abundance and the strength of the radiation field, all of which
vary with galactocentric radius. In general terms, interstellar atomic gas becomes
molecular when the density n and the column density N are sufficiently large that the
rate of H2 formation on dust grains exceeds the rate of molecular photodissociation by
far-ultraviolet (FUV) photons (e.g. Federman et al., 1979). This leads to a characteristic stratified structure for molecular clouds, in which a cold, predominantly molecular
interior is surrounded by warmer, mostly atomic envelope. The outer layers of molecular clouds, where the FUV interstellar radiation field (ISRF) still plays a significant
role in the chemistry and heating, are called photodissociation or photon-dominated
regions (PDRs, for a review see Hollenbach & Tielens, 1999).
The kinetic temperature Tk of the outermost layer of a molecular cloud is a few hundred
Kelvin, and the dominant chemical species are neutral atomic hydrogen (H), atomic
oxygen (O) and ionized carbon (C+ ). Electrons that have been ejected from the dust
grain surfaces via the photoelectric effect are the primary source of heating in this layer,
while cooling occurs through the fine structure lines of metal ions, especially the [C II]
line at 158 µm. At a visual extinction of AV ∼ 0.2 mag (the exact value depends on the
local ratio between the strength of the ISRF G0 and density n, e.g. Federman et al.,
1979), H2 becomes self-shielding to the FUV photons, producing an intermediate layer
with Tk ∼ 100 K where the dominant species are H2 , O and C+ . At AV ∼ 1 mag, C+
recombines with electrons to form atomic carbon (C); at AV ∼ 2 mag, the ISRF is sufficiently attenuated that C becomes incorporated into CO molecules. H2 and CO are the
1.2. Molecular Gas in Dwarf Galaxies
9
major chemical constituents in the innermost regions of molecular clouds, where the
kinetic temperature is ∼ 10 − 20 K. In molecular cloud interiors, cosmic rays provide
the dominant source of heating, while the gas cools via the rotational transitions of CO.
The preceding description of a PDR is highly idealized: in real clouds, the transitions occur across a range of AV , and the numerical value of the visual extinction
corresponding to these transitions depends on n and G0 . The relative importance of
different heating and cooling processes throughout the PDR also depends on n and G0
(Lequeux, 2005). Due to the complexity of molecular cloud chemistry, it is important to
recall that many of our insights have been gained through steady-state models that assume a homogeneous plane-parallel or spherical geometry for PDRs. In reality, the gas
in molecular clouds is clumpy and is also subjected to time-variable phenomena such
as turbulence and shocks. The effect of these properties on the chemistry of molecular
clouds remains an area of active research. Two key results from these investigations
are that a higher mean AV is required for molecule formation in a clumpy medium
(e.g. Spaans & van Dishoeck, 2001), and that H2 formation can occur rapidly in the
strong local overdensities created by shocks in supersonically turbulent gas (Glover &
Mac Low, 2007, 2010).
1.2 Molecular Gas in Dwarf Galaxies
Until recently, most of our empirical knowledge about molecular cloud properties has
been acquired through studying molecular clouds in the Milky Way. Yet the primary
motivation for studying molecular clouds is a quantitative understanding of the processes that regulate the transformation of interstellar gas into stars throughout the
Universe. To achieve this aim, studies of molecular cloud populations in galaxies covering a wide range of masses, luminosities, metallicitities, and Hubble types will be
required. Local dwarf galaxies occupy a special place in this endeavour, since they tend
to be low-metallicity objects with ISM properties that resemble the conditions in young
proto-galaxies.
10
Chapter 1. Introduction
There are good physical reasons to expect that star formation and the molecular gas
content of dwarf galaxies will diverge from the trends observed for massive spiral galaxies. Dwarf galaxies tend to have a lower abundance of dust and heavy elements (e.g.
Garnett, 1990; Richer & McCall, 1995), which should have a strong effect on heating
and cooling processes in the ISM. In particular, the formation of H2 should be inhibited
since cooling through metal lines will be less efficient and the combined surface area of
dust grains will be lower. The destruction of H2 will be enhanced, however, as the lower
dust abundance will reduce the attenuation of FUV radiation. The dynamics of dwarf
galaxies are also unlike those of spirals (e.g. de Blok et al., 2008; Simon et al., 2005; Sofue & Rubin, 2001). On one hand, their rising rotation curves imply that galatic shear
forces are relatively weak, which could promote the formation of molecular clouds (and
stars) due to the low angular momentum of the interstellar gas (Young, 1999). On the
other hand, dwarf galaxies have low stellar surface densities and also lack strong spiral
structure: both of these may be important for accumulating gas into structures with
high density, where shielding against FUV radiation, line cooling and/or gravitational
instabilities can become more effective (e.g. Elmegreen & Parravano, 1994; Li et al.,
2005; Yang et al., 2007). The gravitational potential well of a typical dwarf galaxies is
shallow, moreover, so while its atomic gas content may be high relative to its stellar
and/or dynamical mass, the gas is often at lower average densities than in the starforming disks of normal galaxies. Since shear and large-scale gravitational instabilities
are mostly absent (e.g. Gallagher & Hunter, 1984), the atomic ISM in dwarf galaxies is
more likely to be organized by phenomena such as supernovae, stellar winds and galaxy
interactions (e.g. Begum et al., 2006; Manthey & Oosterloo, 2008). The long-term effect of these processes on the global molecular gas content and star formation rate of
dwarf galaxies is unclear: molecular cloud formation can be promoted in the walls of
swept-up H I shells (e.g. Yamaguchi et al., 2001b), but increased ISM porosity will tend
to expose more of the gas to FUV radiation (Silk, 1997). Due to the shallow potential
well, there is also a higher probability that the gas in dwarf galaxies will be blown out
and/or tidally stripped.
1.3. Observing Molecular Gas
11
Observationally, it is well-established that the CO luminosity of galaxies varies with
Hubble type (e.g. Young & Scoville, 1991). This is partly a mass-scaling effect, i.e.
dwarf galaxies are less massive than spiral galaxies, so the masses of their stellar and
gaseous components are also lower. The ratio between the CO and K-band luminosity,
for example, does not vary between dwarfs and spiral galaxies suggesting that the
molecular gas mass is a constant fraction of the stellar mass in all star-forming galaxies
(Leroy et al., 2005). The ratio between the CO and H I luminosity drops from ∼ 0.9 in
early-type spirals to . 0.1 in dwarf galaxies, however, indicating genuine variations in
the fraction of neutral gas occurring in the molecular phase (e.g. Young & Knezek, 1989;
Leroy et al., 2005). Assuming that CO remains a reliable tracer of H2 , the latter result
would seem to provide solid evidence that the interstellar conditions in dwarf galaxies
are less favourable for the transformation of atomic to molecular gas. It is less clear
whether the properties of individual molecular clouds depend on environment. Recent
comparative studies have concluded that the (CO-derived) physical properties of GMCs
in the Milky Way and other nearby galaxies are relatively homogeneous, although such
studies are still limited to bright GMCs in the most nearby galaxies (Blitz et al.,
2007; Bolatto et al., 2008). The cumulative mass distributions of extragalactic GMC
populations are clearly different (Rosolowsky, 2005), which suggests that the dominant
cloud formation and destruction mechanisms vary between galaxies, even if a 105 M⊙
GMC in a dwarf galaxy, once formed, is indistinguishable from a 105 M⊙ GMC in a
spiral galaxy.
1.3 Observing Molecular Gas
Molecular hydrogen (H2 ) is the major constituent of the cold ISM, but it is difficult
to observe in its ground state. The lowest energy transitions of H2 are quadrupole
transitions with an equivalent temperature of To ≡ ∆E/kB ∼ 510 K, corresponding to
a far-infrared photon with a wavelength of 28.2 µm. Typical conditions in molecular
clouds (T ∼ 10 K, n ∼ 100 cm−2 ) are insufficient to excite these transitions, so the H2
in molecular clouds is not directly detectable. Several indirect empirical methods have
been developed to estimate the mass of cold H2 gas, including observations of optically
12
Chapter 1. Introduction
thin continuum emission from dust mixed with H2 (e.g. Bot et al., 2007; Reach et al.,
1994), and measurements of the absorption of starlight by dust in molecular clouds
(e.g. Dobashi et al., 2008; Paradis et al., 2010). The most common observational technique, however, is to use emission from carbon monoxide (CO) as a tracer. CO is the
second most abundant molecule in the ISM after H2 , with a fractional abundance of
10−4 (Lequeux, 2005). The J = 1 → 0 rotational transition of the CO molecule has an
equivalent temperature of only To = 5.5 K, corresponding to a photon with frequency
ν = 115.271 GHz, and is readily excited by collisions between CO and H2 in a quiescent
molecular cloud. The transition has a high optical depth in molecular clouds (τ ≥ 10),
and is expected to be thermalized (Tkin ≈ Tex ) for H2 number densities greater than a
few hundred cm−3 .
Theoretically, the argument for using CO emission as a quantitative tracer of H2 mass
proceeds as follows. The CO luminosity of molecular cloud with radius R is commonly
defined as
LCO = hTpk iπR2 ∆V
(1.1)
where hTpk i is the CO peak brightness averaged over the cloud area, and ∆V is the
full width at half-maximum (FWHM) linewidth. For a cloud in virial equilibrium,
p
σv = GM/R and hence
r
1
4ρ
,
(1.2)
M = LCO
3πG hTpk i
where ρ is the mean volume density of the cloud. This equation shows that the CO
luminosity of virialised molecular clouds should be directly proportional to their mass,
√
provided that the ratio ρ/Tb is roughly constant.
In the Milky Way, the constant of proportionality between CO luminosity and H2
mass has been empirically verified using several independent methods. These include
i) excitation analysis of
12 CO(J
= 1 → 0) and
13 CO(J
= 1 → 0) emission, assuming
local thermodynamic equilibrium (e.g. Carpenter et al., 1990), ii) comparing the mass
estimated from the CO luminosity to the virial mass estimate, iii) correlation between
12 CO(J
= 1 → 0) emission and visual/near-IR extinction (e.g. Alves et al., 2001;
1.3. Observing Molecular Gas
13
Frerking et al., 1982), and iv) comparison between H2 mass estimates from
12 CO(J
=
1 → 0) and gamma-ray emission (e.g. Strong & Mattox, 1996). The results obtained
by the different methods indicate
XCO ≡
N (H2 )
−1
= 1.8 − 3.5 × 1020 cm−2 (K km s−1 ) ,
I(CO)
(1.3)
where XCO is the empirically-calibrated conversion factor between the molecular hydrogen column density N (H2 ) and the CO integrated intensity I(CO). Throughout
−1
this thesis, we adopt XCO = 2.0 × 1020 cm−2 (K km s−1 )
as the Galactic conversion
factor unless otherwise stated.
While independent methods obtain similar results for the value of XCO within the Milky
Way disk, there are at least two reasons why H2 mass estimates for extragalactic GMCs
derived using XCO should be regarded with caution. First, the quoted value of XCO is
an average, determined from cloud populations that exhibit scatter around a roughly
linear trend, or from low resolution data where individual GMCs are not resolved. The
uncertainty associated with estimating the H2 mass from the CO luminosity of an individual GMC is therefore significantly greater than the uncertainty associated with
an estimate for the combined H2 mass of a GMC population. Second, the appropriate
value of XCO almost certainly depends on the scale of the physical structure that is
being studied. On large scales this caveat is partly technical, since observations with
coarse angular resolution will blend together physically unrelated clouds leading to erroneously large estimates for R and σv (for a detailed discussion, see Israel, 1997). Even
for resolved observations, however, there may be an intrinsic relationship between XCO
and scale. Observations on small scales will pick out the high density substructure of
GMCs, where the filling factor and brightness temperature of the CO emission are high.
Observations on larger scales, by contrast, will incorporate a larger fraction of tenuous
intracloud gas. If GMCs contain a significant mass of H2 gas without CO emission, or
even cold atomic gas, then XCO will tend to increase on larger scales.
The most pressing question regarding the use of XCO , however, is whether CO remains
14
Chapter 1. Introduction
a reliable proxy for H2 under the range of physical conditions that are encountered
in the ISM of galaxies. Observationally, it is well-established that the detectability of
CO emission increases with several parameters that are covariant with a galaxy’s total
mass, including the K and B-band luminosity, metallicity and star formation rate (e.g.
Leroy et al., 2005; Verter, 1987). Of these, the relationship between XCO and metallicity has received the most attention, as the chemistry of H2 and CO molecules in the
ISM has been investigated in detail and the theoretical argument for how the relative
distribution of H2 and CO molecules should change in a low-metallicity environment
is well-developed (e.g. Maloney & Black, 1988). CO and H2 molecules have distinct
formation pathways: H2 mostly forms on the surface of dust grains (Hollenbach &
Salpeter, 1971), whereas CO forms via a number of different ion-neutral and neutralneutral reactions in the gas phase (for a review, see e.g. Sternberg & Dalgarno, 1995).
Both molecules are dissociated by UV photons. H2 molecules readily self-shield, and
can protect themselves against UV photodissociation for H2 column densities greater
than a few times 1020 cm−2 (Draine & Bertoldi, 1996). The survival of CO molecules,
by contrast, relies primarily on the attenuation of UV photons by dust (Lee et al.,
1996). In a Galactic GMC, the UV photons that dissociate CO will penetrate to a
depth within the cloud where the visual extinction is AV ∼ 1 − 2 mag. In environments
with low dust abundance and strong UV radiation fields, the dissociating UV radiation
penetrates deeper into the molecular cloud (relative to the Galactic case), such that the
CO-rich gas occupies a smaller volume nested within the cloud of H2 (see e.g. figure 1
in Bolatto et al., 1999).
Despite the theoretical expectation that the relationship between CO emission and
H2 mass should vary with metallicity, empirical confirmation of this dependence is
still lacking. Resolved CO observations of extragalactic GMCs have tended to obtain
XCO values that are close the Milky Way value, with little evidence for a metallicity
dependence (e.g. Walter et al., 2001; Rosolowsky et al., 2003; Bolatto et al., 2008).
In these studies, XCO was derived by assuming that GMCs achieve virial equilibrium.
However, estimates of XCO derived using dust-based measurements of the H2 mass
have typically detected a steep increase in XCO with declining metallicity (e.g. Israel,
1.4. The Dynamical Properties of Molecular Clouds
15
1997; Rubio et al., 2004; Leroy et al., 2007a). A possible explanation that would
reconcile these results is that the CO linewidth only traces the kinematics of the COemitting interior of a molecular cloud, and not the surrounding ‘CO-dark’ H2 envelope.
The fraction of the cloud mass residing in this envelope may be a strong function
of metallicity, while the physical and chemical properties of the cloud’s CO-emitting
interior may not vary with the cloud’s environment. As a contribution to this debate,
an important practical objective of the survey described in this thesis is to provide
complementary high-quality CO data to legacy surveys of the dust emission in the
Magellanic Clouds by Spitzer and Herschel (Meixner et al., 2006, 2010).
1.4 The Dynamical Properties of Molecular Clouds
The macroscopic physical properties of molecular clouds – size, linewidth and luminosity – are usually measured using CO observations. These properties exhibit scaling
relations that were first noted by Larson (1981), and are often referred to as “Larson’s
Laws”. The Larson scaling relations provide a useful tool to characterize the dynamical
state of molecular clouds, and also serve as a point of reference for comparisons between
different molecular cloud populations.
1.4.1
The Size-linewidth Relationship
The first of Larson’s Laws describes a power-law relationship between a molecular
cloud’s size and velocity dispersion. This size-linewidth relation is expressed as
σv ∝ R β ,
(1.4)
where R is the cloud radius and σv is the one-dimensional velocity dispersion. For a
√
Gaussian line profile, σv is related to the FWHM linewdith via 2 ln 2 × σv = ∆v. For
GMCs in the inner Milky Way, a pioneering study by Solomon et al. (1987, henceforth
S87) found σv = (0.72 ± 0.07)R0.5±0.05 . A re-analysis of the S87 GMC sample using
high resolution
13 CO(J
= 1 → 0) data and a more modern decomposition technique
yields a similar exponent but a lower constant of proportionality, which reflects the high
16
Chapter 1. Introduction
brightness threshold adopted by S87 to define the cloud radius (Heyer et al., 2009).
The size-linewidth relation is usually interpreted as a manifestation of interstellar turbulence. Statistically, turbulent flows can be described via their velocity structure
functions,
Sp (l) = h|v(r) − v(r + l)|p i ,
(1.5)
where l is the separation between two points in the flow and p is the order of the
structure function. For a turbulent energy spectrum E(k) ∝ k−n with 1 < n < 3,
Kolmogorov theory predicts that the second-order structure function should follow a
power law of the form,
S2 (l) = h|∆v|2 i ∝ ln−1 .
(1.6)
The similar functional form of Equations 1.4 and 1.6 suggests that the size-linewidth
relation might codify the velocity coherence of a turbulent flow as a function of spatial lag. In this case, the exponent of the size-linewidth relation is related to the
index of the energy spectrum via β = (n − 1)/2. Observationally, Larson obtained
β = 0.38, in reasonable agreement with the scaling expected for incompressible turbulence (E(k) ∝ k−5/3 Kolmogorov, 1941). Subsequent GMC surveys have tended to
find β ∼ 0.5, closer to the value predicted for shock-dominated Burgers turbulence.
The exact exponent of the turbulent energy spectrum in a magnetized, self-gravitating,
compressible fluid is still under investigation, with recent numerical simulations yielding values between n = −1.74 (corresponding to β = 0.37) and n = −2 (β = 0.5)
(Boldyrev, 2002; Cho & Lazarian, 2003).
In most contexts, the size-linewidth relation refers to a relationship characterising a
molecular cloud ensemble, i.e. a correlation between global measurements of the radius and velocity dispersion for individual clouds. Yet the physical significance of the
size-linewidth relation may be that it applies to ISM structures across a wide range
of spatial scales. The atomic ISM in the LMC exhibits a relationship between size
and velocity dispersion with β ∼ 0.5 (Kim et al., 2007), while a size-linewidth relation
with β ∈ [0.42, 0.55] has also been found to apply within Galactic GMCs (e.g. Heyer
1.4. The Dynamical Properties of Molecular Clouds
17
& Schloerb, 1997). As there is no a priori connection between the dominant source
of turbulence on large and small scales, the invariance of the size-linewidth relation
has been cited as evidence that molecular clouds are transient features in the diffuse
ISM, and that large-scale processes are responsible for the turbulent internal motions
of molecular clouds.
1.4.2
Molecular Clouds are Self-Gravitating
Larson’s second law is that molecular clouds are gravitationally bound. Numerical simulations investigating the formation of molecular clouds in colliding gas flows have cast
some uncertainty over this result, but the original argument behind Larson’s conclusion remains instructive. Here, we follow the basic exposition of the virial theorem for
interstellar gas clouds by McKee (1999). The general form of the virial theorem for any
parcel of fluid is obtained by taking the scalar product of r with the momentum equation, and integrating the result over the volume of interest. The result for a molecular
cloud is
1¨
I = 2(T − Ts ) + M + W,
2
(1.7)
where I is the moment of inertia of the cloud, the 2(T − Ts ) term describes the net
kinetic energy inside and at the cloud surface, M is the magnetic energy and W is the
gravitational energy of the cloud.
The physical significance of the virial theorem for a molecular cloud becomes clearer if
we recast Equation 1.7 in terms of pressure. For a cloud with density ρ, the thermal
energy density is (3/2)ρc2 , where c is the isothermal sound speed, while the kinetic
energy density associated with bulk motions is (1/2)ρv 2 . The total kinetic energy
inside the cloud is then
T =
Z V
3 2 1 2
ρc + ρv
2
2
3
≡ P̄ V,
2
(1.8)
where V is the cloud volume and P̄ is the mean gas pressure inside the cloud. If the
18
Chapter 1. Introduction
kinetic (i.e. thermal + turbulent) pressure in the ambient ISM, Pext , is constant, then
the surface kinetic energy is Ts = (3/2)Pext V . Thus the kinetic energy term can be
expressed as the difference between the kinetic pressure inside and outside the cloud:
2(T − Ts ) = 3(P̄ − Pext )V .
For an isolated cloud, the gravitational energy of the cloud is
W =
Z
3
ρr · gdV = − a
5
GM 2
R
,
(1.9)
where g is the acceleration due to gravity, M is the cloud mass, R is the cloud radius,
G is the gravitational constant, and a is a dimensionless parameter of order unity that
accounts for the shape and density distribution within the cloud. The gravitational
energy term can also be expressed as W ≡ 3PG V , where
PG =
3πa
20
GΣ2 .
(1.10)
In this equation, Σ ≡ M/πR2 is the cloud’s mean mass surface density and PG is the
mean weight of material within the cloud.
If molecular clouds survive longer than a few crossing times, then it is customary to
assume that I¨ = 0, and Equation 1.7 can be rearranged to give
P̄ = Pext + PG (1 − M/|W |)) .
(1.11)
The physical significance of the virial theorem in this formulation is obvious: the average
pressure within the cloud equals the kinetic pressure at the cloud surface plus the
weight of the material inside the cloud, reduced by a factor corresponding to magnetic
support. A similar set of subsitutions allows us to write the total energy of the cloud,
E = T + M + W in terms of the weight of the cloud and the ambient kinetic pressure:
Ē =
3
[Pext − PG (1 − M/|W |))] V.
2
(1.12)
1.4. The Dynamical Properties of Molecular Clouds
19
Clouds that are gravitationally bound have E < 0 and hence PG > Pext in the absence
of a magnetic field. If, on the other hand, Pext > PG then the molecular cloud is
pressure-confined. In this case, the molecular cloud is also likely to be transient, since
turbulence accounts for a large fraction of the ambient kinetic pressure.
The conclusion that molecular clouds are gravitationally bound therefore rests on the
expectation that the weight of molecular clouds is significantly greater than the kinetic pressure in the surrounding ISM (PG > Pext ), and that molecular clouds survive
multiple crossing times (so that I¨ ≈ 0). While there are good supporting reasons for
both propositions, neither is completely secure. In the solar neighbourhood, the total
ISM pressure at the disk midplane is roughly Ptot = 2.2 × 104 K cm−3 (Cox, 2005).
For the kinetic ISM pressure at the cloud surface, the pressure due to cosmic rays and
magnetic fields must be excluded from Ptot . This is because cosmic rays penetrate
the ISM and the cloud, while the magnetic contribution is already accounted for in
the virial theorem. Assuming midplane values of 0.9 and 0.7 × 104 K cm−3 for the
cosmic ray and magnetic pressures respectively (Ferrière, 2001), the ambient kinetic
pressure at the surface of local molecular clouds is roughly Pext ∼ 0.6 × 104 K cm−3 .
The weight of material within the clouds, PG , can be estimated from their mean
mass surface density, obtained via visual extinction or CO observations. Observationally, molecular clouds have Σ ∼ 100 M⊙ pc−2 (e.g. Heyer et al., 2009; Bolatto et al.,
2008), corresponding to AV ∼ 4.6 mag for the Galactic dust-to-gas ratio. In this case,
PG ∼ 1.2 × 105 K cm−3 ≫ Pext , implying that clouds are bound. This conclusion ap-
pears to be inevitable for GMCs observed in CO, since a layer with hydrogen column
density greater than 1.4 × 1021 cm−2 ∼ 0.7 mag is required to shield CO molecules
against photodissociation. For AV ∼ 1.4 mag – i.e. the minimum shielding layer on
both sides of the cloud – PG ∼ 1.1 × 104 K cm−3 which is still greater than the ambient
kinetic pressure in the ISM.
Though the argument for bound clouds seems compelling, there are several important
caveats. First, the calculations presented above apply to the ISM in the solar vicinity.
In other galaxies and other parts of the Milky Way, the dust-to-gas ratio, total ISM
20
Chapter 1. Introduction
pressure, and intensity of the FUV radiation field take on different values, which may
not yield PG > Pext . Second, we assumed that the pressure at the cloud surface is
equivalent to the ambient ISM pressure, which we derived using global averages. Yet
molecular clouds are not randomly distributed throughout the diffuse ISM: instead,
they are preferentially located in regions with high H I column density (Wong et al.,
2009; Blitz et al., 2007). The mass, origin and dynamical significance of the atomic
gas that surrounds GMCs is still a subject of debate, but it is likely that the weight
of these H I envelopes raises the pressure at the molecular cloud surface significantly
above the average kinetic pressure of the ambient ISM (see e.g. Heyer et al., 2001).
A third major source of uncertainty is molecular cloud lifetimes, with modern estimates
ranging between 3 and 100 Myr (Hartmann et al., 2001; Scoville & Wilson, 2004). The
argument for bound clouds that we sketched above requires I¨ ≈ 0, which has traditionally been rephrased as a requirement that the lifetime of molecular clouds tcloud significantly exceeds their dynamical time. Cloud lifetimes estimated using the association between molecular clouds and young stellar phenomena typically find tlif e ∼ 20 − 30 Myr,
exceeding tf f by a factor of a few. As pointed out by Ballesteros-Paredes (2006), however, the condition that I¨ ≈ 0 is not strictly equivalent to tlif e ≫ tf f . For a molecular
cloud to achieve I¨ ≈ 0 in a time-averaged sense, a molecular cloud must oscilllate about
a mean shape and internal mass distribution. But in a dynamic ISM, molecular clouds
can experience a significant flow of mass across their boundaries, suggesting I¨ 6= 0 for
the timescales on which an ISM structure maintains its identity. To complicate the picture still further, numerical simulations by Vázquez-Semadeni et al. (2007) show that
the kinetic and gravitational energies of a cloud undergoing hierarchical gravitational
fragmentation are roughly equal. Contrary to the common assumption that the condition T ∼ W characterises a system in approximate virial equilibrium, T ∼ W arises in
these simulations once gravity dominates the cloud’s non-thermal motions.
1.5. Star Formation on Galactic Scales
1.4.3
21
Molecular Clouds Have Constant Column Density
Larson’s third result was that the mean volume density of molecular clouds is inversely
proportional to their size. This scaling relation is usually stated in terms of a uniform
mass surface density for molecular clouds, Σ ∝ M/R2 = ρR = constant, since volume
densities are not directly calculable from CO observations. As previous authors have
noted, only two of Larson’s Laws are independent. For an isolated, non-magnetic cloud
in virial equilibrium, the mass of a molecular cloud is related to its size and velocity
dispersion by
M=
k5σv2 R
.
αG
(1.13)
In this equation M is the cloud mass and k is a numerical factor that characterises
the internal mass distribution. The virial parameter, α, parameterizes departures from
virial equilibrium: virialised clouds have α = 1, bound clouds have α ≤ 2 and pressureconfined clouds have α ≫ 1. If molecular clouds are virialised and also obey a sizelinewidth relation with β = 0.5, then the virial mass estimate yields Larson’s third law:
M ∝ σv2 R ∝ R2 , and hence Σ = constant. Observationally, GMC samples in the Milky
Way and nearby galaxies are broadly consistent with hΣi ∼ 100 M⊙ pc−2 , although
individual GMCs exhibit ∼ 2 dex scatter around this mean. The origin of this scatter,
and its implications for the dynamical state of molecular clouds remains controversial.
Heyer et al. (2009) have proposed that GMCs achieve dynamical equilibrium, and
that variations in Σ reflect differences in the local magnetic field strength with galactic
environment. Ballesteros-Paredes et al. (2010), by contrast, propose that the variations
in Σ are consistent with GMCs undergoing hierarchical gravitational collapse.
1.5 Star Formation on Galactic Scales
The star formation rate (SFR) is arguably the most important physical parameter in
astrophysics, as it drives the evolution and observed characteristics of galaxies. The star
formation process is inherently complex, however, involving a wide range of lengths,
densities, temperatures and timescales; hence it remains a poorly understood phase in
the life cycle of stars and interstellar gas. Empirically, star formation appears to fol-
22
Chapter 1. Introduction
low clear correlations with several ISM and global galaxy properties (e.g. Leroy et al.,
2008), allowing galaxy evolution models to parameterise the SFR according to simple
prescriptions (e.g. White & Rees, 1978; Navarro & White, 1993; Fu et al., 2010). Yet
a detailed, quantitative theory for how the diffuse interstellar gas assembles itself into
molecular clouds, and how these clouds are subsequently transformed into stars, is still
wanting. From a theoretical perspective, it is imperative to decipher what the empirical
‘laws’ of star formation imply about the physical connection between star formation
and interstellar gas. On the observational front, progress requires extending existing
studies to higher spatial resolution and to galactic environments that cover a broad
range of metallicities, gas densities, magnetic field strengths, etc.
An important achievement by empirical studies was the recognition that the SFR depends on the availability of dense gas. In hindsight, this result is not surprising: all
the star formation that we observe in the Galaxy occurs within molecular clouds. The
original proposition by Schmidt (1959) was that the SFR scales with the gas density
according to
ρ̇∗ ∝ ρngas ,
(1.14)
where ρ˙∗ and ρgas are volume densities. Based on the relative scale height of atomic
gas and young stars in the solar neighbourhood, Schmidt (1959) estimated n ∼ 2.
On theoretical grounds, an exponent of n = 1.5 would be expected if the SFR were
proportional to the ratio of the gas mass to the free-fall time, i.e.
ρ̇∗ ∝
ρgas
∝ ρ1.5
gas
(Gρgas )−0.5
(1.15)
Regardless of the exact value of n, the coefficient of the relationship must be small
since star formation in the Milky Way is observed to be very inefficient (a few M⊙ yr−1 ,
compared to ∼ 250 M⊙ yr−1 that would be expected if the molecular gas were collapsing
on its free-fall timescale, e.g. Zuckerman & Evans, 1974; McKee & Williams, 1997).
Assuming that galactic disks have uniform thickness, then the Schmidt Law can be
1.5. Star Formation on Galactic Scales
23
recast in terms of observable surface densities:
ΣSFR [M⊙ yr
−1
2
kpc ] = A
Σgas
M⊙ pc−2
N
.
(1.16)
A seminal study by Kennicutt (1998) used H I, CO and H α observations to estimate
the global (i.e. disk-averaged) SFR, and atomic and molecular gas surface densities in
∼ 100 normal and starburst galaxies. He obtained a tight relationship between ΣSF R
and the total (atomic + molecular) gas surface densities over six orders of magnitude
(see figure 6 in Kennicutt, 1998), with N = 1.4 ± 0.15 and A = (2.5 ± 0.7) × 10−4 .
Recent efforts have pursued the origin of this correlation by examining the properties
of gas and star formation within galaxies, using radial profiles and/or measurements
within ∼ 0.5 kpc apertures (e.g. Wong & Blitz, 2002; Heyer et al., 2004; Bigiel et al.,
2008; Leroy et al., 2008). These investigations have revealed a tight, approximately linear relationship between the SFR and the molecular gas surface densities, and a much
poorer local correlation between star formation and atomic gas, consistent with our
view of star formation as a molecular process. Current studies indicate a breakdown in
the correlation between ΣSF R and ΣH2 on ∼ 100 pc scales (e.g. Onodera et al., 2010;
Schruba et al., 2010), although the validity of conventional SFR diagnostics on these
scales remains uncertain (cf. Lawton et al., 2010; Li et al., 2010). Focussing on the
“resolved molecular Schmidt Law”, moreover, cannot resolve the question of whether
local or galactic scale processes regulate the conversion of atomic to molecular gas (e.g.
Blitz & Rosolowsky, 2006; Krumholz et al., 2009a; Ostriker et al., 2010).
A second approach to studying galaxy evolution and star formation in the early Universe is to observe galaxies at different redshifts directly. The study of high redshift
galaxies is now a well-developed field, with galaxy samples regularly containing & 50
spectroscopically-confirmed members at z ∼ 5 (e.g. Rhoads et al., 2009; Vanzella et al.,
2009; Douglas et al., 2010). The star formation activity in these young galaxies is often
inferred from rest-frame optical and UV data (e.g. Glazebrook et al., 1999; Stanway
et al., 2003; Ouchi et al., 2004), but the attenutation of optical/UV radiation by interstellar dust complicates the interpretation of the SFRs derived using these methods. In
24
Chapter 1. Introduction
normal star-forming galaxies, dust absorbs ∼ 50% of the stellar radiation at optical/UV
wavelengths (e.g. Calzetti, 2001), while optical SFR diagnostics can underestimate the
SFR in ultraluminous infrared galaxies (ULIRGs) by up to 2.5 dex (e.g. Choi et al.,
2006). Due to their longer wavelengths, radio and mid-/far-infrared emission are unaffected by dust extinction, and they therefore present a practical alternative tracer
of how nascent stars deposit their energy into the ISM, especially in highly obscured
regions.
The use of radio-derived SFRs is mostly due to the strength and ubiquity of the radioFIR correlation, which constitutes a second powerful law of extragalactic star formation
(e.g. Yun et al., 2001, and references therein). The processes that produce the bulk of
the FIR and radio emission in galaxies are very different: the FIR emission is due to
UV photons from young stars that have been absorbed and re-emitted by dust grains,
while the radio emission at GHz frequencies is predominantly nonthermal synchrotron
radiation that arises from cosmic rays spiralling in a magnetic field (Condon, 1992).
Despite these distinct physical mechanisms, the radio-FIR correlation is approximately
linear with a dispersion of . 50% for galaxies spanning three orders of magnitude or
more in mass, gas surface density, photon energy density and magnetic field strength.
Though its utility as a SFR diagnostic at moderate redshift is not in doubt (e.g. Pannella et al., 2009), understanding why the nonthermal radio continuum emission is
coupled to thermal emission from dust grains requires investigating their relationship
in nearby galaxies, where processes across a wide range of angular scales can be probed.
Completion of the Spitzer Infrared Nearby Galaxy Survey (SINGS, Kennicutt et al.,
2003) has stimulated new research into the radio-FIR correlation within galaxies (e.g.
Murphy et al., 2006b, 2008), but the full range of physical models that have been
proposed to explain the global correlation have not yet been thoroughly tested. One
long-standing debate concerns the role of dense gas in maintaining the correlation. If
the magnetic field strength is coupled to the gas volume density and the gas and dust
are well-mixed, then the radio and FIR emission should show a tight relationship, even
on the scale of individual clouds. The potential connection between the radio-FIR and
1.6. The Large Magellanic Cloud: A Laboratory for Extragalactic Star Formation
Studies
25
Kennicutt-Schmidt correlations was made explicit by Niklas & Beck (1997), who proposed that the FIR emission is a robust tracer of the SFR, which is itself determined
by the gas density. The two laws of extragalactic star formation might thus be related
through the molecular gas content of galaxies: in the second half of this thesis, we
examine empirical evidence for such a link in the LMC.
1.6 The Large Magellanic Cloud: A Laboratory for Extragalactic Star Formation Studies
Visible to the naked eye at southern latitudes, the LMC is one of the best-studied
galaxies in the Local Group. A gas-rich dwarf galaxy with an obvious stellar bar and
flocculent spiral structure, it is the prototype for the Sm galaxy type distinguished by de
Vaucouleurs (1959) that lies intermediate between spiral and truly irregular galaxy morphologies. Due to its proximity (50.1 kpc, Alves, 2004), high Galactic latitude (∼ −68◦ )
and face-on orientation (i = 35◦ , van der Marel & Cioni, 2001), the LMC offers the best
view of the interaction between the ISM and star formation in any galaxy, including
the Milky Way. With sub-solar metallicity (Z/Z⊙ ∼ 0.4, e.g. Marble et al., 2010) and
a dust-to-gas ratio 2 to 4 times lower than in the solar neighbourhood (Gordon et al.,
2003), it also provides an excellent laboratory to investigate star formation processes
under similar interstellar conditions as those that prevailed when star formation in the
Universe was at its peak (z ∼ 1, e.g. Heavens et al., 2004).
The LMC star formation history (SFH) may be better understood than for any other
galaxy. A reconstruction of the LMC’s SFH by Harris & Zaritsky (2009) shows that
there was an initial burst of star formation when the bulk of the LMC’s stellar mass was
formed, followed by a long quiescent epoch between 12 and 5 Gyr ago. Having resumed,
star formation in the LMC has been sustained until the present-day with an average
rate of roughly ∼ 0.2 M⊙ yr−1 . The star formation rate in the Small Magellanic Cloud
also peaked near the end of the LMC’s quiescent period (Harris & Zaritsky, 2004),
which may be evidence for a tidal encounter between the two galaxies.
26
Chapter 1. Introduction
Table 1.2 Positional and geometric data for the LMC. References: (1) de Vaucouleurs et al.
(1991) (2) Wong et al. (2009) (3) van der Marel et al. (2002) (4) van der Marel & Cioni (2001)
(5) Staveley-Smith et al. (2003) (6) Alves (2004) (7) Kim et al. (1999) (8) Kallivayalil et al.
(2006).
Characteristic
Optical Centre (J2000)
Kinematic Centre (H I)
Centre of Mass
Stellar Bar Centre
Heliocentric Velocity
Inclination
Distance
B-band diameter, D25
H I diameter
H α diameter
Proper Motion
Value
RA 05h23m34s
Dec -69d45m24s
RA 05h19m30s
Dec -68d53m
RA 05h27m36s
Dec -69h52m
RA 05h25m06s
Dec -69d47m
273 km s−1
35◦
50.1 kpc
10.0◦
10.7◦
6.3◦
µα = 2.03 mas yr−1
µδ = 0.44 mas yr−1
Ref.
Notes
1
2
3
4
5
4
6
1
5
7
8
For ΣHI > 1 M⊙ pc−2
The position and geometry of the LMC are presented in Table 1.2. The global properties of the LMC are summarised in Table 1.3, and briefly described below. The major
components of the LMC are:
i) Dark Matter
The rotation curve V (R) of the LMC rises linearly with galactocentric radius Rgal to
a value of V (R) ∼ 50 km s−1 at Rgal ∼ 4 kpc, after which it remains roughly constant
out to Rgal = 8.9 kpc (van der Marel et al., 2002). The total enclosed mass within this
radius is Mdyn = 8.7 ± 4.3 × 109 M⊙ . This is greater than the combined mass of the H I
and stellar disks (see Table 1.3), indicating that the LMC hosts a dark halo (cf. Alves
& Nelson, 2000). Most of the gas and stars are located within R ∼ 4 kpc, however, and
the dynamical influence of dark matter within the LMC disk is expected to be modest.
1.6. The Large Magellanic Cloud: A Laboratory for Extragalactic Star Formation
Studies
27
ii) Stars
Stars in the LMC have been extensively surveyed in near-infrared to optical bands
(e.g. Zaritsky et al., 2004; Blum et al., 2006; Skrutskie et al., 2006; Saha et al., 2010),
including detailed studies of young stellar clusters and associations (e.g. Hodge, 1988;
Bica et al., 1996). The stellar disk of the LMC is roughly planar, with an off-centre
bar in the inner region. The B-band diameter of the stellar disk is D25 = 10.0◦ (de
Vaucouleurs et al., 1991).2 As a result of tidal stretching, the disk is intrinsically elongated in the direction of the Galactic Centre (van der Marel, 2001). The exact scale
height of the stellar disk depends on the tracer population, but a recent study of LMC
carbon stars shows that the disk is quite thick and radially flared. For an isothermal
disk with a density profile proportional to sech2 (z/z0 ), the best-fitting scale height z0
increases from 0.3 kpc at the LMC centre to 1.5 kpc at Rgal = 5.5 kpc. The LMC does
not host a classical stellar halo (Freeman et al., 1983), although the presence of an
off-plane stellar population (or bulge) has been proposed and extensivelydebated (e.g.
Zaritsky, 2004; Zhao & Evans, 2000; Nikolaev & Weinberg, 2000). The total stellar
mass, derived from the LMC’s extinction-corrected B-band luminosity, is 2.7 × 109 M⊙
(van der Marel et al., 2002).
iii) Gas
The mass of the interstellar gas in the LMC is ∼ 5 × 108 M⊙ (Staveley-Smith et al.,
2003), most of which is in the atomic phase. H I surveys of the LMC (e.g. Luks &
Rohlfs, 1992; Kim et al., 1998; Staveley-Smith et al., 2003) reveal that the neutral ISM
has a turbulent fractal structure (Elmegreen et al., 2001), pockmarked by holes and
H I shells with diameters from tens to hundreds of parsecs (Kim et al., 1999). The H I
disk appears roughly circular in the plane of the sky, and exhibits no obvious correlation with the stellar bar. The shape of the H I power spectrum suggests that most
of the bright filamentary H I emission emerges from a thin (∼ 100 pc) layer, and that
any off-planar atomic gas must be smoothly distributed (Elmegreen et al., 2001; Block
et al., 2010). The H I gas south of the 30 Doradus star-forming complex is characteristed
by unusually high column densities. This region, which has been labelled the ‘south2
D25 is defined as the diameter where B-band surface brightness falls below 25 mag arcsec−2 .
28
Chapter 1. Introduction
Table 1.3 Global Properties of the LMC. References: (1) van der Marel et al. (2002), (2)
Staveley-Smith et al. (2003), (3) Fukui et al. (2008), (4) de Vaucouleurs et al. (1991), (5)
Kennicutt et al. (1995), (6) Harris & Zaritsky (2009).
Property
Dynamical mass
Stellar mass
H I mass
H2 mass
B-band luminosity
H α luminosity
Star Formation Rate
Value
9
8.7 × 10 M⊙
2.7 × 109 M⊙
5.2 × 108 M⊙
5.0 × 107 M⊙
2.3 × 109 L⊙
2.7 × 1040 erg s−1
0.2 M⊙ yr−1
Ref.
1
1
2
3
4
5
6
Notes
Within a 8.9 kpc radius
For M/LV = 0.9 ± 0.2
Within a 3.5 kpc radius, include He
For XCO = 7 × 1020 cm−2 (K km s−1 )−1
Assumes a Salpeter IMF
eastern H I overdensity’ (SEHO) by Nidever et al. (2008), contains roughly 25% of the
LMC’s total H I mass. The Magellanic Bridge, a tidal stream of low column density
H I gas stretching between the LMC and SMC, connects with LMC in the SEHO region.
Previous surveys of the CO emission in the LMC have estimated that the galaxy’s
total molecular mass is ∼ 5 × 108 M⊙ (e.g. Cohen et al., 1988; Fukui et al., 2001, 2008).
The CO emission is organized into discrete clouds that are preferentially located along
filaments with high H I column density (Fukui, 2007; Wong et al., 2009), and are also
strongly associated with young stellar phenomena such as H II regions and clusters (e.g.
Yamaguchi et al., 2001a; Kawamura et al., 2009). Approximately 30% by mass of the
CO-bright molecular gas is located in the SEHO region, within two striking features
known as the ‘molecular ridge’ and the ‘molecular arc’ (Mizuno et al., 2001, see also
Figure 2.2 of this thesis). We describe the results of previous CO surveys of the LMC
in more detail in Section 2.1.1. An absorption survey along LMC sightlines for diffuse
H2 gas obtained a total H2 mass of 8 × 106 M⊙ (Tumlinson et al., 2002), . 2% of the
LMC’s atomic mass. The presence of a significant mass of H2 residing in CO-dark
envelopes surrounding LMC molecular clouds is not strongly excluded by this result, as
the Tumlinson et al. (2002) survey was conducted along sightlines with low extinction.
Ionized gas with Tkin ∼ 104 K in the LMC has been studied using H α (e.g. Henize,
1956; Davies et al., 1976; Kim et al., 1999) and radio continuum observations (e.g.
Haynes et al., 1991; Dickel et al., 2005). The total H α luminosity of the LMC is
1.7. Thesis Outline
29
2.7 × 1040 erg s−1 , of which ∼ 35% occurs in a diffuse extended component (Kennicutt
et al., 1995). The bright H α emission is organized into a complex network of H II
regions and shells. While high-mass star formation is thought to be responsible for
the shell structure in both the atomic and ionized gas phases (e.g. McCray & Kafatos,
1987), the spatial correspondence between catalogued H I and H II shells in the LMC is
generally poor (Kim et al., 1999). The presence of hotter ionized gas (Tkin ∼ 105 K) in
the LMC has been confirmed through the detection of C IV and O VI absorption lines,
and is thought to reside in a hot, ionized corona (Wakker et al., 1998; Howk et al., 2002).
1.7 Thesis Outline
This thesis is organized as follows:
• In Chapter 2, a new survey of the
12 CO(J
= 1 → 0) emission in the LMC
is presented. We consider the total CO luminosity of the LMC in relation to
its other global properties, and compare our findings to the results from nearby
galaxy surveys.
• In Chapter 3, we describe the GMC catalogue that we have constructed from our
survey data. We present an analysis of the physical properties of GMCs without
star formation, and of the velocity gradients within the catalogued GMCs.
• In Chapter 4, we examine the scaling relations between the physical properties of
GMCs in the LMC. We investigate whether the properties of the GMCs vary with
their galactic environment, and test two models for the regulation of molecular
cloud properties.
• In Chapter 5, we present a new image of the 1.4 GHz continuum emission in
the LMC. We construct maps of the radio spectral index and the thermal and
nonthermal components of the radio emission, and use these maps to investigate
cosmic ray loss mechanisms and the star formation rate in the LMC.
• In Chapter 6, we investigate the radio-FIR correlation within the LMC, focussing
on the possible role of dense gas in maintaining a good local correlation.
30
Chapter 1. Introduction
• In Chapter 7, we review the major results of this thesis in light of the scientific
questions that motivated it, and identify several avenues for future research.
2
A
12
CO(J = 1 → 0) Survey of the LMC with the
Mopra Telescope
In this chapter, we present the Magellanic Mopra Assessment (MAGMA) survey of the
12 CO(J
= 1 → 0) emission in the Large Magellanic Cloud (LMC). The survey targets
114 giant molecular clouds identified by NANTEN for high-resolution mapping, with
a combined field-of-view of 3.65 square degrees. Significant
12 CO(J
= 1 → 0) emission
is detected in ∼ 25% of the MAGMA survey region. The total CO luminosity of
the detected emission is 2.5 × 106 K km s−1 pc2 , in excellent agreement with the value
obtained by the NANTEN survey. The average peak brightness temperature of the
CO emission is only ∼ 1 K (Tmb ), which we interpret as evidence that CO-emitting
structures in the LMC are spatially compact. We compare the LMC’s CO emission
to global galaxy properties, finding that the LMC’s total CO luminosity is two orders
of magnitude lower than predicted by correlations between the CO luminosity, stellar
mass and 1.4 GHz radio luminosity of nearby spiral galaxies. Although CO emission
in the LMC is clearly associated with regions of high H I column density and H I peak
brightness, we find a significant tendency for the CO and H I peaks to be spatially offset.
We examine whether the spatial separation or the magnitude of the reduction in the
H I column density at the CO peak varies with properties of the CO and H I emission,
location in the LMC, or the local interstellar conditions, but find no strong trends. We
propose that cold atomic gas with significant opacity in the vicinity of molecular clouds
31
32
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
may be responsible for the observed offset between CO and H I emission peaks.
2.1 Introduction
The star formation history of the Universe is a key problem in contemporary astrophysics, with important implications for our understanding of how galaxies have assembled and evolved through cosmic time. It is now well-established that the universal
star formation rate peaked at a redshift of z ∼ 1, and that it has subsequently declined
by a factor of approximately ten (see e.g. figure 1 Heavens et al., 2004). Locally, star
formation occurs in the coldest (T = 10 − 20 K), and most dense (n = 102 − 106 cm−3 )
regions of the interstellar medium (ISM), where most of the hydrogen exists in the
molecular phase (H2 , Ferrière, 2001). Dust and heavy elements play a crucial role in
regulating the phase balance in the ISM, with higher dust abundances and metallicities
promoting the formation of H2 through extinction and increased cooling (e.g. Lequeux,
2005). On larger scales, stellar gravity appears to play a role in triggering large-scale
instabilities within galactic disks and bringing the interstellar gas to high densities (e.g.
Li et al., 2005; Elmegreen & Parravano, 1994; Yang et al., 2007). That the cosmic star
formation rate was significantly higher in the past is therefore somewhat surprising: at
early epochs, galaxies were less massive and they contained interstellar gas with a lower
dust abundance and metallicity. A high rate of star formation at z ∼ 1 suggests that
molecular gas was abundant at that time – in spite of inhospitable conditions – or that
it was much more efficient at forming stars than the molecular gas that we observe in
the Milky Way and other nearby galaxies.
Local dwarf galaxies provide an important laboratory for investigating the star formation process. Less dusty and less chemically enriched than large spirals, dwarf galaxies
host large reservoirs of atomic gas and strong interstellar radiation fields, and the
gravitational potential of their stellar component is shallow. Shear forces and shocks
associated with spiral density waves are also less dominant in dwarfs, which generally
exhibit rotation curves indicative of solid-body rather than differential rotation. The
similarities between local dwarfs and proto-galaxies at moderate to high redshift sug-
2.1. Introduction
33
gests that detailed study of the molecular gas in nearby dwarf systems may help us to
understand star formation in the early Universe.
While there is clear evidence for ongoing star formation in dwarf galaxies, assessing
their molecular gas content is not straightforward. The bulk of molecular hydrogen
in galaxies cannot be observed directly because the lowest rotational levels of the H2
molecule have excitation energies that are too high to be thermally excited at the low
temperatures in molecular clouds. Carbon monoxide (CO) is commonly used as a tracer
of H2 because CO is the most abundant molecular species after H2 and the J = 1 → 0
transition of the 12 CO isotopologue is readily excited at temperatures and densities that
are typical in molecular gas. The conversion factor XCO between the 12 CO(J = 1 → 0)
integrated intensity and the H2 column density is constrained within a factor of ∼ 2 in
the inner disk of the Milky Way (XCO = 1.8 − 3.5 × 1020 cm−2 (K km s−1 )−1 , e.g. Scov-
ille, 1990), but it represents a critical uncertainty for studies of extragalactic molecular
gas. In metal-poor environments, for example, the formation of CO molecules is likely
to be suppressed due to the lower gas-phase abundance of heavy elements, while their
destruction via photodissociation should be enhanced due to lower dust abundance and
stronger radiation fields (e.g. Dickman et al., 1986; Maloney & Black, 1988). The interplay between dust and metallicity in determining the thermal balance of the molecular
ISM – primarily heating through photoelectric ejection from small dust grains and polycyclic aromatic hydrocarbon molecules (PAHs) and cooling via line emission of carbon
and oxygen species – introduces additional uncertainty about the physical conditions
within molecular clouds in environments with low metallicity and high gas-to-dust ratios, especially if there are also variations in the grain size distribution (e.g. Paradis
et al., 2009).
Empirically, concerns about the reliability of CO emission as a tracer of H2 are justified by observations showing that the CO luminosity of dwarf galaxies is very low (e.g.
Elmegreen et al., 1980; Taylor et al., 1998; Leroy et al., 2005). There are at least three
potential interpretations of this result. CO may be a poor tracer of H2 in these systems,
the star formation efficiency of their molecular gas could be much higher than in the
34
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Milky Way, or – more speculatively – atomic gas in these galaxies might participate
directly in the star formation process. Guided by photodissocation models, studies to
date have focussed on metallicity and variations in XCO as the key variables to explain
the deficiency of CO emission in these systems (e.g. Wilson, 1995; Bolatto et al., 2003).
However, numerous properties of dwarf galaxies differ from those of large spirals, many
of which are covariant with galaxy mass. The topology of the ISM, the rates of cosmic ray production and escape, and the magnetic field strength, for example, are each
likely to vary with mass and are still poorly constrained by observations. Any of these
properties could plausibly alter the covering fraction of molecular gas and/or physical
conditions within molecular clouds and thereby affect the global star formation rate,
so an alternative explanation for the relationship between molecular gas, CO emission
and star formation in dwarf galaxies is not yet ruled out.
The Magellanic Clouds are prime targets to investigate the structure and evolution of
the ISM in galaxies other than the Milky Way. In particular, the proximity and orientation of the Large Magellanic Cloud (LMC, d = 50.1 kpc, i ∼ 35◦ , Alves, 2004; van der
Marel et al., 2002) permit resolved observations of individual molecular clouds, with a
very low probability of confusion along the line-of-sight. Although the LMC is more
massive than many dwarf galaxies in the Local Group, the stellar mass of the LMC is
roughly three orders of magnitude below the stellar mass of either the Milky Way or
M31. The ISM in the LMC is also much more similar to conditions that prevailed in
young galaxies, exhibiting a low metallicity (Z = 0.4Z⊙ , e.g. Marble et al., 2010) and
a low dust-to-gas ratio (∼ 1/3 of the dust-to-gas ratio in the Milky Way disk, Bernard
et al., 2008).1 The LMC therefore offers an excellent opportunity to investigate the
relationship between molecular gas, CO emission and star formation at high spatial
resolution in a low-metallicity environment. To date, mapping surveys of the atomic
gas, radio continuum and dust in the LMC have been completed at 1.′ 0 resolution (or
better, Kim et al., 2003a; Hughes et al., 2007; Meixner et al., 2006, 2010). A map
of the CO emission at comparable resolution is essential for studying how molecular
1
We adopt 12 + log(O/H)= 8.66 ± 0.05 as the solar oxygen abundance (Asplund et al., 2004), and
calculate the metallicity according to log Z = 1.42 + log(O/H) (e.g. Matteucci & Chiosi, 1983).
2.1. Introduction
35
clouds are related to their progenitor atomic gas and their young stellar content, and for
determining how well the CO emission traces the underlying molecular gas reservoir.
With the imminent commissioning of the Atacama Large Millimeter Array (ALMA),
the need for a publicly available, high resolution map of the dense gas distribution in
the LMC has become acute.
The remainder of this introduction outlines the scope of previous CO surveys in the
LMC and briefly reviews their major results. In Section 2.2, we summarise MAGMA’s
observing strategy and describe our data reduction procedure. The calibration of the
multi-epoch MAGMA survey data is discussed in more detail in Section 2.3. The
MAGMA map of integrated intensity CO emission in the LMC is presented in Section 2.4, where we discuss the detection rate, spatial distribution and statistical properties of the CO emission within our survey region. Throughout this thesis, we compare
the MAGMA
12 CO(J
= 1 → 0) data to other tracers of gas and dust in the ISM, and
to empirical estimates for parameters such as the star formation surface density and
the interstellar pressure. The ancillary datasets that we have used for these comparisons are described in Section 2.5, and a preliminary comparison between the spatial
distribution of the CO and H I emission peaks is presented in Section 2.6. We conclude
by assessing the mass of CO-bright molecular gas relative to other components of the
LMC’s mass budget and to its star formation rate, and compare these global ratios to
the results obtained for other nearby galaxies.
2.1.1
Previous
12
The first detection of
CO(J = 1 → 0) Surveys of the LMC
12 CO(J
= 1 → 0) emission from the LMC was reported by Hug-
gins et al. (1975). These authors obtained spectra towards two H II regions (30 Doradus
and N159, Henize, 1956) and two dark nebulae (clouds 47 and 52 in the catalogue of
Hodge, 1972) using a hot electron bolometer-mixer receiver mounted at the coudé focus
of the Anglo-Australian Telescope. CO emission at a radial velocity of 235 km s−1 relative to the local standard-of-rest (LSR) with a linewidth of 9 km s−1 and an antenna
temperature TA∗ = 1.7 ± 0.4 K was detected towards N159; only upper limits could be
measured for the other positions. Due to the lack of millimetre-wave facilities in the
36
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
southern hemisphere at the time, the ensuing search for CO emission at other locations
in the Magellanic Clouds was mostly conducted using the
12 CO(J
= 2 → 1) transition
at 230.54 GHz and targeted known H II regions, OH masers and dark clouds (Israel
et al., 1982). A decade after the detection by Huggins et al. (1975), Israel et al. (1986)
reported positive identifications of CO emission in 11 of 22 positions in the LMC and 6
of 16 positions in the SMC. While far from a complete census of molecular material in
the Magellanic System, these observations demonstrated that the CO emission in the
Magellanic Clouds is intrinsically weak, with brightness temperatures 2 to 4 times lower
than would be expected for Galactic giant molecular clouds (GMCs) at Magellanic distances. Israel et al. (1986) argued that the lower dust abundance in the Magellanic
Clouds permits ultraviolet (UV) photons from the interstellar radiation field to penetrate further into molecular clouds, leading to a higher rate of photodissociation of CO
molecules and a smaller filling factor of CO emission within the telescope beam, and
hence to lower CO brightness temperatures.
The first survey of
12 CO(J
= 1 → 0) emission over a significant fraction of the LMC’s
disk was conducted by Cohen et al. (1988) using the Columbia 1.2 m Millimeter Wave
Telescope at the Cerro Tololo Inter-American Observatory. The resulting map had an
angular resolution of 8′ .8, corresponding to a linear resolution of ∼130 pc at the distance
of 50.1 kpc. Cohen et al. (1988) identified forty molecular clouds within their 6◦ × 6◦
survey region, with typical radii of ∼ 180 pc and typical linewidths of ∼ 11 km s−1 .
They estimated the LMC’s total molecular mass to be 1.4 × 108 M⊙ , assuming that
the CO-to-H2 conversion factor in the LMC was XCO = 1.7 × 1021 cm−2 (K km s−1 )−1 .
While this value of XCO in the LMC seems high by today’s standards, it was consistent
with the expectation that XCO should scale inversely with the metallicity and/or the
dust-to-gas ratio (e.g.
Maloney & Black, 1988). Cohen et al. (1988) reasoned that
variations in the XCO factor, rather than blending of physically separate clouds within
their telescope beam, explained why LMC molecular clouds have low CO luminosities
relative to Milky Way clouds with a similar linewidth (see their figure 2).
The Cohen et al. (1988) survey was followed by a long-running project at the Swedish-
2.1. Introduction
37
ESO Submillimetre Telescope (SEST) to investigate the CO emission from molecular
gas in the Magellanic Clouds. The project obtained maps of the
13 CO(J
= 1 → 0) and
12 CO(J
12 CO(J
= 1 → 0),
= 2 → 1) emission in molecular cloud complexes asso-
ciated with sixteen Henize (1956) star formation regions in the LMC, complemented
by single-pointing observations towards a further ∼ 100 positions, mostly selected as
bright infrared sources in the catalogue of Schwering & Israel (1990). The full width at
half maximum (FWHM) SEST beam (45′′ at 115 GHz and 23′′ at 230 GHz) represented
a ten-fold improvement in angular resolution over the Cohen et al. (1988) survey, but
the combined field-of-view for the SEST Key Programme maps in the LMC is only 1
square degree, and mapping was mostly conducted for regions with active high-mass
star formation.
Results from the SEST Key Programme observations towards the LMC have been presented in a series of papers by Israel et al. (1993), Kutner et al. (1997), Johansson et al.
(1998), Garay et al. (2002) and Israel et al. (2003b). By comparing the CO luminosity
of molecular clouds to their virial mass estimate, the SEST studies derived an average
value for the CO-to-H2 conversion factor of XCO = 4.3 ± 0.6 × 1020 cm−2 (K km s−1 )−1
for LMC molecular clouds, much closer to the Galactic value than earlier studies indicated. They obtained
13 CO(J
= 1 → 0)/12 CO(J = 1 → 0) isotopologue ratios of ∼ 10,
approximately twice the average value observed for molecular clouds in the inner Milky
Way disk, and
12 CO(J
= 2 → 1)/12 CO(J = 1 → 0) transitional ratios close to unity,
which would seem to exclude the possibility that the
12 CO(J
= 1 → 0) emission
is optically thin. In a summary of results from the SEST Key Programme, Israel
et al. (2003b) argued that the molecular line ratios and the overall low intensity of
CO emission reflect a low CO abundance in the LMC and a smaller filling fraction of
CO-emitting gas within LMC molecular clouds. These conclusions are supported by
C II observations, which show that the envelope region with ionized carbon but without carbon monoxide is larger for molecular clouds in the LMC than in the Galaxy
(Mochizuki et al., 1994).
Most recently,
12 CO(J
= 1 → 0) emission in the LMC has been surveyed extensively by
38
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
NANTEN, a 4 metre radio telescope operated by Nagoya University at Las Campanas
Observatory in Chile. The NANTEN survey was completed in two phases. The first
phase, described by Fukui et al. (1999), obtained a map of the integrated intensity
CO emission I(CO) with a 3σ sensitivity of 1.8 K km s−1 . Observations conducted
during the second phase improved this sensitivity limit by a factor of two (Fukui et al.,
2008). The aim of the NANTEN survey was to obtain a complete inventory of the CObright molecular gas in the LMC, with sufficient resolution (2.′ 6) to identify individual
GMCs. The survey has been used to construct a catalogue of 230 GMCs and 42 smaller
clouds (presented in Fukui et al., 2008), which have been classified according to their
association with star-forming phenomena (Yamaguchi et al., 2001a; Kawamura et al.,
2009). Assuming steady state evolution and an age of 10 Myr for the SWB0 stellar
clusters catalogued by Bica et al. (1996), this classification scheme has been used to
derive an evolutionary timescale for GMCs in the LMC. Other key results include a
factor of ∼ 2 enhancement in the number and mass surface density of CO-emitting
clouds around the edges of supergiant shells (Yamaguchi et al., 2001b), and a GMC
mass spectrum that is significantly steeper than in the Milky Way disk (Fukui et al.,
2001), indicating that small cloud structures contain a higher fraction of the LMC’s
total molecular mass. Detailed comparisons of the H I and CO emission in the LMC
using the NANTEN CO data and a combined Australia Telescope Compact Array
(ATCA) and Parkes H I survey (Kim et al., 2003a) have been presented by Wong et al.
(2009) and Fukui et al. (2009). The former analysis showed that CO emission in the
LMC is associated with large H I column density and H I peak brightness, but that
these quantities are relatively poor predictors of where CO emission will be detected.
The latter study concluded that GMCs are surrounded by envelopes of atomic gas that
are gravitationally bound to the GMCs. The mean value for the CO-to-H2 conversion
factor of GMCs in the LMC, based on NANTEN measurements of their CO luminosity
and virial mass, is XCO = 7 × 1020 cm−2 (K km s−1 )−1 (Fukui et al., 2008).
2.2. The MAGMA LMC Survey
39
2.2 The MAGMA LMC Survey
2.2.1
Observing Strategy
MAGMA observations of the
12 CO(J
= 1 → 0) emission from molecular clouds in the
LMC are conducted at the Mopra Telescope, which is situated near Coonabarabran,
Australia.2 At 115 GHz, the Mopra Telescope has a FWHM beam size of 33′′ , corresponding to a spatial resolution of 8 pc at our assumed distance to the LMC. Due to
the large angular size of the LMC’s gas disk, and the small covering fraction of the
12 CO(J
= 1 → 0) emission, we use the NANTEN survey of Fukui et al. (2008) to select
regions of bright 12 CO(J = 1 → 0) emission for high-resolution mapping. MAGMA ob-
servations target 114 NANTEN GMCs with CO luminosities LCO > 7000 K km s−1 pc2 ,
and peak integrated intensities > 1 K km s−1 in the NANTEN cloud catalogue. These
clouds represent ∼ 50% of the GMCs in the catalogue, but contribute ∼ 70% of the
LMC’s total CO luminosity.
MAGMA observations are conducted in “on-the-fly” (OTF) raster-mapping mode. A
grid of 5′ × 5′ fields is placed over the region surrounding each molecular cloud target.
The field centres are separated by 4.′ 75 in right ascension (RA) and declination (Dec);
this 15′′ overlap ensures full coverage of the molecular cloud and facilitates mosaicking.
In OTF mode, the telescope takes data continuously while scanning across the sky.
Along each row of an OTF field, individual spectra are recorded every 14′′ , so that the
telescope beam is oversampled in the scanning direction. The spacing between rows is
10′′ , also oversampling the beam. Each row is preceded by an off-source (emission-free)
integration situated approximately 10 to 20′ from the field centre; an absolute location
for the OFF spectra was selected for each molecular cloud target in order to ensure a
consistent sky subtraction. To minimize scanning artefacts, each field is mapped twice:
an initial pass is made with the telescope scanning in the RA direction, and a second
orthogonal pass is then conducted. The data presented in this thesis were obtained
during the southern hemisphere winters of 2005 to 2009. The analysis in Chapters 3
2
The Mopra Telescope is managed by the Australia Telescope, which is funded by the Commonwealth
of Australia for operation as a National Facility by the CSIRO.
40
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
and 4 uses a subset of the MAGMA data that was obtained prior to the end of 2008,
at which time ∼ 60% of the cloud targets had been scanned in the RA direction only.
A system temperature measurement is obtained with an ambient load at the start of
each OTF map and every 20 to 30 minutes thereafter. In the interval between these
measurements, the system temperature is monitored using a noise diode. Typical system temperatures for the survey observations are between 500 and 600 K; observing
is abandoned when system temperatures exceed ∼1000 K. Our intention is to obtain
data with uniform sensitivity, so OTF fields with average system temperatures above
∼ 850 K are re-observed. Between each OTF map, the pointing of the antenna is verified by observing the nearby SiO maser RDor. The pointing solution is updated (and
re-verified) if the pointing error in azimuth or elevation is greater than 8′′ . Prior to
correction, the pointing errors are typically below 10 arcsec.
In 2005, the Mopra Telescope was equipped with a dual polarisation SIS receiver that
produced 600 MHz instantaneous bandwidth for observing frequencies between 86 and
115 GHz (Moorey et al., 1997). The correlator at that time could be configured for
bandwidths between 4 and 256 MHz across the receiver’s 600 MHz band (Wilson et al.,
1992). Our 2005 observations targeted the molecular ridge region discussed by Ott
et al. (2008) and Pineda et al. (2009) (see Figure 2.2), with some data obtained for
additional fields near RA 05h16m, Dec -68d10m (J2000) and RA 05h24m, Dec -69d40m
(J2000). For all 2005 observations, the correlator was configured with 1024 channels
over a 64 MHz bandwidth centred on 115.16 MHz, which provided a velocity resolution
of 0.16 km s−1 per channel across a reliable velocity bandwidth of ∼ 120 km s−1 . As this
is not quite sufficient to cover the total radial velocity range of the LMC’s CO emission,
the centre of the observing band was placed near the peak of CO spectrum obtained by
NANTEN for the region being observed. From 2006 onwards, the data were recorded
using the newly installed MMIC receiver and the University of New South Wales Digital
Filter Bank (MOPS).3 In the narrowband configuration used for the MAGMA survey
3
The University of New South Wales Digital Filter Bank used for the observations with the Mopra
Telescope was provided with support from the Australian Research Council.
2.2. The MAGMA LMC Survey
41
observations, MOPS can simultaneously record dual polarisation data for up to sixteen
138 MHz windows situated within an 8 GHz band. Each 138 MHz window is divided
into 4096 channels; for our survey observations at 115 GHz, this configuration provides a
velocity resolution of 0.09 km s−1 per channel across the velocity range [90,410] km s−1 .
The Mopra beam has been described by Ladd et al. (2005). These authors identify three
components - the ‘main beam’, and the inner and outer ‘error beams’ - that contribute
to the antenna response. The presence of these non-negligible error beams implies that
the telescope efficiency, η, will depend on source size. In the 2004 observing season,
Ladd et al. (2005) derived a main-beam efficiency factor of ηmb = 0.42 for observations
at 115 GHz, and an ‘extended’ beam efficiency of ηxb = 0.55 for sources that are comparable to the size of the inner error beam (∼1.′ 3). We consider the extended beam
efficiency factor to be more appropriate for the MAGMA survey observations, since
Galactic GMCs have a typical size of 40 pc (Blitz, 1993), corresponding to an angular
size of 2.′ 7 at the distance of the LMC.
To monitor the reliability of the flux calibration, we observed the standard source
Orion KL (RA 05h35m14.5s, Dec -05d22m29.56s (J2000)) once per 12 hour observing
session throughout our survey. The Orion KL spectra were obtained at elevations
between 30 and 55◦ , i.e. across a similar range of elevations as our survey observations.
In 2005, we measured a median peak brightness temperature for Orion KL of 55±3 K (in
TA∗ units, where the quoted uncertainty is the median absolute deviation). According
to the SEST documentation,4 the peak antenna temperature of Orion KL is TA∗ ∼
71 K, corresponding to a main beam temperature of Tmb ∼ 102 K for an efficiency
factor of ηmb = 0.7 (e.g. Garay et al., 2002). This suggests that data from the two
telescopes can be placed on the same brightness temperature scale using a factor of
η = 0.54 ± 0.03 for the Mopra data, in excellent agreement with the Mopra extended
beam telescope efficiency derived by Ladd et al. (2005). In subsequent years, the
average peak brightness temperature that we have measured for Orion KL has varied.
The average peak brightness of Orion KL and corresponding conversion factors that we
4
http://www.apex-telescope.org/sest/html/telescope-calibration/calib-sources/orionkl.html
Chapter 2. A
Orion KL Peak TA* (K)
42
70
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
2006
2007
2008
60
50
40
30
111.0
111.5
112.0
112.5
113.0
Centre Frequency (GHz)
Figure 2.1 The peak CO brightness of Orion KL plotted as a function of the centre frequency
of the MOPS observing band. The observed correlation, corresponding to ∼ 1 K per 100 MHz
shift in the MOPS centre frequency, was used to derive an empirical correction to the Orion KL
peak brightness measurements at different epochs in order to place the MAGMA data on a
self-consistent brightness temperature scale. The different plot symbols represent measurements obtained from three example frequency scans conducted between 2006 and 2008. For
each frequency scan, the Orion KL spectra were obtained in succession during good observing
conditions. The dashed vertical lines indicate the range of centre frequencies that were used
to obtain Orion KL spectra throughout the survey, while the dotted vertical lines indicate the
range used for LMC mapping observations.
2.2. The MAGMA LMC Survey
43
Table 2.1 The median peak brightness of Orion KL during different epochs of the MAGMA
survey. The centre frequency of the MOPS observing band νc and the conversion factor η that
we used to place the data on a self-consistent brightness temperature scale are also listed.
Epoch
hTpk i
[TA∗
2005
2006
2007
Jun 2008
Jul – Sep 2008
2009
νc
η
K]
[MHz]
55 ± 2
115262
0.54
41 ± 4
111550
0.38
48 ± 2
111550
0.45
40 ± 1
111460
0.39
50 ± 1
111460
0.48
111460
0.48
50 ± 1
applied to the different survey epochs are tabulated in Table 2.1. For data at 115 GHz
obtained with MOPS, we found that the gain varied with the centre frequency of the
MOPS observing band by ∼ 1 K (TA∗ ) per 100 MHz (Figure 2.1). The conversion factors
that we applied to the MAGMA data include empirically-derived corrections for (i) the
different observing band configurations that were used for the Orion KL spectra and
survey observations between 2006 and 2007, and (ii) the relative Doppler shift of the
emission from Orion KL and the LMC. These corrections are small, however, with the
largest correction corresponding to a 5% adjustment in the conversion factor.
2.2.2
Data Reduction
The processing of the MAGMA survey data involved four main steps. An initial correction to align the position and time stamp information in the raw data files was applied
to data obtained in 2005, using the mopfix task of the MIRIAD software package
(Sault et al., 1995b). Bandpass calibration and baseline-fitting were performed using
the AIPS++ livedata package. Livedata estimates the bandpass for each row of an
OTF map using the preceding OFF scan and then fits a user-specified polynomial to
the spectral baseline. We chose to fit the spectral baselines with a first-order polynomial, rejecting raw data that exhibited baselines with higher order ripples. The spectra
were combined to form a spectral line cube using the AIPS++ gridzilla package.
Each (x, y, v) cell within the final cube is sampled multiple times by the OTF scans:
44
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
gridzilla averages the spectra contributing to the emission within each cell according
to a convolution kernel, beam profile and weighting scheme specified by the user.
During the initial years of the MAGMA survey, we found it efficient to process regions
that contained a few molecular cloud complexes independently. We gridded these data
subcubes using a cell size of 9′′ × 9′′ . As more MAGMA data have been acquired,
our preference has been to grid all the spectra into a single cube covering the entire
LMC with a cell size of 15′′ × 15′′ . In either case, we aggregated the data from both
polarisations and scanning directions. The data were weighted by the inverse of the
noise variance based on the system temperature measurements. We used a truncated
Gaussian convolution kernel with a FWHM of 1.′ 0 and a cutoff radius of 30′′ , producing
output cubes with effective angular resolution of 45 arcsec.
While it could process contiguous OTF fields, gridzilla was not modified to mosaic
data recorded with different correlator configurations until the middle of 2009. Prior
to this software upgrade, survey data obtained in different years required separate processing. The data were converted to a consistent flux scale using the conversion factors
derived from our Orion KL observations (Table 2.1), then the MIRIAD task imcomb,
which weights the input data by the inverse of the RMS noise, was used to combine
data for regions that were observed over multiple epochs into a single data cube. Upgrades to the livedata and gridzilla packages in mid-2009 simplified the reduction of
multi-epoch Mopra data. The conversion factor required to place data on a consistent
flux scale is now accepted as input by livedata, and gridzilla is able to grid together
data at a common frequency, even if the data were recorded with different correlator
configurations. Processing of the MAGMA survey data since these upgrades has exploited these software improvements. All data are now processed simultaneously, after
resampling the raw spectra to a common channel width of 33.68 kHz with the mopfix
task. The parameters for baseline-fitting and our adopted convolution kernel have remained unchanged. In order to increase the signal-to-noise (S/N ), we fold the data in
the spectral domain and convolve them with a 40′′ Gaussian kernel to produce an output data cube with a final angular resolution of 1.′ 0 and velocity resolution 0.53 km s−1 .
2.3. Flux Validation
45
The catalogue described in Chapter 3 and analysed in Chapter 4 is constructed from
data that were acquired between 2005 and 2008. These data were processed using the
former approach, i.e. combining data from different years in the final data reduction
step. The data presented in Section 2.4 include observations conducted during the 2009
season, and were processed using the newer reduction procedure.
2.3 Flux Validation
The Mopra Telescope has been extensively upgraded in recent years, with major works
including the re-shaping of the dish, and the installation of a new receiver and spectrometer. The study by Ladd et al. (2005) describes the important parameters of the
observing system for the period 2000 to 2004, but the characteristics of the 3 millimetre
Mopra observing system have not been formally reviewed since the installation of the
MMIC receiver and MOPS. While these changes to the Mopra observing system complicate the calibration of the MAGMA survey data, we are fortunate that there are
published SEST observations of several molecular clouds in the MAGMA sample, and
that the unsmoothed MAGMA data have comparable angular and spectral resolution
to the SEST data. As described above, we use regular observations of Orion KL to
place the multi-epoch MAGMA survey data on a self-consistent brightness temperature
scale. We can validate this calibration by comparing Mopra and SEST measurements
of the
12 CO(J
= 1 → 0) peak brightness, FWHM linewidth and peak integrated inten-
sity towards positions in the LMC that have been observed by both telescopes.
We compiled published SEST measurements of
12 CO(J
= 1 → 0) emission in the LMC
from the studies by Chin et al. (1997), Kutner et al. (1997), Johansson et al. (1998),
Garay et al. (2002) and Israel et al. (2003a,b). The
12 CO(J
= 1 → 0) data described
by these studies – mostly obtained by the ESO-SEST Key Programme CO in the Magellanic Clouds – have angular resolution of 45′′ and spectral resolution of 0.11 km s−1 ,
and were transformed to a Tmb scale using main-beam efficiency factors between 0.7
and 0.74. To match these characteristics as closely as possible, we use MAGMA data
46
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
with effective angular resolution of 45′′ and a spectral resolution of 0.18 km s−1 . The
CO emission parameters at each position were then determined by fitting a Gaussian
function to the
12 CO(J
= 1 → 0) line profile. Line profile fitting was used to estimate
the CO emission parameters by at least four of the six SEST studies that we refer to.
The exceptions are Chin et al. (1997), who do not specify how their measurements were
derived, and Kutner et al. (1997), who integrate directly over the CO line profile but
do not state the velocity limits that they applied at each position. In total, we were
able to compare MAGMA and SEST measurements of the
12 CO(J
= 1 → 0) peak
brightness Tpk and FWHM linewidth ∆v at 45 positions, and measurements of the
peak CO integrated intensity I(CO) at 30 positions. The CO emission parameters obtained by MAGMA and reported by the SEST studies are listed in Table 2.2. Overall,
the measurements are in good agreement: the median ratio of the SEST to MAGMA
measurement is 1.1 for Tpk , 1.0 for the FWHM linewidth, and 1.1 for I(CO), with a
dispersion in the ratio of . 20% in all cases.
On average, the MAGMA Tpk and I(CO) measurements are 10% lower than the SEST
measurements. Although this discrepancy is small, we are interested to determine
whether the total CO luminosity of molecular clouds identified in the MAGMA survey
are also systematically lower than would be inferred from the SEST data. To test this,
we selected clouds in the SEST studies that could be identified with molecular clouds
in the MAGMA catalogue (presented in Chapter 3). In contrast to the CO emission
parameters presented in Table 2.2, the MAGMA measurements of total CO luminosity
are typically ∼ 10% higher than the corresponding SEST measurements, with a dispersion in the ratio of ∼ 20%. MAGMA’s lower measurements of Tpk and I(CO) at
the cloud peaks may therefore reflect Mopra’s non-negligible inner error beam and/or
the gridding process – both of which tend to increase the effective angular resolution –
rather than a brightness temperature offset between the SEST and MAGMA datasets.
Since the ratios between the total and peak measurements show opposing trends of
similar magnitude, and they are consistent with unity in both cases, we consider that
the accuracy of our calibration strategy to be satisfactory.
2.3. Flux Validation
Table 2.2:
47
12
CO(J = 1 → 0) emission parameters towards 45 positions in the LMC, as
measured by MAGMA and SEST. The position and radial velocity listed in columns 1 to 3
refer to the MAGMA measurement. The final column lists the cloud identification used in
the corresponding SEST paper. References: (1) Chin et al. (1997) (2) Garay et al. (2002) (3)
Kutner et al. (1997) (4) Johansson et al. (1998) (5) Israel et al. (2003b) (6) Israel et al. (2003a).
RA
Dec
VLSR
(J2000)
(J2000)
km s−1
MAGMA
SEST
Ref.
Notes
Tpk
∆v
I(CO)
Tpk
∆v
I(CO)
05:13:22.6
-69:22:46
235.4
7.6
5.0
40.3
7.9
5.2
44.1
1
N113
05:22:06.1
-67:58:14
282.6
5.6
6.2
36.9
6.5
6.0
40.2
1
N44BC
05:39:38.9
-69:45:34
237.9
5.5
7.4
43.2
7.2
7.0
48.4
1
N159HW
05:39:49.5
-71:09:39
228.6
3.9
6.1
25.3
4.9
5.5
29.0
1
N214DE
05:43:28.1
-69:25:53
248.9
2.9
4.6
13.7
3.3
4.9
17.0
2
A
05:44:30.5
-69:25:23
229.0
5.1
6.5
35.2
5.8
4.9
30.2
2
C
05:44:39.1
-69:28:04
227.3
3.6
6.6
25.1
3.8
5.6
22.9
2
D
05:44:51.6
-69:21:11
228.3
3.4
5.5
19.4
3.1
5.8
19.2
2
E
05:46:35.9
-69:34:52
231.1
2.5
3.9
10.1
2.4
4.3
11.1
2
F
05:39:49.6
-70:02:55
231.3
1.7
5.3
9.6
2.2
9.7
15.8
3
Center 1
05:39:17.9
-70:07:08
236.5
3.1
6.3
20.6
3.8
6.9
23.1
3
Center 2
05:39:28.1
-70:12:05
224.4
2.4
6.6
16.7
2.9
6.8
20.4
3
Center 4
05:40:43.2
-70:10:06
227.6
2.9
4.9
15.1
3.7
5.2
17.8
3
Center 6
05:40:52.4
-70:13:33
224.8
3.0
4.8
15.0
3.5
8.2
19.1
3
Center 7
05:40:59.0
-70:20:32
228.9
2.9
5.1
15.6
3.3
5.8
19.0
3
Center 10
05:40:42.2
-70:28:10
229.2
3.5
4.7
17.4
4.8
5.3
21.2
3
Center 12
05:40:28.0
-70:30:39
228.0
2.4
6.8
17.4
3.3
6.2
20.3
3
Center 14
05:39:55.5
-71:07:44
236.0
2.0
6.0
12.6
2.6
6.8
16.1
3
South 2
05:39:49.5
-71:09:39
228.6
4.9
5.9
30.7
5.2
6.8
33.9
3
South 3
05:40:00.0
-71:12:28
229.4
1.2
7.4
9.0
1.4
5.8
9.3
3
South 4
05:40:24.3
-71:13:27
216.9
2.1
3.0
6.6
2.4
3.3
8.1
3
South 5
05:38:31.0
-69:02:15
249.3
1.7
4.9
8.7
2.2
4.5
···
4
30Dor-06
05:36:14.8
-69:01:55
272.3
1.4
6.5
9.8
1.1
6.7
···
4
30Dor-07
05:35:54.0
-69:02:09
258.8
2.6
5.5
14.9
2.3
5.9
···
4
30Dor-08
05:38:49.6
-69:04:39
249.2
1.5
10.4
15.9
1.4
11.2
···
4
30Dor-10
05:38:39.3
-69:07:35
246.2
1.2
2.9
3.5
1.4
3.4
···
4
30Dor-15
05:35:49.6
-69:12:41
239.7
2.4
4.4
10.9
2.1
4.0
···
4
30Dor-27
05:38:31.9
-69:16:47
250.8
1.4
4.0
5.8
1.4
3.5
···
4
30Dor-33
05:39:08.6
-69:29:58
257.2
2.2
3.5
8.1
3.8
3.5
···
4
N158-1
05:38:56.6
-69:34:41
250.3
2.0
10.7
22.1
2.1
6.0
···
4
N158-5
05:39:29.8
-69:39:59
241.2
1.9
7.5
14.7
1.6
5.8
···
4
N160-5
05:40:14.4
-69:44:43
233.8
4.0
6.8
28.9
5.2
7.6
···
4
N159-E
05:39:40.3
-69:45:26
238.1
5.7
7.1
43.2
6.6
6.0
···
4
N159-W
05:41:00.8
-69:46:17
233.3
1.7
3.1
5.4
1.6
4.3
···
4
N159-1
05:39:28.5
-69:46:53
234.1
4.5
5.4
25.8
4.9
5.5
···
4
N159-2
05:40:00.8
-69:50:42
235.4
4.7
7.9
39.6
5.8
8.5
···
4
N159-S
Continued on next page . . .
48
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Table 2.2 – Continued
RA
Dec
VLSR
MAGMA
SEST
Ref.
Notes
(J2000)
(J2000)
km s−1
Tpk
∆v
I(CO)
Tpk
∆v
I(CO)
I(CO)
I(CO)
05:32:32:9
-66:27:15
289.2
2.5
4.5
11.9
3.5
4.8
16.7
5
N55
04:55:37.9
-66:28:15
276.8
1.8
4.9
9.2
1.6
2.7
4.5
6
2
04:55:36.6
-66:34:17
279.7
3.0
4.8
14.8
2.6
5.7
15.6
6
4
04:56:49.7
-66:24:28
285.3
2.1
5.7
12.6
2.5
6.1
16.0
6
10
04:57:48.4
-66:28:49
280.2
3.1
4.0
12.7
3.0
3.8
12.0
6
15
04:58:10.2
-66:18:58
271.0
2.3
3.7
8.7
2.5
3.9
10.9
6
18
04:58:51.1
-66:09:49
278.2
1.6
3.8
6.5
2.0
3.9
8.5
6
27
04:58:45.0
-66:08:15
276.6
2.6
3.5
9.7
2.9
3.9
11.3
6
28
04:58:53.3
-66:07:19
274.9
2.9
3.0
9.3
2.5
3.2
8.5
6
29
2.4 Data Presentation
The MAGMA map of 12 CO(J = 1 → 0) integrated intensity in the LMC is presented in
Figure 2.2. This map was produced using the smooth-and-mask technique described by
Helfer et al. (2003). We adopt this approach because significant CO emission is rarely
detected in more than a few velocity channels, so direct integration over the total
observed velocity range would produce a map dominated by noise. As per the smoothand-mask technique, we generated a mask by smoothing the CO data cube to 90′′ and
blanking pixels with emission below three times the RMS noise level in the smoothed
cube. We transferred this mask to the original data cube, and summed the unmasked
pixels across the LSR velocity range [180,320] km s−1 . The maps in Figures 2.2 and 2.3
show that CO emission in the LMC is distributed in clumps and/or filamentary structures, and that these structures are associated with regions of high atomic gas column
density. Several of the larger GMCs identfied by NANTEN (e.g. LMC N J0522-6756)
are resolved into multiple distinct objects at MAGMA’s higher resolution, but the majority of NANTEN GMCs show a one-to-one correspondence with a bright, spatially
compact region of emission in the MAGMA I(CO) map. The large angular extent of
the LMC relative to the average size of the CO-emitting regions makes it difficult to
convey the structure of individual cloud complexes and their overall spatial distribution
in a single map. To provide a more detailed view of the molecular cloud complexes,
2.4. Data Presentation
49
Figure 2.2 A map of CO integrated intensity in the LMC by MAGMA (greyscale). The thin
black outlines indicate the coverage of the MAGMA survey. The black cross indicates the
position of 30 Doradus; we refer to the large survey region that encloses and extends south from
30 Dor as the “molecular ridge”, and the chain of molecular cloud complexes situated directly
east of the molecular ridge as the “molecular arc”. The black ellipse indicates where the stellar
surface density, Σ∗ , is greater than 100 M⊙ pc−2 ; we refer to this region as the “stellar bar”.
50
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.3 A map of the atomic gas column density in the LMC from the H I survey by Kim
et al. (2003a), overlaid with blue contours representing regions in the MAGMA I(CO) map
with I(CO) = 2.0 K km s−1 . The units of the map are H cm−2 .
we present MAGMA maps of ∼ 1.5◦ ×1.5◦ subregions within the LMC in Appendix 2.A.
Across most of the LMC, the CO emission is confined to a narrow velocity range
(< 10 km s−1 ) and the line profiles are single-peaked. Some notable exceptions include
the molecular ridge, the molecular cloud complex located between the LMC4 and LMC5
superbubbles (Meaburn, 1980), and the star-forming region N44 (Henize, 1956). Example
12 CO(J
= 1 → 0) spectra obtained by MAGMA across the LMC are presented
alongside the I(CO) maps in Appendix 2.A.
To illustrate the overall velocity distribution of the CO emission, channel maps are presented in Figure 2.4. These channel maps are produced from a masked version of the
2.4. Data Presentation
51
CO data cube, which was constructed using the smooth-and-mask technique described
above. The nine panels of Figure 2.4 show velocity channels of width ∆V = 12 km s−1
across the LSR velocity range [196,304] km s−1 . Approximately half of the total CO
luminosity in the MAGMA survey region arises at LSR velocities between 210 and
240 km s−1 , i.e. the velocities associated with the molecular ridge and arc in the southeast of the LMC. A map of the intensity-weighted CO velocity centroid, constructed
from the masked CO data cube, is shown in Figure 2.5[a]. In general, the CO emission
follows the velocity field of the H I emission (Figure 2.5[b]), although some divergence
between the H I and CO velocity centroids is evident in the south-east of the LMC. This
is because the H I line profiles exhibit two distinct velocity components in this region
(e.g. Luks & Rohlfs, 1992), while the CO emission tends to be associated with one of
the H I components only.
The MAGMA survey region (indicated by the thin black outline in Figure 2.2) contains
210350 15′′ ×15′′ map pixels, corresponding to a combined field-of-view of 3.65 square
degrees.
CO emission was positively identified at the 5σ level in 55170 pixels of
the I(CO) map, with a total CO luminosity within the MAGMA survey region of
2.33 × 106 K km s−1 pc2 . Lowering our threshold for a significant detection to 3σ in-
creases the CO luminosity to 2.72 × 106 K km s−1 pc2 . For these estimates, the sensi√
tivity limit at each pixel in the I(CO) map was estimated as N × RM S × δv, where
N is the number of channels with significant emission included by the blanking mask,
δv = 0.53 km s−1 is the width of a single velocity channel, and RM S is the 1σ noise
per channel along the sightline. Averaged across the MAGMA survey region, the 1σ
sensitivity limit is 0.15 K km s−1 , but since the smooth-and-mask technique includes a
different number of channels in the integration at different positions within the map,
the I(CO) sensitivity limit is also spatially variable. A further source of variations is
the 1σ noise per channel, which ranges between 0.10 K to 0.55 K across the MAGMA
LMC map. These fluctuations arise because some fields had only been scanned in one
direction by the end of 2009, while changes in the observing conditions (e.g. weather,
telescope elevation) lead to minor differences in the RMS noise level for regions where
observations are complete. Figure 2.6[a] presents a map of the 1σ noise fluctuations
52
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.4 Individual channel maps for the CO emission in the LMC by MAGMA. The LSR
velocity range of each channel is indicated at the top right of each panel. The black contours
correspond to I(CO) = 1.5 km s−1 , and the black ellipse indicates the location of the LMC’s
stellar bar.
2.4. Data Presentation
53
Figure 2.5 (a) MAGMA map of the intensity-weighted velocity centroid of the CO emission in
the LMC. (b) Velocity centroid of the H I emission, constructed using data from the H I survey
by Kim et al. (2003a). The maps in both panels use the same colour stretch, which runs linearly
from 195 to 305 km s−1 (LSR). The contours in both panels indicate I(CO) = 2 K km s−1 .
54
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
per 0.53 km s−1 channel; a histogram representing the distribution of the 1σ noise fluctuations across the MAGMA survey region is shown in Figure 2.6[b].
Assuming a CO-to-H2 conversion factor of XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 , the
total mass of molecular gas detected by MAGMA, which we calculate by applying XCO
to all pixels in the I(CO) map in Figure 2.2 with 5σ detections, is 1.0 × 107 M⊙ . Including pixels with CO emission detected above 3σ significance increases the total mass
estimate to 1.2 × 107 M⊙ . Both estimates include a factor of 1.36 by mass to account
for the presence of helium. For reference, Fukui et al. (2008) obtain a molecular mass of
1.4 × 107 M⊙ for the entire LMC, assuming an identical helium contribution and XCO
value.
The frequency distributions of CO peak brightness and CO integrated intensity in the
MAGMA survey region are shown in Figure 2.7. In both panels, the open histogram
includes all map pixels, and the solid grey histogram represents pixels with 5σ upper
limits. The difference between the two histograms represents pixels where we can be
confident that we have detected genuine emission. The upper axis of Figure 2.7[a]
indicates the equivalent hydrogen nucleon column density in the CO-bright molecular gas phase, N (H)mol = 2N (H2 ), assuming XCO = 2 × 1020 cm−2 (K km s−1 )
−1
.
Roughly 10% of pixels in the MAGMA survey region have N (H)mol ≥ 1021 cm−2 , but
less than 0.1% have N (H)mol ≥ 1022 cm−2 . The brightest CO emission in the LMC
is detected in the molecular ridge near RA 05h39m50s, Dec -70d08m (J2000) where
I(CO) = 41 K km s−1 and Tpk = 4.4 K. The GMCs associated with the N44, N113 and
N159 star-forming complexes (Henize, 1956), and a GMC in the molecular arc (LMC
N J0544-6923) are the only other regions with I(CO) ≥ 25 K km s−1 . These regions
also tend to have high CO peak brightness temperatures (Tpk & 4 K).
As emphasised by the SEST Key Programme papers, the CO emission in the LMC
appears to be intrinsically weak. Kutner et al. (1997) demonstrated that the Orion
molecular cloud (OMC) would show main beam CO brightness temperatures of ∼ 20 K
at the cloud peaks, falling to ∼ 4 K in regions of extended emission, if it were ob-
log(Number of pixels)
2.4. Data Presentation
55
[b]
4
3
2
1
0.1
0.2
0.3
0.4
0.5
RMS Tmb [K]
Figure 2.6 (a) Spatial distribution of the RMS noise per 0.53 km s−1 velocity channel across
the MAGMA survey region. The units are Kelvins. (b) Frequency distribution of the RMS
noise fluctuations.
56
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
log(N(H)molecular/[cm−2])
20.0
20.5
21.0
21.5
22.0
[a]
4
4
3
3
2
2
1
1
−1.0
−0.5
0.0
0.5
1.0
log(I(CO)/[K km s−1])
1.5
log(Number of pixels)
log(Number of pixels)
19.5
[b]
4
3
2
1
−0.5
0.0
0.5
log(Peak Tmb(CO)/[K])
Figure 2.7 Frequency distributions of the (a) CO integrated intensity and (b) CO peak brightness in the MAGMA survey. The open histograms represent all pixels in the survey region,
while the grey histograms represent pixels where we did not detect significant emission at the
5σ level. The upper axis in panel (a) indicates the equivalent hydrogen nucleon column density
−1
in the CO-bright molecular gas phase, assuming XCO = 2 × 1020 cm−2 (K km s−1 ) .
served with 10 pc resolution. We verified that there is a genuine discrepancy between
the properties of the CO emission in the LMC and the Milky Way by obtaining peak
temperature maps of the Perseus, Ophiuchus and Ara OB1 molecular clouds, all of
which are less massive (∼ 104 M⊙ ) and host lower levels of star formation activity than
OMC (Ridge et al., 2006; Arnal et al., 2003).5 After degrading the maps to a common
resolution of 10 pc, we found average Tpk values of 4.6 to 5.6 K for the three Galactic
clouds. For comparison, the typical peak brightness temperature of significant (> 3σ)
CO emission in the MAGMA survey region is 1.1 K, and only 1% of sightlines have
Tpk > 3 K.
The main beam brightness temperature of molecular line emission is given by (e.g.
5
Data for the Perseus and Ophiuchus clouds were obtained from the COMPLETE archive,
http://www.cfa.harvard.edu/COMPLETE/data html pages/data.html. Unpublished 12 CO(J = 1 →
0) observations of Ara OB1 were conducted by the author at the Mopra Telescope in 2006. These data
were reduced according to the procedure outlined in Section 2.2.2. We note that for the comparison
with Galactic clouds, we used the unsmoothed MAGMA data.
2.5. Ancillary Data
57
Bourke et al., 1997)
Tmb = f [J(Tex ) − J(Tbg )] [1 − exp(−τ )]
(2.1)
where Tex is the excitation temperature and τ the optical depth of the transition,
Tbg = 2.73 K is the background temperature, f is the filling factor of the emitting
regions within the telescope beam, and
J(T ) =
hν
1
.
k [exp(hν/kT ) − 1]
(2.2)
In this equation, ν is the observed frequency, and h and k are the Planck and Boltzmann
constants respectively. Previous analyses of CO emission along LMC sightlines have
found
12 CO(J
12 CO(J
= 2 → 1)/12 CO(J = 1 → 0) transitional ratios close to unity and
= 1 → 0)/13 CO(J = 1 → 0) isotopologue ratios close to 10 (e.g Garay et al.,
2002; Israel et al., 2003b; Wang et al., 2009), suggesting that the
12 CO(J
= 1 → 0)
emission is well-thermalized and optically thick (τ ≫ 1). In this case, Equation 2.1
shows that lower CO line intensities in the LMC may reflect lower kinetic temperatures
in the molecular gas (Tex ≈ Tkin for optically thick emission, e.g. Wilson, 2009) and/or a
smaller filling fraction of CO-emitting material within the telescope beam. For optically
thick gas with a uniform temperature of Tkin = Tex = 20 K, the range of Tpk values
observed in the LMC corresponds to filling factors between 5 and 40%. It is likely that
there are significant temperature gradients within molecular clouds such the gas in the
cloud interior is colder than gas located near the cloud surface or newly formed stars,
but the observed CO brightness temperatures are sufficiently low that the CO emission
must partially cover the Mopra beam for gas temperatures higher than ∼ 5.5 K (i.e.
the energy of the upper level of the
12 CO(J
= 1 → 0) transition, Wilson, 2009).
2.5 Ancillary Data
The key characteristics of ancillary datasets used in this thesis are summarized in
Table 2.3. The original maps cover different fields-of-view, and have different angular
resolutions and pixel sizes. Unless otherwise noted, we regrid the maps to a common
58
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Table 2.3 Characteristics of the ancillary datasets used in this work. The values in column 4
are measured over a 7.◦ 5 × 7.◦ 5 region covering the gas disk of the LMC. The flux density of the
median-filtered 1.4 GHz radio continuum map is listed in parentheses in column 4. References:
(1) Meixner et al. (2006) (2) Hughes et al. (2007) (3) Kim et al. (2003a) (4) Fukui et al. (2008)
(5) Gaustad et al. (2001).
Band
Source
24µm
70µm
160µm
1.4 GHz
HI
12
CO(J = 1 → 0)
Hα
Spitzer
Spitzer
Spitzer
ATCA+Parkes
ATCA+Parkes
NANTEN
SHASSA
Resolution
(arcmin)
0.1
0.3
0.63
0.67
1.0
2.6
0.83
Luminosity,
Mass or Total Flux Density
7.97 × 103 Jy
1.36 × 105 Jy
2.93 × 105 Jy
426 Jy (364 Jy)
5.3 × 108 M⊙
3.5 × 106 K km s−1 pc2
2.6 × 1040 erg s−1
Ref.
1
1
1
2
3
4
5
pixel scale (typically 15′′ × 15′′ or 20′′ × 20′′ ) and convolve them to a common angular
resolution (1.′ 0) for quantitative analysis. The images are truncated to cover a 7.◦ 5 × 7.◦ 5
region centred on the position RA 05h23m35s, -69d41m22s (J2000), and are gridded
using the NCP projection, which is a special case of an orthographic SIN projection
with a tangent point at the north celestial pole. This region, which we refer to as
“the whole LMC”, is completely covered by all the ancillary datasets except for the
NANTEN CO survey and the Spitzer infrared maps. The NANTEN CO map has an
irregular field-of-view that approximately encompasses the central 6◦ × 6◦ of the LMC.
The Spitzer maps omit triangular regions in each corner of our “whole LMC” area, but
they cover all parts of the LMC’s gas disk with N (HI) >∼ 1021 cm−2 . The total (i.e.
spatially integrated) flux densities within the maps are listed in Table 2.3; for the gas
tracers, the integrated fluxes are expressed in mass or luminosity units. The ancillary
maps are displayed at their natural resolution in the figures of this Section.
2.5.1
H I Data
To trace the atomic gas in the LMC, we use the H I spectral line cube presented by
Kim et al. (2003a), which combines data from the ATCA (Kim et al., 1998) and the
Parkes single-dish telescope (Staveley-Smith et al., 2003). The angular resolution of
the H I data is 1.′ 0, well-matched to the reduced MAGMA CO data. The H I data
2.5. Ancillary Data
59
cube has a velocity resolution of 1.65 km s−1 , with an H I column density sensitivity of
7.2 × 1018 cm−2 per channel. We construct an H I integrated intensity emission map
of the LMC I(HI) by integrating the H I data cube over the heliocentric velocity range
196 to 353 km s−1 . We assume that the H I emission is optically thin everywhere, and
derive a map of the LMC’s H I column density, N (HI), according to
N (HI) [ cm−2 ] = 1.823 × 1018 I(HI) [ K km s−1 ].
(2.3)
The resulting N (H I) map was presented above in Figure 2.3. We note that our estimate for N (H I) is likely to be a lower limit since the H I emission in the LMC may
have significant optical depth, especially along the sightlines towards molecular clouds
(Dickey et al., 1994; Marx-Zimmer et al., 2000). A map of the H I peak brightness was
also created from the H I spectral line cube, and is presented in Figure 2.8.
2.5.2
Far-infrared Data
To trace emission from dust, we use Spitzer mosaics of the 24, 70 and 160 µm farinfrared (FIR) emission in the LMC obtained by the Surveying Agents of Galaxy Evolution Legacy Program (SAGE, Meixner et al., 2006) using the Multiband Imaging
Photometer (MIPS, Rieke et al., 2004). The angular resolution of these maps is 6′′ , 18′′
and 38′′ , and the surface brightness sensitivity to diffuse emission is 1, 5 and 10 MJy sr−1
at 24, 70 and 160 µm respectively. For all three bands, we use the full enhanced LMC
mosaics that are publicly available through the Spitzer Science Centre archive.6 Each
of the FIR maps is shown in a separate panel of Figure 2.9.
The Spitzer observations for the SAGE project were scheduled at two different epochs,
separated by an interval of three months, in order to minimize striping artefacts and to
constrain source variability. We use images that are produced by combining both epochs
of observations. Processing of the SAGE Legacy data includes steps to remove residual
instrumental signatures and to subtract background emission at 24 and 70 µm, but
6
http://ssc.spitzer.caltech.edu/spitzermission/observingprograms/legacy/sage/.
delivery documentation, authored by M. Sewilo, is also available at this URL.
The data
60
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.8 A map of the H I peak brightness in the LMC, overlaid with red contours representing
regions in the the MAGMA I(CO) map with I(CO) = 2.0 K km s−1 . The map is displayed in
Kelvin units.
2.5. Ancillary Data
61
Figure 2.9 A map of the 24 µm emission in the LMC by the SAGE Legacy Program (Meixner
et al., 2006), overlaid with red contours representing regions in the MAGMA I(CO) map with
I(CO) = 2.0 K km s−1 . A square-root intensity scale has been used to emphasise the characteristics of the diffuse emission. Black pixels correspond to surface brightnesses greater than
30 MJy sr−1 , ∼ 1% of the peak value in the map. The map is displayed in MJy sr−1 units.
62
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.9 (cont.) The SAGE map of 70 µm emission in the LMC, overlaid with I(CO) =
2.0 K km s−1 MAGMA contours. A square-root intensity scale has been used to emphasise the
characteristics of the diffuse emission. Black pixels correspond to surface brightnesses greater
than 130 MJy sr−1 , ∼ 1% of the peak value in the map. The map is displayed in MJy sr−1
units.
2.5. Ancillary Data
63
Figure 2.9 (cont.) The SAGE map of 160 µm emission in the LMC, overlaid with I(CO) =
2.0 K km s−1 MAGMA contours. A square-root intensity scale has been used to emphasise the
characteristics of the diffuse emission. Black pixels correspond to surface brightnesses greater
than 250 MJy sr−1 , ∼ 10% of the peak value in the map. The map is displayed in MJy sr−1
units.
Chapter 2. A
log(Flux Density/[Jy])
64
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
6
5
4
3
2
−2
0
2
4
6
log(Frequency/[GHz])
Figure 2.10 The global spectrum of the LMC, covering radio to infrared frequencies. The open
circles represent literature values collated by Israel et al. (2010), while the filled circles represent
our measurements for the three SAGE maps.
not at 160 µm. The average 160 µm surface brightness in blank regions of sky regions
away from the disk of the LMC is 10.5 MJy sr−1 ; we adopt this constant value as our
estimate for the background emission at 160 µm and subtract it from the map. We
caution, however, that the dominant source of 160 µm background emission is Milky
Way cirrus, which may not be well-represented by a uniform offset or plane. Some
authors have used a Parkes map of the H I emission at Galactic velocities and an
assumed value of the gas-to-dust ratio to model the infrared emission from dust in the
LMC foreground (e.g. Bernard et al., 2008). Variations in the dust-to-gas ratio and
the distributions of foreground gas and dust on spatial scales below the resolution of
the Parkes data (14.′ 3) remain important sources of uncertainty for maps that have
been processed in this manner. The flux density measurements that we obtain for all
three MIPS bands are in reasonable agreement with the global LMC spectral energy
distribution published by Israel et al. (2010, see Figure 2.10).
2.5. Ancillary Data
2.5.3
65
1.4 GHz Radio Continuum Data
We use a map of the 1.4 GHz radio continuum emission in the LMC that was produced
by combining data from the Parkes Telescope and the ATCA. The ATCA observations
were conducted simultaneously with the H I survey by Kim et al. (1998). The construction and characteristics of the combined ATCA+Parkes 1.4 GHz map are described in
detail in Chapter 5.
2.5.4
NANTEN CO Data
As noted in Section 2.1.1,
12 CO(J
= 1 → 0) emission in the LMC has been exten-
sively surveyed by NANTEN. The 3σ I(CO) sensitivity of the NANTEN survey data
is approximately 0.9 K km s−1 , corresponding to a hydrogen nucleon column density of
N (H)mol ∼ 3.6 × 1020 cm−2 , assuming XCO = 2 × 1020 cm−2 (K km s−1 )
−1
. The survey
incorporates 27,000 observed positions over an irregularly shaped area of ∼ 6◦ × 6◦ centered on the B1950 position RA 05h20m, Dec -69d00m (Fukui et al., 2001, 2008). The
FWHM beam of the NANTEN telescope at 115 GHz is 2.′ 6 and spectra for the LMC
survey were obtained using a 2′ grid spacing. The spectrometers were two acoustooptical spectrometers with 2048 channels each. The narrow-band (NB) spectrometer
has a velocity coverage of 100 km s−1 and a resolution of 0.1 km s−1 , whereas the wideband (WB) spectrometer has a velocity coverage of 650 km s−1 and a resolution of
0.65 km s−1 . Of the 27,000 positions in the survey, roughly 25% were observed with
the NB spectrometer, while the rest were observed with the WB spectrometer.
The integrated intensity map shown in Figure 2.11 was produced from the NANTEN
data cube using a smooth-and-mask technique. The data were first folded in the spectral
domain to a velocity channel width of 1.95 km s−1 . A blanking mask was defined
using the 3σ contour of a smoothed version of the data cube, which was generated
by convolving the binned cube with a Gaussian kernel with FWHM=5.′ 2. To create
the final CO integrated intensity map, the blanking mask was applied to the original
binned cube, which was then summed over the LSR velocity range [200,300] km s−1 .
66
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.11 A map of CO integrated intensity emission in the LMC obtained by the NANTEN
survey (Fukui et al., 2008). The black contour levels indicate I(CO) = 1, 4, 7 and 10 K km s−1 .
The thin light grey outlines indicate the MAGMA survey coverage, and the thick grey contours
represent stellar mass surface densities of 20, 50 and 100 M⊙ pc−2 in the map produced by Yang
et al. (2007).
2.5. Ancillary Data
2.5.5
67
Stellar Mass Surface Density
To trace the mass distribution within the LMC’s stellar disk, we use the stellar mass
surface density map presented in figure 1c of Yang et al. (2007). The map is based on
number counts of red giant branch (RGB) and asymptotic giant branch (AGB) stars,
selected by their colours from the Two Micron All Sky Survey Point Source Catalogue
(Skrutskie et al., 2006). The star counts are binned into 40 pc × 40 pc pixels, and
then convolved with a Gaussian smoothing kernel with σ = 100 pc. The resulting
map is normalized to a measure of the stellar mass surface density by adopting a total
stellar mass for the LMC of 2 × 109 M⊙ (Kim et al., 1998). The resolution of the
stellar mass surface density map is considerably coarser than the angular resolution of
our MAGMA CO data, so it is possible that the average stellar mass surface density
is underestimated on small scales due to beam dilution. RGB and AGB stars are
relatively old populations, however, so their spatial distribution is likely to be smooth.
In particular, we do not expect them to be strongly clustered in the vicinity of molecular
clouds (e.g. Nikolaev & Weinberg, 2000). Contours representing stellar surface densities
of 20, 50 and 100 M⊙ pc−2 are indicated in Figure 2.11.
2.5.6
H α Data
To trace ionized gas in the LMC, we use the Southern H α Sky Survey Atlas (SHASSA,
Gaustad et al., 2001). Each SHASSA image covers a 13◦ × 13◦ field-of-view, with an
angular resolution of 0.′ 8. To isolate the H α emission, the survey used a NB imaging
system consisting of an H α filter with 3.2 nm bandwidth and a dual-band notch filter
that transmitted a 6.1 nm band of continuum radiation on either side of the H α emission
line. For our analysis, we use the continuum-subtracted map of H α emission in the
LMC. Although the calibration of the SHASSA intensity scale includes an empirical
correction for contamination by the forbidden lines of [N II] at 658.34 nm and 654.81
nm, we caution that the transmission of the SHASSA H α filter includes these lines
(see figure 1 of Gaustad et al., 2001). The 1σ surface brightness sensitivity of the
SHASSA H α images is 2 Rayleighs. The total H α luminosity that we measure for
the LMC (uncorrected for extinction) is 2.6 × 1040 erg s−1 , in good agreement with the
68
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.12 SHASSA map of H α emission in the LMC (Gaustad et al., 2001). A square-root
intensity scale has been used to emphasise the characteristics of the diffuse emission. Black
pixels correspond to surface brightnesses greater than 550 R, ∼ 5% of the peak value in the
map. The map is displayed in Rayleigh units.
values reported by Kennicutt et al. (1995) and Kennicutt et al. (2008) using H α images
obtained at other telescopes. The SHASSA map, overlaid with CO integrated intensity
contours from MAGMA, is shown in Figure 2.12.
2.5.7
Interstellar Radiation Field
To estimate the interstellar radiation field (ISRF) at the locations of molecular clouds
within the LMC, we use the dust temperature (Td ) map presented in figure 7 of Bernard
et al. (2008). The map is derived using the ratio of the IRIS 100 µm and SAGE 160 µm
emission maps (Miville-Deschênes & Lagache, 2005; Meixner et al., 2006),7 assuming
7
‘IRIS’ is an abbreviation for Improved Reprocessing of the IRAS Survey. As described in MivilleDeschênes & Lagache (2005), the zodiacal light subtraction, absolute calibration and scanning stripe
2.5. Ancillary Data
69
that dust emission can be modelled as a grey body:
Iν ∝ ν β Bν (Td ),
(2.4)
with β = 2 at FIR wavelengths. Bernard et al. (2008) find that dust temperatures in
the LMC vary from 12 K up to 34.7 K, with an average value of 18.3 K. This is significantly colder than previous determinations, especially for estimates that attempted
to constrain the dust temperature using the IRAS 60 µm flux density. As noted by
Bernard et al. (2008), emission at 60 µm is highly contaminated by out-of-equilibrium
emission from very small dust grains (VSGs), and this is especially true in the LMC,
due to the presence of excess 70 µm emission. Temperatures derived from the IRAS
60/100 µm flux density ratio may therefore be strongly overestimated.
For dust grains in thermal equilibrium, the strength of the radiation field, G0 , is related
to the dust temperature by G0 ∝ Td4+β (e.g. Lequeux, 2005). The average strength of
G0 across the entire LMC is thus only a factor of ∼ 1.3 greater than in the solar
neighbourhood, G0,⊙ = 0.539 eV cm−3 (Weingartner & Draine, 2001), where the dust
temperature is 17.5 K (assuming β = 2, Boulanger et al., 1996). At the locations
observed by MAGMA, G0 /G0,⊙ varies between 0.5 and 58.8, with a median value of 1.7.
Our estimate for the strength of the radiation field near the well-known star-forming
region N159W is very low (G0 /G0,⊙ = 8.4) compared to the value obtained by previous
estimates (e.g. Israel et al., 1996; Pineda et al., 2008, 2009). Part of the discrepancy
may be due to beam dilution since the resolution of the Bernard et al. (2008) dust
temperature map is 4.′ 0, which corresponds to a spatial scale of 60 pc in the LMC.
However, we also note that our method for determining G0 /G0,⊙ is extremely sensitive
to the assumed dust temperature, which is colder than reported by previous analyses.
For regions with significant CO emission in the Bernard et al. (2008) dust temperature
map, the mean (maximum) formal error on Td is 2% (12%). These errors do not include
variations in the dust emissivity spectral index, however, which is probably the most
significant source of uncertainty for estimating the dust temperature (see e.g. Israel
suppression of the IRIS images is better than for the IRAS Sky Survey images.
70
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12 CO(J
= 1 → 0) Survey of the LMC with Mopra
et al., 2010; Bot et al., 2010). Despite the uncertainties regarding the absolute value of
G0 /G0,⊙ , our analysis mostly concerns the relative strength of the radiation field within
the LMC, and our conclusions do not rely on an absolute calibration of G0 . Finally,
we note that while the resolution of the Bernard et al. (2008) dust temperature map
is coarser than the angular resolution of our MAGMA CO data, it should provide a
reasonable estimate for the average dust temperature on scales larger than ∼ 30 pc. On
smaller scales, the average dust temperature and radiation field may be underestimated
due to beam dilution.
2.5.8
Star Formation Rate Surface Density
To estimate the star formation rate surface density ΣSF R within the LMC, we convolve
the SHASSA map of the H α emission (Gaustad et al., 2001) and the SAGE 24 µm
emission map (Meixner et al., 2006) to a common resolution of 1.′ 0, and then combine
them according to the prescription of Calzetti et al. (2007):
SF R = 5.3 × 10−42 [L(Hα) + 0.031L(24 µm)] .
(2.5)
The integrated star formation rate (SFR) that we obtain across the central 7.5◦ × 7.5◦
of the LMC’s disk is 0.17 M⊙ yr−1 , in good agreement with other global estimates (e.g.
Harris & Zaritsky, 2009, see also Chapter 5). The different wavebands used to trace
the SFR, e.g. Hα, UV and 1.4 GHz radio continuum, probe different characteristic
timescales: UV emission, for example, arises from stellar populations younger than
100 Myr, while H α emission probes a more restricted time interval (0 to 10 Myr). Different SFR tracers in the LMC nevertheless yield a similar SFR of ∼ 0.2 M⊙ yr−1 . A
combination of 24µm with Hα or UV emission has recently become a popular method
for estimating the star formation rate of entire galaxies, since it includes tracers of both
obscured (24 µm) and unobscured (Hα/UV) star formation, and is therefore less sensitive to variations in dust content than using the H α or UV emission alone. For spatially
resolved studies, the calibration in Equation 2.5 has only been tested on scales above
∼ 0.5 kpc (Kennicutt et al., 2007, 2009), so its application on the scale of individual
GMCs within the LMC must be regarded with some caution. Effects that are likely to
2.5. Ancillary Data
71
be important on the scale of individual star-forming regions include the evolutionary
history and mass distribution of the young stellar population, the dust geometry, and
the transparency (i.e. density plus dust abundance) of the surrounding ISM (for an
overview of these issues, see e.g. Calzetti & Kennicutt, 2009). Since molecular clouds
are destroyed and dispersed by the star formation rate process, moreover, the H α and
dust emission associated with a star-forming GMC can extend beyond the region with
significant CO emission, especially at later evolutionary stages. These caveats will apply to comparisons between the properties of resolved GMCs and any of the global SFR
indicators, not just Equation 2.5.
2.5.9
Interstellar Pressure
We estimate the total pressure at the boundary of molecular clouds in the LMC using
the expression given by Elmegreen (1989) for a two-component disk of gas and stars in
hydrostatic equilibrium:
σg
πG
Σg Σg + Σ∗ .
Ph =
2
σ∗
(2.6)
In this expression, σg and σ∗ are the velocity dispersions of the gas and stars respectively, Σg is the mass surface density of the gas and Σ∗ is the stellar mass surface density.
The term in brackets on the right hand side of Equation 2.6 is an estimate for the total
dynamical mass within the disk gas layer. We assume a constant velocity dispersion of
σg = 9 km s−1 for the gas, based on the average dispersion of the H I line profiles across
the LMC (see also Wong et al., 2009), and σ∗ = 20 km s−1 for the stars (van der Marel
et al., 2002). For Σ∗ , we use the stellar mass surface density map of Yang et al. (2007)
described above, and we estimate Σg ≡ ΣHI = 1.089 × 10−20 N (HI) directly from the
H I column density map. The conversion between N (H I) and Σg includes a factor of
1.36 by mass for the presence of helium. We note that the H I and stars make similar
contributions to the total mass surface density at the locations of molecular clouds in
the LMC: hΣ∗ i = 48 M⊙ pc−2 , and hΣg i = 30 M⊙ pc−2 . For comparison, Elmegreen
(1989) adopted hΣ∗ i = 55 M⊙ pc−2 and hΣg i = 12 M⊙ pc−2 as characteristic values in
the Milky Way disk.
72
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12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Along sightlines with significant CO emission, our definition of Ph provides an estimate
of the pressure at the surface of the molecular cloud rather than at the disk midplane,
since the weight of the molecular cloud is likely to make a significant contribution to
the total midplane pressure. Further caveats are i) the assumption that the disk is
supported against gravity solely by the observed velocity dispersions, and ii) that the
interaction between the LMC and the Galactic halo could make a significant contribution to the kinematic gas pressure that is not accounted for by our simple estimate in
Equation 2.6.
2.6 Discussion
2.6.1
Qualitative Comparison with Gas and Dust Tracers
In Section 2.5, we presented maps that illustrate the distribution of
12 CO(J
= 1 → 0)
emission in the LMC with respect to emission at other wavebands, including tracers
of atomic gas (H I), dust (FIR) and high-mass star formation (H α). It is obvious
from these maps that molecular gas tends to be located in regions of the LMC with
high FIR intensity, H I column density and H I peak brightness, although there are
numerous regions in the LMC that exhibit high values of N (H I) and Tpk (HI) where
CO emission is not detected. At 70 and 160 µm, there is a diffuse extended component of the dust emission that resembles the H I column density map more than the
CO integrated intensity, but the high intensity peaks at these wavelengths are better
correlated with the CO map than the local H I maxima. Diffuse emission is detected
but is less pronounced at 24 µm, which peaks strongly at locations with both CO and
H α emission. Some of the well-known H II regions in the LMC are associated with
an increased concentration of CO emission (e.g. N44, N11, Henize, 1956), but there
are several large molecular cloud complexes where strong H α and 24 µm emission are
absent, e.g. near RA 05h47.5m, Dec -70d40m and RA 05h16m, Dec -68d10m (J2000).
It remains an open question whether these molecular clouds are young (and will form
massive stars in the future), or if there is a physical reason why high-mass star formation is inhibited in these clouds. Finally, we note that Figure 2.9 reveals several
compact sources of bright dust emission that are associated with regions of high H I
2.6. Discussion
73
column density and H I peak brightness, e.g. near RA 05h18.5m, Dec -69d25m and RA
05h35.5m, Dec -66d00m (J2000). These structures were not targeted for observation by
the MAGMA survey because the NANTEN survey did not detect strong CO emission
at these locations. The excellent correspondence between the CO and dust emission
peaks elsewhere in the MAGMA survey region recommends these sources for future
high-resolution
12 CO(J
= 1 → 0) observations, as it is possible that the non-detections
by NANTEN are due to beam dilution.
2.6.2
Separation of H I and CO Peaks
One of the more intriguing results from an analysis of the MAGMA data in the 30 Dor
molecular ridge region was that I(CO) peaks are located adjacent to local maxima in
the I(HI) and Tpk (HI) maps, rather than being coincident with them (Ott et al., 2008).
These offsets are not seen using the lower resolution NANTEN CO survey data. Ott
et al. (2008) proposed a number of different mechanisms that could plausibly produce
an offset between the I(CO) I(HI) and Tpk (HI) peaks on ∼ 30 pc scales, including rapid
conversion of warm atomic hydrogen into H2 molecules, dynamical accretion of atomic
gas on molecular clouds, physical separation of molecular and atomic gas phases due to
mechanical feedback from nascent massive stars, and significant H I opacity in the cold
atomic gas phase, which is presumably more dominant in molecular cloud envelopes
than in the ambient ISM.
Visual comparison of the MAGMA I(CO), I(HI) and Tpk (HI) maps suggests that these
spatial offsets are not confined to the molecular ridge region (e.g. Figure 2.13). To quantify the magnitude of these offsets, we measured the angular separation between 295
peaks in the MAGMA I(CO) map with I(CO) > 3 K km s−1 and their nearest local
I(HI) and Tpk (HI) maxima, using the H I maps described in Section 2.5. We imposed
very few criteria on the characteristics of the local H I and CO maxima. We identified
the local CO maxima by eye, requiring I(CO) ≥ 3 K km s−1 and that the intensity
at each local maximum was higher than for the surrounding 8 pixels. We note that
large molecular clouds in the MAGMA survey tend to contain multiple I(CO) peaks,
whereas smaller clouds tend to contain a single position that satisfies our definition
74
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Figure 2.13 Maps of I(HI) (panels [a] and [c]) and Tpk (HI) (panels [b] and [d]) for two example
clouds in the MAGMA survey region. For all panels, the H I emission is represented by the
greyscale image and the CO integrated intensity is indicated by the black contours. The contour
interval is 2 K km s−1 , and the lowest contour represents 1.5 K km s−1 .
2.6. Discussion
75
Figure 2.14 The location of local maxima in the MAGMA I(CO) map of the LMC (red
squares). The black contour indicates where I(CO) = 2.0 K km s−1 . The molecular clouds that
appear to lack CO peaks with I(CO) ≥ 3 K km s−1 were observed in 2009 or 2010, after the
analysis in this section was completed.
of a local I(CO) maximum. A map illustrating the location of the I(CO) peaks is
presented in Figure 2.14. For the H I peaks corresponding to each local CO maximum,
we simply selected the pixel nearest to the I(CO) peak position with an amplitude exceeding that of all its neighbours, requiring that I(HI) ≥ 650 K km s−1 (corresponding
to N (H) = 1.2 × 1021 cm−2 ) for a local I(HI) maximum, and Tpk (HI) ≥ 30 K for a local Tpk (HI) maximum. We then estimated the angular separation between the I(CO),
I(HI) and Tpk (HI) peaks belonging to each CO-H I pair. The angular separations and
the offsets along the axes of right ascension and declination were calculated using the
formulae presented in Appendix 2.B.
76
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Our method for identifying CO-H I pairs does not presuppose a relationship between
the local I(HI) and Tpk (HI) maxima, nor does it specify a minimal spatial extent for
them (i.e. a local maximum constituted by a single pixel is acceptable). These criteria
can produce some identifications that are counter-intuitive: an I(CO) peak located on
a gradient in the I(HI) map, for example, can be associated with an isolated I(HI) peak
rather than the stationary point that terminates the region of rising I(HI) values. As
we are most interested to determined whether the offset between the CO and H I peaks
is statistically significant, we prefer to include identifications that underestimate the
true separation between physically connected H I and CO peaks, rather than impose additional phenomenological criteria that might introduce a bias towards non-zero offsets.
In Figure 2.15[a], we plot a probability density map for the RA and Dec offsets between the I(CO) peaks and the local I(HI) maxima. In this map, colour represents
likelihood: red cells contain the most CO-H I pairs, while black cells are empty. A
probability density map for the RA and Dec offsets between the CO peaks and the
local Tpk (HI) maxima is shown in panel [b] of the same figure. The angular offsets
are not clustered tightly within any particular quadrant in either panel of Figure 2.15,
which suggests that displacement is not due to an error in the registration of the CO
and H I maps.
While the probability density map reveal very few CO-H I pairs with separations greater
than ∼ 2 ′ , it is apparent that the I(HI) peak is overall more likely to be displaced from
the I(CO) peak than to coincide with it. For Tpk (HI), the likelihood of coincidence
appears somewhat greater but the probability distribution of the pair separations is
still broad. For both the I(CO)-I(HI) and I(CO)-Tpk (HI) pairs, the median angular
separation is 1.′ 0 ± 0.′ 3, where the quoted uncertainty is the median absolute deviation.
At our assumed distance to the LMC and a face-on geometry, this arclength translates
to an average spatial separation of 15 ± 5 pc. Accounting for the true geometry and
viewing angles of the LMC only marginally increases this estimate (to 16 ± 5 pc, see
Appendix 2.B).
2.6. Discussion
77
Dec offset from ICO peak [arcmin]
I(HI)
Tpk(HI)
[a]
[b]
2
2
0
0
−2
−2
−2
0
2
−2
RA offset from ICO peak [arcmin]
0
2
RA offset from ICO peak [arcmin]
Spatial Offset [parsecs]
Figure 2.15 The individual panels in this figure plot the angular displacement along the RA
and Dec axis between MAGMA I(CO) peaks and local maxima in the (a) I(HI) and (b) Tpk (HI)
maps. In both panels, the colour scaling saturates at 10 CO-H I pairs. The maximum number
of pairs in a single cell is 10 and 14 for panels [a] and [b] respectively.
[a]
[b]
[c]
50
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
0.5
1.0
1.5
log(I(CO)/[K km s−1])
0
21.0
21.2
21.4
21.6
21.8
log(N(HI)/[cm−2])
22.0
0
0.4
0.6
0.8
1.0
1.2
1.4
1.6
log(σv(HI)/[km s−1])
Figure 2.16 The spatial separation between a I(CO) peak and the local I(HI) maximum,
plotted as a function of (a) CO integrated intensity (b) H I integrated intensity and (c) H I
velocity dispersion at the location of the I(CO) peak.
78
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
As there seems to be a genuine separation between the I(CO) and H I peaks in the
LMC, we investigated whether the magnitude of the spatial offset varied systematically
with parameters that we can observe. More specifically, we searched for correlations
between the spatial separation and i) properties of the H I and CO emission, ii) geometric quantities such as galactic position angle, and iii) environmental properties such as
the stellar mass surface density. We also checked whether there was a tendency for the
galactic position angle of the H I peaks to be positively or negatively offset relative to
the galactic position angle of the CO peak, which might be expected if the offsets were
due to galactic rotation, or if the H I peaks were preferentially displaced towards larger
or smaller galactocentric radii. We evaluated the correlations using the Spearman rank
correlation coefficient, r, a non-parametric rank statistic that measures the strength of
monotone association between two variables. The statistical significance of r is assessed
by calculating the corresponding p-value, which is the two-sided significance level of r’s
deviation from zero. We consider p-values less than 0.01 to provide statistically significant evidence against the null hypothesis (that there is no underlying correlation
between the variables). We regard |r| values greater than 0.6 as strong correlations (or
anti-correlations if r < 0), |r| values between 0.4 and 0.6 as moderate correlations, and
|r| values between 0.2 and 0.4 as weak correlations.
The quantities that we examined and the results of the correlation tests are tabulated
in Table 2.4. No strong correlations or anti-correlations were detected. In particular,
we note that there is no relationship between the magnitude of the spatial offset and
the H α surface brightness, which would seem to rule out that the action of stellar winds
and/or supernovae mechanically displaces the atomic gas from the region surrounding
the molecular cloud. Indeed, the largest offsets tend to be associated with weak I(CO)
emission, low H I column densities and narrow H I linewidths (Figure 2.16), which are
characteristics that are more typical of molecular clouds without signs of high-mass
star formation (see Chapter 3). The absence of a correlation between the magnitude of
the offset and the LMC’s overall geometry suggests that the offset is due to small-scale
processes in the ISM, rather than a galactic scale mechanism.
2.6. Discussion
79
Table 2.4 Results of Spearman rank correlation tests between the separation of I(CO) and
I(HI) peaks and different properties of the CO and H I emission, location in the LMC and
conditions in the local ISM (column 2). The results of correlation tests between these properties
and the ratios I and P (see text) are listed in columns 3 and 4 respectively. The format of the
results is (r, p), where r is the rank correlation coefficient and p is the two-sided significance
level of r’s deviation from zero.
Property
CO integrated intensity
H I integrated intensity
H I peak brightness
H I velocity dispersion
Galactocentric Radius
Galactic Position Angle
Radial velocity
Stellar mass surface density
H α surface brightness
Interstellar Radiation Field
Spatial offset
(r, p)
I
(r, p)
P
(r, p)
(-0.12,0.04)
(-0.08,0.20)
(-0.06,0.30)
(-0.03,0.66)
(0.03,0.64)
(-0.05,0.44)
(0.12,0.05)
(-0.04,0.51)
(0.08,0.15)
(0.13,0.03)
(0.05,0.36)
(0.31,< 0.01)
(0.21,< 0.01)
(0.22,< 0.01)
(-0.01,0.91)
(0.01,0.86)
(-0.13,0.03)
(0.03,0.56)
(-0.06,0.32)
(-0.15,0.01)
(-0.01,0.87)
(0.28,< 0.01)
(0.48,< 0.01)
(0.10,0.09)
(0.05,0.44)
(-0.11,0.05)
(0.06,0.34)
(-0.08,0.17)
(-0.06,0.28)
(-0.10,0.08)
In addition to their separation, we examined whether there are relationships between
the H I column density and H I peak brightness at the I(CO) and H I peaks. In general, the variation in I(HI) and Tpk (HI) between the two positions is small: the ratio
between the H I column densities at the two positions, I ≡ I(HI)CO /I(HI)HI , varies
between 0.5 and 1.0, with a median value of 0.88 ± 0.07. The median value of the H I
column density at the I(CO) peaks is 3 × 1021 cm−2 ≈ 30 M⊙ pc−2 . The ratio between
the H I peak brightnesses P ≡ Tpk (HI)CO /Tpk (HI)HI varies by a similar magnitude, and
the median value of Tpk (HI) at the I(CO) peaks is 72 ± 12 K. Assuming that the H I
emission is optically thin, the average decrement in the H I column density is also small,
∆N (HI) = 3.5 ± 2.2 × 1020 cm−2 , which is equivalent to ∼ 3 × 103 M⊙ within a circular
region with a radius of 15 pc. This should be considered a lower limit, however, as
the H I emission from atomic gas in the vicinity of molecular clouds is likely to have
some opacity. Absorption experiments indicate opacity-corrected H I column densities
exceed the optically thin estimate by factors of ∼ 1.3 to 2 along LMC sightlines (Dickey
et al., 1994; Marx-Zimmer et al., 2000), but this would not increase our estimate for
the H I mass decrement to be comparable to the range of molecular cloud masses that
Chapter 2. A
log(∆ N(HI)/[cm−2]
80
22
12 CO(J
[a]
= 1 → 0) Survey of the LMC with Mopra
22
21
21
20
20
19
19
−2
−1
0
1
log(∆ Peak Tb(HI)/[K])
2
[b]
−2
−1
0
1
log(∆ σv(HI)/[km s−1])
Figure 2.17 The decrement in H I column density between the I(CO) emission peak and the
local I(HI) peak, plotted as a function of the decrement in (a) H I peak brightness and (b) H I
velocity dispersion at the two positions.
are observed in the LMC (104 to a few times 106 M⊙ ). We therefore regard it unlikely
that the difference in the H I column density represents atomic gas that has lately been
converted in H2 molecules.
As before, we searched for correlations between I, P and ∆N (HI) and the properties
listed in Table 2.4. We found no evidence for variations corresponding to location in
the LMC or local interstellar conditions. ∆N (HI) tends to increase for CO-H I pairs
where the absolute difference in the H I peak brightness and H I velocity dispersion at
the location of the I(CO) and I(HI) peaks is also high (Figure 2.17). These correlaR
tions must be interpreted with caution, as I(HI) = Tb dv is dependent on both the H I
brightness and linewidth. Nevertheless, we note that correlations of this nature could
arise if the separation between the CO and H I peaks were due to an increased fraction
of cold atomic gas along sightlines towards molecular clouds. In other galaxies, the
presence of cold atomic gas has been linked to H I emission with narrower linewidths
(e.g. Young et al., 2003) and high peak brightness (e.g. Braun, 1997), but the impact
on the observed H I column density of an increasing cold gas fraction is not immediately
obvious.
2.6. Discussion
81
A detailed analysis of the H I line profiles is beyond the scope of this discussion, but
we can estimate the impact of cold H I on the observed H I brightness temperature.
For cloudlets of cold gas immersed in a warm intercloud medium, the observed H I
brightness temperature can be approximated by
Tb = qf Tb,warm + f Tb,cold + (1 − q) f Tb,warm exp(−τc ) + (1 − f )Tb,warm .
(2.7)
In this equation (modified from equation 4.13 of Lequeux, 2005), τc is the optical depth
in the cold gas, f is the beam filling fraction of the cold gas, q is the fraction of
warm gas located in front of the cold cloud, and Tb,warm and Tb,cold are the brightness
temperatures of the emission from the warm and cold gas respectively. The optical
depth of the warm gas is very low, so its brightness temperature is approximately
Tb,warm ≈ τw Tk,warm , where Tk,warm is the kinetic temperature and τw is the optical
depth in the warm gas. The brightness temperature of the cold gas, by contrast,
is Tb,cold = Ts [1 − exp(τc )], where Ts is the spin temperature of the 21cm H I spinflip transition, which we assume equals the kinetic temperature of the cold atomic gas,
Tk,cold . A grid of solutions for Equation 2.7 for plausible values of Tb,warm , Tk,cold , τc and
f is presented in Table 2.5. The value of q is difficult to constrain observationally, and
here we assume q = 0.5, which corresponds to the cold gas being located at the mid-way
point. Smaller values of q, i.e. a larger fraction of the warm gas being located behind
the cold gas, would lead to smaller values of Tb . For Tb,warm ∼ 100 K, Tk,cold ∼ 20 K
and τc = 0.5 − 1.5, Equation 2.7 shows that the observed H I brightness temperature
will decrease by 10 to 20 K as the cold gas covers a larger fraction of the telescope
beam. We note, however, that the behaviour of Tb is sensitive to the values that we
adopt for the brightness temperatures of the cold and warm gas: for Tb,warm ∼ 50 K
and Tk,cold ∼ 40 K, for example, Tb increases rather than decreases with f .
2.6.3
CO Emission and Global Properties of the LMC
In Section 2.4, we showed that our measurement of the total CO luminosity within the
MAGMA survey region corresponds to a molecular gas mass of 1.0 to 1.2 × 107 M⊙ ,
assuming XCO = 2 × 1020 cm−2 (K km s−1 )−1 . MAGMA observations target molecu-
82
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
Table 2.5 Grid of solutions to Equation 2.7 for different input values of the optical depth in the
cold gas τc , the brightness temperature of the warm gas Tb,warm , and the kinetic temperature
of the cold gas Tk,cold, and the beam filling fraction of the cold gas f . In all cases, we assume
that the fraction of warm gas located in front of the cold gas is 50%, i.e. q = 0.5. The resulting
H I brightness temperature for each combination of input parameters is shown in columns 4 to
6.
Tb,warm [K]
Tk,cold [K]
τc
50
50
50
50
50
50
50
50
50
100
100
100
100
100
100
100
100
100
150
150
150
150
150
150
150
150
150
20
20
20
40
40
40
60
60
60
20
20
20
40
40
40
60
60
60
20
20
20
40
40
40
60
60
60
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
0.5
1.0
1.5
Observed Tb [K]
f = 0.1 f = 0.5 f = 1.0
50
50
50
51
51
51
51
52
53
99
98
98
100
99
99
100
101
101
148
147
146
149
148
147
149
149
149
49
48
48
53
55
56
57
61
64
94
91
88
98
97
96
102
103
104
139
133
129
143
139
136
147
145
144
48
47
46
56
59
62
64
72
77
88
81
77
96
94
92
104
106
108
128
115
107
136
128
123
144
141
138
2.6. Discussion
83
lar clouds that contribute 70% of the LMC’s total CO luminosity, so this result is in
excellent agreement with the NANTEN estimate for the LMC’s total molecular mass,
MH2 ,LMC = 1.4 × 107 M⊙ , after re-scaling the value reported by Fukui et al. (2008) to
use the same XCO value. Most of the CO emission detected by NANTEN would therefore seem to be located in the spatially compact, high-brightness structures identified
by MAGMA, rather than in a diffuse, low-brightness component that is fainter than
MAGMA’s sensitivity limit. In this Section, we compare the molecular gas content of
the LMC to estimates for the galaxy’s atomic mass, stellar mass and star formation
rate. The statistical study of CO emission in ∼ 40 dwarf galaxies within 20 Mpc by
Leroy et al. (2005) serves as a useful reference for this comparison. In particular, we
are interested to determine whether the LMC – which has a comparable stellar and
dynamical mass but a lower CO luminosity and higher star formation rate than the
dwarf galaxies in the Leroy et al. (2005) sample – exhibits similar relationships between
its global properties and CO-bright molecular gas content as these systems.
Comparison with Atomic Gas
Fukui et al. (2008) estimated that the total (CO-bright) molecular mass of the LMC
was 10% of its atomic mass (5 × 108 M⊙ , Staveley-Smith et al., 2003). This is likely to
be an upper limit since it assumes XCO = 7 × 1020 cm−2 (K km s−1 )−1 , and that the
H I emission is optically thin. Studies of H I absorption reveal that a cool atomic gas
component with T ∼ 35 K and peak optical depths of τ = 0.5 − 1.5 is prevalent in the
LMC (Dickey et al., 1994; Marx-Zimmer et al., 2000). These optical depths suggest that
the true H I column density along these sightlines is approximately τ /[1 − exp(−τ )] =
1.3 − 2.0 times greater than the values derived assuming that H I emission is optically
thin (e.g. Dickey et al., 2003). Sightlines with Tpk (HI) & 35 K cover 30% of the area
that we used to estimate the mass of the LMC. If N (H I) along these sightlines was
underestimated by 50%, then the total mass of atomic gas in the LMC would be
30% greater than the value obtained by Staveley-Smith et al. (2003). Using the same
method as Fukui et al. (2008), we derive a mean XCO value for molecular clouds in
the MAGMA survey that is 50% lower than their adopted value (see the next chapter).
We conclude that the total mass of CO-bright molecular gas in the LMC is unlikely
84
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
to exceed 3.5 × 107 M⊙ , and that it represents . 5% of the galaxy’s total neutral (i.e.
atomic plus molecular) gas content. This is lower than the mean molecular-to-atomic
gas mass ratio obtained by Leroy et al. (2005, see their figure 3b), who found that
molecular gas in dwarf galaxies typically amounts to ∼ 30% of the atomic gas content,
albeit with considerable scatter. By contrast, the ISM of large spirals can be dominated
by molecular gas, with molecular-to-atomic gas ratios greater than unity (see Young &
Scoville, 1991, and references therein).
Comparison with Stellar Mass
Assuming that CO emission is a reliable tracer of H2 , the molecular mass of the LMC
is also low relative to other components of the galaxy’s mass budget. Leroy et al.
(2005) found that the ratio between the CO-derived molecular mass and the integrated
B-band luminosity of galaxies is roughly constant: hMmol [M⊙ ]/LB [L⊙ ]i = 0.16 ± 0.01
for spiral galaxies and hMmol /LB i = 0.13 ± 0.02 for dwarfs. Leroy et al. (2005) assume
−1
XCO = 2 × 1020 cm−2 (K km s−1 )
and multiply their hydrogen-only mass estimates
by 1.36 to account for the presence of helium. We have used these same assumptions
for our estimate of the LMC’s total molecular mass (MH2 ,LMC = 1.4 × 107 M⊙ ), but
we obtain only Mmol /LB = 0.006 for the LMC. This value is more similar to the ratio
observed for nearby, low-metallicity dwarf galaxies such as the SMC, NGC 6822 and
NGC 1569, for which Mmol /LB ∼ 0.001 (Leroy et al., 2007b).
Comparison with Star Formation Rate
The CO emission in the LMC is also low relative to its star formation rate (SFR).
In the LMC, there is reasonably good agreement between different SFR calibrations,
with different monochromatic and multi-wavelength estimators indicating a SFR of
∼ 0.2 M⊙ yr−1 (assuming a Salpeter IMF, see e.g. Hughes et al., 2007) This value is
consistent with a reconstruction of the LMC’s star formation history using colourmagnitude diagrams obtained by the Magellanic Clouds Photometric Survey (Harris &
Zaritsky, 2009). The ratio between the SFR and the CO luminosity is therefore much
higher in the LMC than in large spiral galaxies: if the LMC followed the relationship
between the SFR and total CO luminosity described by Murgia et al. (2002) for spiral
2.6. Discussion
85
galaxies in the FCRAO Extragalactic CO Survey (Young et al., 1995), it would have a
SFR of only 0.004 M⊙ yr−1 . A similar result is observed for the SMC, where the SFR
predicted by Murgia et al. (2002) is 0.0001 M⊙ yr−1 , a factor of ∼ 20 lower than the
observed SFR (0.05 M⊙ yr−1 , Wilke et al., 2004).
The ratio between a galaxy’s star formation rate and molecular gas mass can be inverted to estimate the molecular gas consumption (or cycling) timescale, τH2 , which
describes the time that would be required to convert all the available molecular gas into
stars. For a SFR of 0.2 M⊙ yr−1 , the molecular gas associated with CO emission in the
LMC would be depleted in 0.1 Gyr. This is extremely short compared to the timescales
inferred for normal spiral galaxies – the mean molecular gas consumption timescale for
the galaxies studied by Murgia et al. (2002) is 2.8 Gyr, with most galaxies exhibiting
τH2 values between 1 and 9 Gyr – and to the LMC’s own star formation history, which
exhibits a sustained average SFR of 0.2 M⊙ yr−1 since the end of a quiescent epoch
∼ 5 Gyr ago (Harris & Zaritsky, 2009). We note that SFR-CO relation determined by
Murgia et al. (2002), ΣSF R = 2.6 × 10−4 Σ1.3
H2 , predicts that the molecular gas consumption timescale should increase for dwarf galaxies, i.e. a trend that is opposite to the
value of τH2 that we infer for the LMC. In this respect, the LMC again diverges from
the dwarf galaxies with CO detections studied by Leroy et al. (2005), which conform
to the Murgia et al. (2002) SFR-CO relationship and for which hτH2 i = 1.8 Gyr.
Overall, our comparison between the CO emission and global properties of the LMC
suggests that the LMC’s molecular gas content is appreciably different to the molecular gas within CO-rich, late-type galaxies. This result is especially interesting since we
show in the next chapter that the properties of individual CO-bright molecular clouds
in the LMC, including the CO-to-H2 conversion factor, are not dramatically different to
the properties of Galactic molecular clouds. A possible explanation that would reconcile these results is that diffuse CO-bright molecular gas is more prevalent in late-type
galaxies than in the LMC, where the CO emission arises almost exclusively in molecular
cloud structures.
86
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
2.7 Summary
In this chapter, we presented Mopra Telescope observations of the
12 CO(J
= 1 → 0)
emission in the Large Magellanic Cloud (LMC). The data described here were obtained
by the Magellanic Mopra Assessment (MAGMA) project, an ongoing mapping survey of
the molecular gas in the Magellanic Clouds. In the LMC, MAGMA observations have
targeted the brightest 114 molecular clouds in the catalogue of Fukui et al. (2008),
which in total contribute ∼ 70% of the LMC’s total CO luminosity. We report the
following results and conclusions:
1. Within the 3.65 square degrees surveyed by MAGMA, we detected ∼ 1.1×107 M⊙ of
molecular gas, assuming a CO-to-H2 conversion factor of XCO = 2×1020 cm−2 (K km s−1 )−1 .
Significant CO emission was detected in ∼ 25% of the survey area.
2. The total CO luminosity of significant emission within the MAGMA survey region
is 2.5 × 106 K km s−1 pc2 , in excellent agreement with the value obtained by the NANTEN survey (Fukui et al., 2008). Together with the low peak brightness temperature of
the CO emission, this indicates that CO-emitting structures in the LMC are spatially
compact.
3. Across the LMC, emission peaks in the MAGMA CO integrated intensity map peaks
are offset from local maxima in the H I integrated intensity and H I peak brightness maps
by 15 ± 5 pc on average.
4. There is only a modest difference in the values of the H I column density and H I
peak brightness that are measured at the positions of a I(CO) peak and the local
H I maxima. Although we cannot definitively exclude other mechanisms, we propose
that an increasing fraction of cold atomic gas with significant opacity in the vicinity
of molecular clouds is responsible for the apparent separation between the H I and CO
peaks.
2.7. Summary
87
5. The mass of CO-bright molecular gas in the LMC is . 5% of the atomic gas content.
The CO luminosity of the LMC relative to its stellar mass and star formation rate is
approximately two orders of magnitude lower than the ratios observed for nearby spiral
galaxies.
88
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
2.A Subregion Maps
To illustrate the level of detail manifested by the MAGMA survey data, each panel
of Figure 2.18 presents the I(CO) map of a ∼ 1.5◦ × 1.5◦ subregion within the LMC.
Example CO line profiles from a selection of positions within each subregion are shown
beneath the maps.
2.A. Subregion Maps
Tmb(CO) [K]
3
[a]
89
[b]
[c]
[d]
[e]
3
2
2
1
1
0
0
3
[f]
[g]
[h]
[i]
[j]
3
2
2
1
1
0
0
200
250
200
250
200
250
200
250
200
250
Radial velocity [LSR, km s−1]
Figure 2.18 MAGMA maps of CO integrated intensity for sixteen ∼ 1.5◦ × 1.5◦ subre-
gions within the LMC. The black contours correspond to intervals of I(CO) = 2.0 km s−1 for
1.5 ≤ I(CO) ≤ 9.5 km s−1 . For I(CO) > 9.5 km s−1 , the contour interval is 4 K km s−1 . The
grey outlines indicate the coverage of the MAGMA survey. The spectra in the lower panel correspond to the following positions (J2000): (a) (05:40:54.2, -70:44:03) (b) (05:40:56.6, -70:23:25)
(c) (05:40:44.6, -70:28:10) (d) (05:40:57.1, -70:33:24) (e) (05:48:15.7, -70:39:1) (f) (05:43:56.4,
-71:07:40) (g) (05:40:12.6, -71:11:51) (h) (05:40:05.7, -71:33:04) (i) (05:44:31.7, -71:28:56) and
(j) (05:41:16.9, -70:55:52).
90
Chapter 2. A
Tmb(CO) [K]
3
[a]
[b]
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
[c]
[d]
[e]
3
2
2
1
1
0
0
3
[f]
[g]
[h]
[i]
[j]
3
2
2
1
1
0
0
200
250
200
250
200
250
200
250
200
250
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:27:03.7, -71:24:03) (b) (05:26:54.3, -71:17:47) (c) (05:23:26.2, -71:38:21)
(d) (05:29:27.8, -71:02:59) (e) (05:17:18.9, -71:13:22) (f) (05:32:12.8, -71:13:47) (g) (05:24:22.6,
-70:27:56) (h) (05:27:27.6, -70:36:23) (i) (05:19:47.5, -70:45:59) and (j) (05:30:51.6, -71:07:24).
Tmb(CO) [K]
2.A. Subregion Maps
3
91
[a]
[b]
[c]
[d]
3
2
2
1
1
0
0
200 220 240 260
200 220 240 260
200 220 240 260
200 220 240 260
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.) The spectra in the lower panel correspond to the following positions
(J2000): (a) (05:15:05.7, -70:33:44) (b) (05:12:11.3, -70:30:05) (c) (05:12:30.0, -70:25:11) and
(d) (05:04:40.9, -70:54:25).
92
Chapter 2. A
Tmb(CO) [K]
4
[a]
[b]
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
[c]
[d]
[e]
4
2
2
0
0
4
[f]
[g]
[h]
[i]
[j]
4
2
2
0
0
200
250
200
250
200
250
200
250
200
250
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:40:02.4, -69:50:47) (b) (05:37:06.2, -69:48:10) (c) (05:40:45.1, -70:09:51)
(d) (05:39:32.0, -70:11:59) (e) (05:39:39.0, -69:45:35) (f) (05:48:24.7, -70:08:02) (g) (05:45:24.2,
-69:50:19) (h) (05:44:25.5, -69:26:22) (i) (05:38:50.0, -69:04:23) and (j) (05:35:53.1, -69:02:23).
2.A. Subregion Maps
Tmb(CO) [K]
3
[a]
93
[b]
[c]
[d]
[e]
3
2
2
1
1
0
0
3
[f]
[g]
[h]
[i]
[j]
3
2
2
1
1
0
0
200
250
200
250
200
250
200
250
200
250
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:19:14.1, -69:38:08) (b) (05:19:31.3, -69:08:26) (c) (05:24:38.7, -69:14:58)
(d) (05:17:33.3, -69:15:12) (e) (05:24:16.9, -69:39:02) (f) (05:28:13.8, -69:52:46) (g) (05:25:06.8,
-69:40:40) (h) (05:21:08.9, -70:13:35) (i) (05:21:10.3, -70:00:57) and (j) (05:22:10.2, -69:41:41).
94
Chapter 2. A
Tmb(CO) [K]
4
[a]
[b]
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
[c]
[d]
[e]
4
2
2
0
0
4
[f]
[g]
[h]
[i]
[j]
4
2
2
0
0
200
250
200
250
200
250
200
250
200
250
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:08:09.5, -69:02:38) (b) (05:11:11.8, -68:50:37) (c) (05:09:52.5, -68:53:12)
(d) (05:12:56.2, -69:34:59) (e) (05:09:25.6, -69:23:33) (f) (05:14:31.8, -70:11:02) (g) (05:04:52.8,
-70:07:36) (h) (05:14:00.7, -69:36:15) (i) (05:13:21.2, -69:22:43) and (j) (05:08:39.3, -69:24:37).
2.A. Subregion Maps
Tmb(CO) [K]
3
95
[a]
[b]
[c]
3
[d]
2
2
1
1
0
0
3
[e]
[f]
[g]
3
[h]
2
2
1
1
0
0
200
250
200
250
200
250
200
250
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (04:50:48.6, -69:19:08) (b) (04:54:02.0, -69:11:30) (c) (04:54:22.9, -69:29:37)
(d) (04:52:42.5, -69:11:31) (e) (04:57:10.8, -69:11:41) (f) (04:57:14.9, -68:55:53) (g) (04:51:55.3,
-69:23:03) and (h) (04:48:53.3, -69:09:54).
Chapter 2. A
Tmb(CO) [K]
96
3
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
[a]
[b]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont). The spectra in the lower panel correspond to the following positions
(J2000): (a) (05:55:51.4, -68:11:04) and (b) (05:45:27.0, -67:07:31).
2.A. Subregion Maps
Tmb(CO) [K]
3
97
[a]
[b]
[c]
[d]
3
2
2
1
1
0
0
3
[e]
[f]
[g]
[h]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:31:59.8, -68:28:08) (b) (05:30:52.5, -68:33:45) (c) (05:35:21.4, -67:35:16)
(d) (05:35:50.6, -68:44:36) (e) (05:32:52.4, -67:30:13) (f) (05:32:28.7, -67:41:29) (g) (05:31:47.4,
-67:44:00) and (h) (05:34:32.3, -68:12:41).
98
Chapter 2. A
Tmb(CO) [K]
3
[a]
12 CO(J
[b]
= 1 → 0) Survey of the LMC with Mopra
[c]
[d]
[e]
3
2
2
1
1
0
0
3
[f]
[g]
[h]
[i]
[j]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:15:45.1, -67:58:57) (b) (05:16:37.8, -68:13:17) (c) (05:13:48.2, -67:24:16)
(d) (05:22:05.8, -67:58:03) (e) (05:21:24.2, -67:47:13) (f) (05:26:54.6, -68:53:25) (g) (05:21:29.5,
-68:46:48) (h) (05:17:36.8, -68:48:45) (i) (05:22:03.9, -68:28:01) and (j) (05:24:21.9, -68:26:22).
Tmb(CO) [K]
2.A. Subregion Maps
99
3
[a]
[b]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.) The spectra in the lower panel correspond to the following positions
(J2000): (a) (04:57:16.8, -68:26:10) and (b) (05:03:49.2, -67:20:01).
Tmb(CO) [K]
100
Chapter 2. A
3
[a]
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
[b]
[c]
[d]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.) The spectra in the lower panel correspond to the following positions
(J2000): (a) (04:52:59.4, -68:05:40) (b) (04:48:57.7, -68:36:34) (c) (04:49:30.0, -68:29:55) and
(d) (04:49:38.0, -68:22:12).
Tmb(CO) [K]
2.A. Subregion Maps
101
3
[a]
[b]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.) The spectra in the lower panel correspond to the following positions
(J2000): (a) (05:32:32.1, -66:27:3) and (b) (05:37:15.3, -66:19:50).
102
Chapter 2. A
Tmb(CO) [K]
3
[a]
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
[b]
[c]
[d]
3
2
2
1
1
0
0
3
[e]
[f]
[g]
[h]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (05:25:47.0, -66:13:47) (b) (05:26:18.9, -66:02:28) (c) (05:22:49.4, -65:40:59)
(d) (05:20:07.6, -66:52:12) (e) (05:22:46.7, -67:07:19) (f) (05:23:14.5, -66:42:51) (g) (05:17:28.8,
-66:43:01) and (h) (05:25:10.7, -66:14:51).
Tmb(CO) [K]
2.A. Subregion Maps
3
103
[a]
[b]
[c]
[d]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.) The spectra in the lower panel correspond to the following positions
(J2000): (a) (05:12:04.3, -67:10:39) (b) (05:03:35.4, -67:10:39) (c) (05:04:47.2, -66:49:20) and
(d) (05:03:08.8, -65:53:44).
104
Chapter 2. A
Tmb(CO) [K]
3
[a]
12 CO(J
[b]
= 1 → 0) Survey of the LMC with Mopra
[c]
[d]
[e]
3
2
2
1
1
0
0
3
[f]
[g]
[h]
[i]
[j]
3
2
2
1
1
0
0
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
240 260 280 300
Radial velocity [LSR, km s−1]
Figure 2.18 (cont.)
The spectra in the lower panel correspond to the following positions (J2000): (a) (04:57:51.0, -66:29:01) (b) (04:59:24.0, -66:19:49) (c) (04:58:08.1, -66:18:55)
(d) (05:00:48.4, -66:22:29) (e) (04:58:45.6, -66:08:02) (f) (04:47:38.4, -67:12:19) (g) (04:52:10.2,
-67:09:21) (h) (04:52:11.6, -66:54:58) (i) (04:52:13.6, -66:58:47) and (j) (04:55:37.3, -66:34:10).
2.B. Angular Separation Formulae
105
2.B Angular Separation Formulae
In Section 2.6.2, we discussed the angular and spatial separation between peaks in
the MAGMA I(CO) map and the local I(HI) and Tpk (HI) maxima. In all cases, the
apparent (i.e. on-sky) separation between the CO and H I peaks is small (less than
∼ 2′ ), so we can estimate the overall angular separation and the angular displacements
along the right ascension and declination axes using small angle approximations. More
specifically, if the CO peak position is (αCO ,δCO ) and the H I peak position is (αHI ,δHI ),
then the displacement along the declination axis is simply
∆δ = |δCO − δHI |,
(2.8)
while the displacement along the right ascension axis is approximately
∆α = |αCO − αHI | cos((δCO + δHI )/2).
(2.9)
We calculate the overall angular separation between the two positions, γ, using the full
formula:
cos γ = cos(90◦ − δCO ) cos(90◦ − δHI ) + sin(90◦ − δCO ) sin(90◦ − δHI )
× cos(αCO − αHI ).
(2.10)
To convert from angular units to the spatial domain, we convert to “in-disk” coordinates assuming the LMC geometry reported by Wong et al. (2009). In this case, a
sky position (α, δ) in the LMC can be transformed to the position (x, y) in a Cartesian
coordinate system for which the (x, y) plane contains the LMC disk and the x-axis is
along the line-of-nodes, according to equation 2 of van der Marel (2001):
D0 cos i sin ρ cos(φ − Θfar )
,
cos i cos ρ − sin i sin ρ sin(φ − Θfar )
D0 sin ρ sin(φ − Θfar )
.
y=
cos i cos ρ − sin i sin ρ sin(φ − Θfar )
x=
(2.11)
(2.12)
In these equations, D0 is the distance to the LMC, i = 35◦ is the inclination of the
106
Chapter 2. A
12 CO(J
= 1 → 0) Survey of the LMC with Mopra
LMC disk relative to the plane of the sky, and the angular coordinates (ρ, φ) are defined
as the angular separation and position angle between the position (α, δ) and the origin
(α0 , δ0 ), for which we adopt the LMC’s kinematic centre RA 05h19.5m, Dec -68d53m
(J2000) (Wong et al., 2009). Θfar = Θ + 90◦ , where Θ = 122.◦ 5 is the position angle of
the receding line-of-nodes measured anticlockwise from North (van der Marel & Cioni,
2001).
3
Properties of MAGMA GMCs: I. Overview
We present a catalogue of 125 giant molecular clouds (GMCs) in the Large Magellanic
Cloud (LMC), generated from the MAGMA
12 CO(J
= 1 → 0) survey data. The com-
bined mass of the catalogued GMCs is 1.2 × 107 M⊙ , assuming a CO-to-H2 conversion
factor XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 . We assess the selection effects that bias
the catalogue, and test the reliability of the algorithms that we use to identify and
parameterise GMCs by processing trial datasets through our data reduction pipeline.
The simplest properties – size, linewidth, peak CO brightness and total CO luminosity
– of model clouds that satisfy our criteria for inclusion in the MAGMA catalogue are
recovered within a factor of a few for small clouds (R ≤ 25 pc), and more accurately
for large clouds. The physical properties of the catalogued GMCs are consistent with
the properties of the GMCs identified by NANTEN in the LMC, despite the differences
in resolution and sensitivity between the two surveys. We compare the properties
of GMCs with and without signs of high mass star formation, finding that non-starforming GMCs have lower peak CO brightness than star-forming GMCs. Relative to
their virial mass, the CO luminosity of non-star-forming GMCs is ∼ 50% lower on average than the CO luminosity of GMCs with high-mass star formation. We analyse the
velocity field of the MAGMA molecular clouds, identifying linear gradients for ∼ 50%
of our sample. The GMC gradients range in magnitude from 0.01 to 0.64 km s−1 pc−1 ,
and contribute significantly to the non-thermal component of the cloud velocity dispersion. The gradients appear spatially organized in relation to the spiral structure of
107
108
Chapter 3. Properties of MAGMA GMCs: I. Overview
the LMC’s gas disk, and we detect a weak trend for the GMC velocity gradient to be
aligned with the velocity gradient in the surrounding atomic gas. We conclude that
cloud velocity gradients may not be a sign of uniform rotation, and that GMCs in the
LMC may remain kinematically coupled to their environment.
3.1 Introduction
Molecular gas is the dominant component of the interstellar medium (ISM) in the inner disks of spiral galaxies (e.g. Young & Scoville, 1991). In regions with high pressure
and high extinction, the molecular gas phase may be extensive and diffuse (Elmegreen,
1993), but under more typical interstellar conditions it is organized into discrete cloud
complexes with masses of ∼ 105 to 106 M⊙ and sizes of ∼ 20 to 50 pc (Blitz, 1993), implying volume-averaged densities of hnH2 i ∼ 100 cm−3 . In normal (i.e. non-starburst)
galaxies, these giant molecular clouds (GMCs) are the basic unit of structure in the
molecular ISM. Most of the star formation activity in galaxies occurs within GMCs,
but our knowledge of the processes that regulate the physical and chemical conditions
in GMCs is far from complete. Measuring the basic properties of resolved extragalactic
GMC populations – and determining whether they are similar to GMCs in the Milky
Way – represents an important advance towards understanding how star formation
proceeds throughout the Universe.
The molecular clouds identified in the Solomon et al. (1987, henceforth S87) survey of
CO emission in the inner Milky Way remain our basic yardstick for the characteristic
properties of GMCs. The clouds in the S87 catalogue have masses between 103 and
107 M⊙ , sizes between 1 and 100 pc, one-dimensional velocity dispersions between 1 and
10 km s−1 , and CO luminosities ranging between 102 and a few times 106 K km s−1 pc2 .
The observed linewidths of CO emission in GMCs indicate the presence of supersonic
turbulence: the thermal CO linewidth corresponding to typical GMC temperatures
of 10 – 30 K is less than 0.3 km s−1 . The origin of non-thermal motions in molecular clouds is still a matter of debate, however, with evidence for energy injection on
3.1. Introduction
109
both small and large scales (summarised in e.g. McKee & Ostriker, 2007). Reasonable
agreement between the mass estimates for Milky Way GMCs obtained under the assumption of virial equilibrium and independent approaches using excitation analyses
(e.g. Carpenter et al., 1990), dust continuum emission (e.g. Boulanger et al., 1998) and
γ-ray emission (e.g. Abdo et al., 2010) suggests that Galactic GMCs manage to achieve
rough dynamical equilibrium, or are at least marginally bound. Although their mean
density is relatively low, emission lines from molecular species with critical densities
greater than 104 cm−3 are commonly observed in Galactic GMCs, suggesting that the
mass distribution within GMCs is highly clumped. In this case, a large fraction of a
GMC’s total mass is concentrated in the densest substructures, while a more tenuous
intracloud gas occupies the bulk of the cloud volume.
While resolved studies of extragalactic GMC populations will become routine with
ALMA, the twin requirements of high resolution and high sensitivity mean that obtaining extragalactic datasets comparable to the S87 molecular cloud sample has been
feasible for only a few Local Group galaxies. By the late 1980s, a number of studies had mapped the CO emission from individual GMCs in M31 (e.g. Vogel et al.,
1987; Lada et al., 1988), but the first statistically significant survey of extragalactic
GMCs was conducted by Wilson & Scoville (1990), who identified 38 molecular clouds
within a ∼ 2′ × 2′ region in the inner disk of M33. Subsequent milestones in the field
include surveys of the GMC populations in M31, M33, IC10 and M64 (Rosolowsky,
2007; Rosolowsky & Blitz, 2005; Engargiola et al., 2003; Leroy et al., 2006), a survey
of molecular clouds in the outer Milky Way (Heyer et al., 2001), and mapping of the
CO emission in the Magellanic Clouds by the NANTEN telescope (Fukui et al., 1999;
Mizuno et al., 2001; Fukui et al., 2008). Analysis of extragalactic GMC populations
has suggested that the properties of molecular clouds may vary with interstellar conditions. Molecular clouds in NGC 6822 and the Small Magellanic Cloud (SMC), for
example, appear to be smaller and less massive than Galactic clouds (e.g. Wilson, 1994;
Muller et al., 2010), while a trend for the mean CO-to-H2 conversion factor, XCO , to
increase with decreasing metallicity has frequently been reported (e.g. Taylor et al.,
1998). Yet much of the apparent galaxy-to-galaxy variation could be due to the incon-
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Chapter 3. Properties of MAGMA GMCs: I. Overview
sistent sensitivity and resolution of the observations and/or methodological differences
(Sheth et al., 2008). Using a consistent method to identify and measure the properties
of ∼ 100 resolved GMCs in a sample of twelve galaxies, a recent comparative study by
(Bolatto et al., 2008, henceforth B08) concluded that GMCs in fact demonstrate nearly
uniform properties across the Local Group.
Dwarf galaxies play an important role in the attempt to characterise GMC properties
because they extend the observed range of environmental conditions to lower metallicities, lower dust-to-gas ratios, stronger radiation fields, lower rotational shear and weaker
stellar potentials than are typically encountered in massive spiral galaxies. Each of these
variations in the interstellar environment has the potential to influence the dynamical
state of the GMCs, or to modify the relationship between the underlying distribution
of molecular hydrogen and the CO emission that is used as its tracer. The Magellanic Clouds are especially important systems for this endeavour, as they are the only
galaxies outside the Milky Way where a single-dish telescope can resolve the majority of the molecular cloud population. Recent efforts to assess the GMC population
of the LMC include a survey of the CO emission across the entire LMC disk by the
4 m NANTEN telescope (henceforth “the NANTEN survey” Fukui et al., 2001, 2008)
and an extensive programme of mapping and pointed observations by the SwedishESO Submillimetre Telescope (SEST) under the auspices of the Key Project CO in the
Magellanic Clouds (Israel et al., 2003b, and references therein). The NANTEN survey provided the first complete inventory of GMCs in any galaxy, but did not resolve
molecular cloud structures smaller than ∼40 pc (we adopt 50.1 kpc for the distance to
the LMC Alves, 2004). The SEST observations, though of comparable resolution to
the MAGMA data, were frequently undersampled and targeted well-known H II regions.
The rest of this chapter is organized as follows. In Section 3.2, we describe the methods
that we have used to generate a catalogue of GMCs from the MAGMA LMC survey
data. We assess selection effects that may bias the catalogue, and describe the results
of processing model cloud datasets through our data reduction pipeline, including our
signal identification and cloud decomposition algorithms. We summarise the physical
3.2. The GMC Catalogue
111
properties of the catalogued GMCs in Section 3.3, and compare our measurements to
the results obtained by the NANTEN survey in Section 3.4. In addition to the question
of whether GMCs in the LMC are similar to GMCs in the Milky Way and other nearby
galaxies, we investigate whether GMCs without signs of high-mass star formation exhibit distinct physical properties (Section 3.5). Correlations between LMC structure,
cloud properties and the velocity field in MAGMA GMCs are examined in Section 3.6.
In Section 3.7, we discuss whether our results are consistent with the view that GMC
properties are uniform across diverse interstellar environments, and whether rotation
is dynamically significant for LMC clouds. We conclude with a summary of our key
results in Section 3.8. Throughout this chapter, position angles are measured in a
counterclockwise direction from north, for which we specify P.A. = 0◦ .
3.2 The GMC Catalogue
3.2.1
Identifying GMCs
To identify GMCs in the MAGMA data subcubes and measure their properties, we have
used the algorithms presented by Rosolowsky & Leroy (2006, implemented in IDL as
part of the CPROPS package). CPROPS uses a dilated mask technique to isolate
regions of significant emission within spectral line cubes, and a modified watershed
algorithm to assign the emission into individual clouds. Moments of the emission along
the spatial and spectral axes are used to determine the size, linewidth and flux of the
clouds, and optional corrections for the finite sensitivity and instrumental resolution
may be applied to the measured cloud properties. Each step of the CPROPS method
is described in detail by Rosolowsky & Leroy (2006).
Regions of significant emission within the MAGMA data subcubes are initially identified by finding pixels with emission greater than a threshold of 4σ across two contiguous
velocity channels where the RMS noise σ is measured using a signal-free region of the
data cube. The mask around the core regions is then expanded to include all the pixels
connected to the core with emission greater than 1.5σ across at least two consecutive
112
Chapter 3. Properties of MAGMA GMCs: I. Overview
Figure 3.1 Velocity channel maps of the CO emission from an example GMC in the MAGMA
catalogue. The black contour indicates the emission region that CPROPS identifies as belonging to the cloud. The velocity axis of the MAGMA data subcube and CPROPS assignment
cube has been binned to a channel width of 2.1 km s−1 for illustration only. The radial velocity
is indicated at the top left of each panel, and the black circle in the lower right corner represents
the Mopra beam.
channels. We explored a range of values for the threshold and edge parameters in the
masking process, and found that these values distinguished credible emission regions
(i.e. the mask did not expand excessively into the noise) and also yielded reliable measurements for the properties of faint clouds. The emission identified with an isolated
cloud in the MAGMA dataset is illustrated in Figure 3.1.
Once regions of significant emission have been identified, CPROPS assigns the emission
to individual cloud structures. To generate the preliminary list of GMC candidates, we
used the default parameters for the identification of GMCs that are recommended in
Rosolowsky & Leroy (2006). In this case, the parameters of the decomposition are moti-
3.2. The GMC Catalogue
113
vated by the observed physical properties of Galactic GMCs: spatial sizes greater than
∼ 10 pc, linewidths of several km s−1 , and brightness temperatures less than ∼ 10 K.
We adopt this approach because our goal is to describe the properties of GMCs in the
LMC and to investigate how these properties might differ to the properties of GMCs
in other galaxies. As noted by Rosolowsky & Leroy (2006), GMCs contain structure
across a wide range of size scales, so identifying the clumpy substructure – with a size
scale of ∼ 1 pc and typical linewidth of ∼ 1 km s−1 – within the clouds in our spectral
line cubes would require different decomposition parameters than the ones that we have
used. While the properties and scaling relations of this substructure is an important
topic for investigation, we defer this analysis to a future work. A previous analysis
of the MAGMA data in the molecular ridge region employed another decomposition
algorithm (GAUSSCLUMPS, Pineda et al., 2009), which identified structures that
are typically smaller (with radii between 6 and 20 pc) than the GMCs described here.
Our initial list of GMC candidates contained 232 objects. After cross-checking the
CPROPS cloud identifications against the NANTEN 12 CO(J = 1 → 0) data cube and
the MAGMA data to verify that the identified objects were genuine, we rejected 54 features that were clearly noise peaks or map edge artefacts. To ensure that the properties
of clouds in our final list are reliable, we impose a signal-to-noise threshold S/N ≥ 5 and
reject objects with measurement errors for the radius and velocity dispersion that are
greater than 20%. We further require that CPROPS is able to apply the corrections for
sensitivity and instrumental resolution successfully (i.e. these corrections do not result
in undefined values, see below). These criteria exclude a further 53 cloud candidates,
which we refer to as the “excluded emission regions” (EERs). The position and radial
velocity of the EERs are tabulated in Appendix 3.A of this chapter (Table 3.7). The
resulting sample of GMCs, which we henceforth refer to as the “MAGMA catalogue”,
contains 125 clouds. The position, radial velocity and physical properties of GMCs
in the MAGMA catalogue are presented in Appendix 3.B (Table 3.8). To verify the
results of our analysis, we define a “high quality” subsample of GMCs in the MAGMA
catalogue, which contains 57 clouds with S/N ≥ 9 and for which the uncertainties in
the radius and velocity dispersion measurements are less than 15%.
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Chapter 3. Properties of MAGMA GMCs: I. Overview
We adopt the default CPROPS definitions to derive the basic physical properties of
GMCs in the MAGMA cloud catalogue. The cloud radius is defined as R = 1.91σR pc,
where σR is the geometric mean of the second moments of the emission along the cloud’s
major and minor axes. The velocity dispersion σv is the second moment of the emission
distribution along the velocity axis, which for a Gaussian line profile is related to the
√
FWHM linewidth, ∆v, by ∆v = 8 ln 2σv . The CO luminosity of the cloud LCO is
simply the emission inside the cloud integrated over position and velocity, i.e.
LCO [ K km s
−1
2
pc ] = D
2
π
180 × 3600
2
ΣTi , δvδxδy
(3.1)
where D is the distance to the LMC in parsecs, δx and δy are the spatial dimensions
of a pixel in arcseconds, and δv is the width of one channel in km s−1 . The mass of
molecular gas estimated from the GMC’s CO luminosity, MCO is calculated as
MCO [M⊙ ] ≡ 4.4
XCO
2 × 1020 [ cm−2 (K km s−1 )−1 ]
LCO ,
(3.2)
where XCO is the assumed CO-to-H2 conversion factor, and a factor of 1.36 is applied
to account for the mass contribution of helium. The fiducial value of XCO used by
CPROPS is XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 . The virial mass is estimated as
Mvir [M⊙ ] = 1040σv2 R, which assumes that molecular clouds are spherical with truncated ρ ∝ r −1 density profiles (MacLaren et al., 1988). CPROPS estimates the error
associated with a cloud property measurement using a bootstrapping method, which is
described in section 2.5 of Rosolowsky & Leroy (2006).
In addition to the basic properties reported by CPROPS, we define the CO surface brightess as the total CO luminosity of a cloud divided by its projected area,
I(CO) [ K km s−1 ] ≡ LCO /πR2 . The molecular mass surface density ΣH2 is defined
as the virial mass divided by the projected cloud area, ΣH2 [M⊙ pc−2 ] ≡ Mvir /πR2 .
At times, we distinguish between ΣH2 and the molecular mass surface density inferred
from the CO luminosity: ΣH2 ,CO [M⊙ pc−2 ] ≡ MCO /πR2 . A mean CO-to-H2 conver-
3.2. The GMC Catalogue
115
sion factor for each GMC may be estimated from the ratio of its virial mass to its CO
luminosity: XCO [ cm−2 (K km s−1 )
−1
] ≡ Mvir [M⊙ ]/(2.2LCO ) [ K km s−1 pc2 ]. We note
that our definitions of XCO and ΣH2 assume that GMCs manage to achieve dynamic
equilibrium: if the degree of virialisation is not constant for LMC molecular clouds,
then variations in XCO and ΣH2 may instead reflect differences between the dynamical
state of the clouds. We estimate the uncertainties in XCO , I(CO), ΣH2 and ΣH2 ,CO
using standard error propagation rules.
As emphasized by Rosolowsky & Leroy (2006), the resolution and sensitivity of a dataset
influence the derived cloud properties. In order to reduce these observational biases,
they recommend extrapolating the cloud property measurements to values that would
be expected in the limiting case of perfect sensitivity (i.e. a brightness temperature
threshold of 0 K), and correcting for finite resolution in the spatial and spectral domains
by deconvolving the telescope beam from the measured cloud size, and deconvolving
the width of a spectral channel from the measured linewidth. The procedures that
CPROPS uses to apply these corrections are described in Rosolowsky & Leroy (2006,
see especially figure 2 and sections 2.2 and 2.3). The cloud property measurements
listed in Table 3.8 have been corrected for resolution and sensitivity bias; unless otherwise noted, we use these measurements in our analysis.
3.2.2
Selection Effects
Prior to examining the properties of molecular clouds in the LMC observed by MAGMA,
it is essential to characterise the selection effects that bias the catalogue. Potentially
important effects include our criteria for selecting target clouds, the finite angular and
spectral resolution of the Mopra Telescope, the sensitivity of the MAGMA observing
strategy, the procedure that we use to grid the spectral line data, the CPROPS algorithms for identifying and decomposing emission within spectral line cubes into cloud
objects, the CPROPS methods for deriving the physical properties of the identified
clouds, and the signal-to-noise and error criteria that are used to determine whether a
cloud is included in the MAGMA catalogue. In this section, we describe these effects
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Chapter 3. Properties of MAGMA GMCs: I. Overview
and assess the completeness of our cloud catalogue.
Preliminary Considerations: Survey Design and Signal Identification
As explained in Section 2.2, MAGMA observations in the LMC targeted the brightest
114 clouds in the NANTEN cloud catalogue of Fukui et al. (2008). All of the target
clouds have CO luminosities greater than 7000 K km s−1 pc2 and peak CO integrated
intensities greater than 1 K km s−1 , as measured by NANTEN. At the higher angular
resolution of MAGMA, the larger NANTEN clouds are often resolved into multiple discrete clouds, some of which are faint (see Section 3.4). While the MAGMA catalogue
therefore includes clouds with CO luminosities down to LCO ∼ 3 × 103 K km s−1 pc2 ,
isolated low luminosity clouds were not selected for observation and hence faint molecular clouds are under-represented in the MAGMA catalogue. The MAGMA survey is
not strictly flux-limited, moreover, since we require that the target NANTEN clouds
have peak I(CO) > 1 K km s−1 . This criterion was adopted after tests in 2005 and
2006 indicated that the sensitivity of our observing strategy (i.e. two orthogonal scans
per OTF field) limited us to detecting
12 CO(J
= 1 → 0) emission in regions with
I(CO)NANTEN ≥ 1 K km s−1 . There are five GMCs in the NANTEN catalogue with
LCO > 7000 K km s−1 pc2 and peak I(CO) less than 1 K km s−1 : LMC N J0458-7022,
LMC N J0502-6903, LMC N J0515-7002, LMC N J0504-6802 and LMC N J0526-6742.
The first three of these GMCs are unresolved by NANTEN, but the latter two have
radii of 50 and 64 pc respectively. The LCO values of the excluded clouds range from
7000 K km s−1 pc2 to 1.1 × 104 K km s−1 pc2 . While it is uncertain whether low surface
brightness GMCs would be identified as a single object at MAGMA’s higher angular resolution, we must regard LCO = 1.1 × 104 K km s−1 pc2 (rather than 7000 K km s−1 pc2 )
as the MAGMA survey’s completeness limit.
The criteria that CPROPS uses to identify significant emission regions in the MAGMA
data cubes and to determine whether they are suitable for decomposition into cloud
objects constitute a second important source of bias for the MAGMA catalogue. After
identifying regions with significant emission using the dilated mask technique outlined
3.2. The GMC Catalogue
117
above, decomposition only proceeds if the resulting emission region has a projected
area larger than twice the beam area (∼ 100 pixels), and if the intensity at the peak
exceeds the intensity at the edge of the region by more than a factor of two. The
MAGMA catalogue therefore does not include clouds with very narrow linewidths (i.e.
. 1 channel) or spatially compact clouds, even if they have high peak CO brightness.
Regardless of their size, molecular clouds with uniformly low CO brightness across their
projected area will also be excluded, either because they lack a core of high intensity
(≥ 4σ) pixels or because the intensity contrast between the core and the edge of the
cloud is low.
There are nine NANTEN GMCs that were observed by MAGMA which do not appear in the list of cloud candidates generated by CPROPS. With the exception of
LMC N J0509-6912, all of these GMCs had only been scanned once prior to the 2009
winter season. The LMC N J0509-6912 region had been scanned twice by the end of
2008, but the emission arises in two compact clumps, one of which is located on the
edge of the MAGMA data subcube and outside the region where NANTEN measured
I(CO) ≥ 1 K km s−1 . Repeat observations over a slightly larger area for this region
have been scheduled for 2010. The LCO values for the NANTEN GMCs without Mopra detections range between 0.7 and 1.9 × 104 K km s−1 pc2 ; we adopt the upper value
as our current catalogue’s completeness limit. We note that CPROPS identifies cloud
candidates corresponding to six of the undetected GMCs when the orthogonal scans
of these regions (obtained in 2009) are included, so the completeness limit of the final
cloud catalogue, which will be generated from the complete MAGMA dataset, should
be closer to the limit imposed by the survey’s design (i.e. 1.1 × 104 K km s−1 pc2 ; Wong
et al, in preparation).
In summary, clouds that are rejected by CPROPS tend to have low total CO luminosity and/or low CO surface brightness. Similar criteria were used to construct the
MAGMA survey target list, so isolated clouds that would be rejected by CPROPS
tend not to have been selected for observation by MAGMA. The CPROPS criteria remain an important consideration, however, since they may exclude small and/or faint
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Chapter 3. Properties of MAGMA GMCs: I. Overview
MAGMA clouds that form part of larger unresolved GMCs in the NANTEN survey.
Testing CPROPS on Model Cloud Datasets
Rosolowsky & Leroy (2006) have discussed the ability of their extrapolated moment
method to measure the radius and linewidth of molecular clouds across a range of instrumental resolutions and sensitivities. Compared to other methods, CPROPS performs
well in the low signal-to-noise and marginal angular resolution regime that characterises
extragalactic molecular cloud observations. Ideally, however, we would like to assess
how the entire procedure for generating the MAGMA catalogue – i.e. gridding the data,
identifying and decomposing regions of significant emission into GMCs and parameterising their properties using the extrapolated moment method – affects the final cloud
property measurements. To test this, we generated 250 spectral line cubes containing
model molecular clouds with the MIRIAD task fakeotf, using a simple 3-dimensional
elliptical Gaussian to represent a molecular cloud. The major and minor axis, linewidth
and peak CO brightness of each model cloud were chosen at random from parameter
ranges that approximately overlap with the properties of the molecular clouds identified in the MAGMA survey (see Table 3.1). The clouds are not otherwise physically
realistic: in particular, we do not require that they follow the observed scaling relations for molecular cloud properties (e.g. Larson, 1981). We generated three versions
of the model cloud dataset, varying the noise level in the data cubes: i) σ = 0.3 K per
0.53 km s−1 channel, comparable to the noise in regions that have been mapped twice;
ii) σ = 0.5 K per 0.53 km s−1 channel, comparable to the noise in regions that were
only observed once, and iii) σ = 0.01 K per 0.53 km s−1 channel, i.e. negligible noise.
We refer to these as the “standard”, “noisy” and “low noise” trial data respectively.
All three trial datasets were processed using the same gridding, signal identification
and cloud decomposition producedures that were used to generate the MAGMA cloud
catalogue.
i) Detection Limits
For the standard trial dataset, CPROPS identified 222 of the 250 input clouds. The
3.2. The GMC Catalogue
119
Table 3.1 Parameters used to generate the model cloud dataset.
Parameter
Major and minor axes
Range
[2,83] pc
Velocity Dispersion
[0.26,10.01] km s−1
Peak CO Brightness
[0.7,6.7] K
clouds that escape detection by CPROPS tend to be small, although a few larger
clouds with very narrow linewidths and low peak CO brightness also remain undetected. The minimum size of the model clouds is 2.6 pc and the minimum peak CO
brightness is 0.7 K; for the detected clouds, the corresponding minima are R = 4.6 pc
and Tmax = 0.8 K. Imposing the criteria that we use to generate the MAGMA catalogue excludes a further 68 clouds; these are mostly excluded by our requirement
that CPROPS is able to deconvolve the telescope beam from the radius measurement
successfully (60 clouds) and, to a lesser degree, that the uncertainty in the radius measurement is less than 20% (7 clouds). The minimum size and peak CO brightness of
model clouds that would be included in the catalogue are 11.7 pc and 0.8 K respectively.
The minimum size of the catalogued clouds is not especially sensitive to the clouds’
peak CO brightness: unresolved clouds with low CO brightness are not identified by
CPROPS, while the catalogue criteria remove the remaining unresolved clouds with
high CO brightness.
For the noisy trial dataset, CPROPS identified fewer (168) of the input clouds. Once
again, the clouds that escape identification by CPROPS tend mostly to be small clouds,
although relative to the standard trial dataset, there are more big clouds with low peak
CO brightness that are also non-detections. The minimum size and peak CO brightness of the detected clouds are R = 7.3 pc and Tmax = 1.4 K. Our catalogue criteria
exclude a further 41 clouds; as before, these are mostly excluded by our requirement
that CPROPS is able to deconvolve the telescope beam from the radius measurement
successfully (30 clouds). Clouds with a signal-to-noise beneath our threshold (9 clouds)
also tend to have large uncertainties in their radius measurement. The minimum size
and peak CO brightness of model clouds that would be included in the catalogue are
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Chapter 3. Properties of MAGMA GMCs: I. Overview
11.7 pc and 1.4 K respectively. The size threshold for the catalogued clouds does not
vary strongly with peak CO brightness for the same reason noted above.
In the low noise dataset, CPROPS identified 249 of the input clouds; the single cloud
that escaped detection was compact (R = 2.6 pc) and faint (Tmax = 0.8 K). The catalogue criteria exclude 90 clouds, such that the minimum size and peak CO brightness
of model clouds that would be included in the catalogue are 10.8 pc and 0.8 K respectively. Most of the excluded clouds are small, but there are four clouds with R > 40 pc
and narrow linewidths that are excluded due to the large uncertainty in their linewidths.
In summary, CPROPS is more successful at detecting small clouds, and clouds with
low CO luminosity and/or low CO surface brightness in data cubes with higher sensitivity. This is not a surprising result, although it is worth noting that CPROPS will
yield different cloud property measurements for data sets with different noise levels as
a result of its signal identification algorithm, even if a correction for sensitivity bias
is applied. For the MAGMA GMC catalogue, the detection bias against small clouds
in regions with poorer sensitivity is mitigated by our requirement that the deconvolution correction is successful: this causes clouds that are significantly smaller than the
telescope beam to be rejected, regardless of their signal-to-noise. Spatial variations
in sensitivity across the MAGMA survey region will, however, produce corresponding
variations in the detection rate for clouds with low CO luminosity and low CO surface
brightness; we would expect these clouds to be under-represented in the catalogue for
regions that had only been observed once prior to end of 2009.
ii) Accuracy of Cloud Property Measurements
As well as the factors that determine whether model clouds will be detected by CPROPS
or included in the MAGMA catalogue, we also need to assess how well the extrapolated
moment method implemented in CPROPS recovers the properties of the clouds and
whether the accuracy of the cloud property measurements is uniform across the range
of observed values. In Figures 3.2 to 3.10, we plot the ratio between a measured cloud
property and its true (i.e. input) value against the i) radius, ii) velocity dispersion,
3.2. The GMC Catalogue
121
iii) peak CO brightness and iv) major-to-minor axis ratio of the model clouds in the
standard trial dataset. In these plots, the open squares represent clouds that would be
included in the MAGMA catalogue, and grey filled circles represent clouds that would
be considered “high quality” according to the criteria defined in Section 3.2.1. The
red crosses are resolved clouds that are identified by CPROPS but would be rejected
from the catalogue, and the blue open triangles represent unresolved clouds identified
by CPROPS (also rejected from the catalogue). Corresponding plots for the noisy and
low noise trial data are not shown, as they follow the trends observed for the standard
trial data set.
Figures 3.2 to 3.10 show that the accuracy of the cloud property measurements is sensitive to the size and the linewidth of the model clouds; systematic trends with Tmax and
the major-to-minor axis ratio of the model clouds are less distinct. Some cloud property
measurements (e.g. I(CO) and the major-to-minor axis ratio) appear to be less accurate for highly elongated structures but this is mostly a size effect: the model clouds
with the largest major-to-minor axis ratios tend to be barely resolved in the direction
perpendicular to their major axis. Overall, CPROPS tends to underestimate the radius, velocity dispersion, Tmax and major-to-minor axis ratio of the model clouds. What
is more troubling, however, is that the accuracy of these measurements is not constant,
and that these variations are not reflected in the uncertainties reported by CPROPS.
For clouds with Rmodel ∈ [10, 15] pc, the average ratio between the measured and input
radius is ∼ 60%, increasing to ∼ 90% for clouds with Rmodel ≥ 25 pc. The ratio between the measured and input velocity dispersions, by contrast, decreases from ∼ 95%
for clouds with σv,model ≤ 2 km s−1 to ∼ 85% for clouds with σv,model ≥ 4 km s−1 . The
accuracy of the total CO luminosity measurements exhibits a similar variation with
σv . Tmax and the major-to-minor axis ratio are underestimated more significantly for
small clouds, although this is more likely to result from beam dilution and the gridding
process than CPROPS.
The errors in the R and σv measurements are not especially large, but their impact on
cloud properties that are derived from a combination of R and σv can become signifi-
122
Chapter 3. Properties of MAGMA GMCs: I. Overview
[b] Tsys 400K
R: Measured/Model
R: Measured/Model
[a] Tsys 400K
1.5
1.0
0.5
0.0
0.5
1.0
1.5
1.5
1.0
0.5
0.0
2.0
R: Measured/Model
R: Measured/Model
1.5
1.0
0.5
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0.0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
1.5
1.0
0.5
0.0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.2 Ratio between the measured radius and the input radius of the model clouds in
the standard trial data set (see text), plotted as a function of the input (a) radius, (b) velocity
dispersion, (c) peak CO brightness, and (d) major-to-minor axis ratio of the clouds. For all
panels, blue open triangles represent unresolved clouds, red crosses represent resolved clouds,
open squares represent clouds that would be included in the MAGMA catalogue, and grey filled
circles represent a “high quality” subsample of the included clouds. The vertical error bars are
derived from the uncertainty in the cloud radius measurement reported by CPROPS using the
normal error propagation rules. The grey shaded region and dotted vertical lines in panel (a)
represent the range of input radii for the 250 model clouds; the dashed vertical lines represent
the observed radii of GMCs in the MAGMA catalogue.
3.2. The GMC Catalogue
123
[b] Tsys 400K
σv: Measured/Model
σv: Measured/Model
[a] Tsys 400K
1.5
1.0
0.5
0.0
1.0
1.5
1.5
1.0
0.5
0.0
2.0
σv: Measured/Model
σv: Measured/Model
1.5
1.0
0.5
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0.0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
1.5
1.0
0.5
0.0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.3 Ratio between the measured and input value of σv for the model clouds, plotted
as a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness, and (d)
major-to-minor axis ratio. Plot symbols and error bars are the same as in Figure 3.2. The grey
shaded region and dotted vertical lines in panel (b) represent the range of σv values for the 250
model clouds; the dashed vertical lines represent the observed values of σv for GMCs in the
MAGMA catalogue.
Chapter 3. Properties of MAGMA GMCs: I. Overview
[a] Tsys 400K
Tmax: Measured/Model
Tmax: Measured/Model
124
1.5
1.0
0.5
0.0
1.0
1.5
[b] Tsys 400K
1.5
1.0
0.5
0.0
2.0
Tmax: Measured/Model
Tmax: Measured/Model
[c] Tsys 400K
1.5
1.0
0.5
0.0
1
2
3
4
5
−0.5
0.0
0.5
1.0
log(σv/[km s−1]): model
log(R/[pc]): model
6
log(Tmax/[K]): model
7
[d] Tsys 400K
1.5
1.0
0.5
0.0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.4 Ratio between the measured and input value of Tmax of the model clouds, plotted
as a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness and (d)
major-to-minor axis ratio of the model clouds. The panels, plot symbols and error bars are the
same as in Figure 3.2. The grey shaded region and dotted vertical lines in panel (c) represent the
range of Tmax values for the 250 model clouds; the dashed vertical lines represent the observed
values of Tmax for GMCs in the MAGMA catalogue.
125
Axis Ratio: Measured/Model
Axis Ratio: Measured/Model
3.2. The GMC Catalogue
[a] Tsys 400K
1.5
1.0
0.5
0.0
1.0
1.5
[b] Tsys 400K
1.5
1.0
0.5
0.0
2.0
−0.5
Axis Ratio: Measured/Model
Axis Ratio: Measured/Model
[c] Tsys 400K
1.5
1.0
0.5
0.0
1
2
3
4
5
Tmax [K]: model
0.0
0.5
1.0
log(σv/[km s−1]): model
log(R/[pc]): model
6
7
[d] Tsys 400K
1.5
1.0
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
log(Axis Ratio): model
Figure 3.5 Ratio between the measured and input value of the major-to-minor axis ratio for
the model clouds, plotted as a function of the input (a) radius, (b) velocity dispersion, (c) peak
CO brightness and (d) major-to-minor axis ratio. Plot symbols and error bars are the same as
in Figure 3.2. The grey shaded region and dotted vertical lines in panel (d) represent the range
of Γ values for the 250 model clouds; the dashed vertical lines represent the observed values of
Γ for GMCs in the MAGMA catalogue.
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Chapter 3. Properties of MAGMA GMCs: I. Overview
[b] Tsys 400K
LCO: Measured/Model
LCO: Measured/Model
[a] Tsys 400K
1.5
1.0
0.5
0.0
1.0
1.5
1.5
1.0
0.5
0.0
2.0
LCO: Measured/Model
LCO: Measured/Model
1.5
1.0
0.5
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0.0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
1.5
1.0
0.5
0.0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.6 Ratio between the measured and value of LCO for the model clouds, plotted as
a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness, and (d)
major-to-minor axis ratio. Plot symbols and error bars are the same as in Figure 3.2.
3.2. The GMC Catalogue
127
[b] Tsys 400K
Mvir: Measured/Model
Mvir: Measured/Model
[a] Tsys 400K
1.5
1.0
0.5
0.0
1.0
1.5
1.5
1.0
0.5
0.0
2.0
Mvir: Measured/Model
Mvir: Measured/Model
1.5
1.0
0.5
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0.0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
1.5
1.0
0.5
0.0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.7 Ratio between the measured and input value of Mvir for the model clouds, plotted
as a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness, and (d)
major-to-minor axis ratio. Plot symbols and error bars are the same as in Figure 3.2.
128
Chapter 3. Properties of MAGMA GMCs: I. Overview
[b] Tsys 400K
ICO: Measured/Model
ICO: Measured/Model
[a] Tsys 400K
3
2
1
0
1.0
1.5
3
2
1
0
2.0
ICO: Measured/Model
ICO: Measured/Model
3
2
1
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
3
2
1
0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.8 Ratio between the measured and input value of I(CO) for the model clouds, plotted
as a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness, and (d)
major-to-minor axis ratio. Plot symbols and error bars are the same as in Figure 3.2.
3.2. The GMC Catalogue
129
[b] Tsys 400K
ΣH2: Measured/Model
ΣH2: Measured/Model
[a] Tsys 400K
3
2
1
0
1.0
1.5
3
2
1
0
2.0
ΣH2: Measured/Model
ΣH2: Measured/Model
3
2
1
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
3
2
1
0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.9 Ratio between the measured and input value of ΣH2 for the model clouds, plotted
as a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness, and (d)
major-to-minor axis ratio. Plot symbols and error bars are the same as in Figure 3.2.
130
Chapter 3. Properties of MAGMA GMCs: I. Overview
[b] Tsys 400K
XCO: Measured/Model
XCO: Measured/Model
[a] Tsys 400K
1.5
1.0
0.5
0.0
1.0
1.5
1.5
1.0
0.5
0.0
2.0
XCO: Measured/Model
XCO: Measured/Model
1.5
1.0
0.5
1
2
0.0
0.5
1.0
[d] Tsys 400K
[c] Tsys 400K
0.0
−0.5
log(σv/[km s−1]): model
log(R/[pc]): model
3
4
5
Tmax [K]: model
6
7
1.5
1.0
0.5
0.0
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
log(Axis Ratio): model
Figure 3.10 Ratio between the measured and input value of XCO for the model clouds, plotted
as a function of the input (a) radius, (b) velocity dispersion, (c) peak CO brightness, and (d)
major-to-minor axis ratio. Plot symbols and error bars are the same as in Figure 3.2.
3.2. The GMC Catalogue
131
cant. For clouds with Rmodel . 20 pc, the CO surface brightness can be overestimated
by a factor of three or more, and the CO-to-H2 conversion factor may be underestimated by a similar amount (Figures 3.8 and 3.10). The ratio between the input
and measured virial mass (Figure 3.7) is scattered around an average value of ∼ 60%;
some of this scatter can be attributed to a systematic decline in the accuracy of the
virial mass measurement for clouds with small Rmodel and for clouds with large σv,model .
A lower noise level in the trial data set tends to decrease the scatter in the plots in
Figures 3.2 to 3.5 and therefore accentuate the systematic nature of the variations that
we have outlined above. This is important, since it suggests that the less accurate measurements for small clouds do not arise because a significant fraction of their emission is
indistinguishable from the background noise. However, the uncertainty in the size measurement of small clouds is more likely to exceed our rejection threshold (∆R/R ≥ 0.2)
in data with poorer sensitivity, such that the accuracy of the catalogue may improve
in regions with greater noise fluctuations, even though it becomes less complete.
It is important to recall that our model clouds are highly idealised representations of
real molecular clouds. Our tests cannot determine whether the variable accuracy of the
cloud property measurements will be significant compared to uncertainties introduced
by physical effects that are not included in our model (e.g. large-scale velocity gradients, complex cloud geometries, spatial clustering and/or velocity blending of clouds).
Nevertheless, our analysis offers some useful general conclusions. First, we have seen
that we should expect our cloud property measurements to exhibit some degree of scatter: even if the underlying cloud population is homogeneous, this scatter may exceed
the uncertainties reported by CPROPS. Second, we have learnt that particular care
should be taken when interpreting the properties of small clouds: the values of R, Tmax
Mvir and XCO are increasingly underestimated, and I(CO) and ΣH2 are increasingly
overestimated, as the cloud radii approach the FWHM of the telescope beam. Our
decision to exclude clouds that are barely resolved or have highly uncertain size measurements from the MAGMA GMC catalogue therefore appears to be prudent, but it
is not especially conservative.
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Chapter 3. Properties of MAGMA GMCs: I. Overview
3.3 Properties of GMCs in the LMC
3.3.1
Overview
The GMCs in the MAGMA catalogue have radii ranging between 13 and 160 pc, velocity dispersions between 1.0 and 6.1 km s−1 , peak CO brightnesses between 1.2 and
7.1 K, CO luminosities between 103.5 and 105.5 K km s−1 pc2 , and virial masses between
104.2 and 106.8 M⊙ . The clouds tend to be elongated, with a median axis ratio of 1.7.
Assuming a CO-to-H2 conversion factor of XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 , the
total mass of the catalogued GMCs is 1.2 × 107 M⊙ , in good agreement with the mass
that we derive by summing all the significant CO emission within the MAGMA survey
area (see Section 2.4).
3.3.2
Spatial Distribution and Cloud Geometry
Frequency distributions for the distance to the LMC’s kinematic centre dKC , galactic
position angle and radial velocity VLSR of the MAGMA GMCs are presented in Figure 3.11. We adopt RA 05h19m30s, Dec -68d53m (J2000) for the location of the LMC’s
kinematic centre, a disk inclination of 35◦ , and 340◦ as the position angle of the receding line-of-nodes (Wong et al., 2009). The distribution of dKC is plotted such that the
annuli corresponding to the dKC bins have equal area, assuming that the LMC’s disk
is intrinsically circular. The GMC number surface density decreases by a factor of ∼ 2
between dKC = 0.5 and 2.5 kpc, with some indication for a deficiency of GMCs near
dKC ∼ 1.5 kpc. By multiplying each GMC by its mass, Figure 3.11[a] can be translated into the molecular mass surface density distribution of the catalogued clouds
(Figure 3.12[a]). The deficiency at dKC ∼ 1.5 kpc is even more pronounced in this plot,
corresponding to almost an order of magnitude decrease in the molecular mass surface
density. The reason for this gap is uncertain. The H I mass surface density does not
decline appreciably at dKC ∼ 1.5 kpc (refer figure 10 in Wong et al., 2009), but we note
3.3. Properties of GMCs in the LMC
133
that the tidal force (e.g. Blitz & Glassgold, 1982),
d
V2
T (R) ≡ 2 −
R
dR
V2
R
,
(3.3)
peaks at dKC ∼ 1.6 kpc for the geometry and rotation curve reported by Wong et al.
(2009). In this equation, V (R) is the rotational velocity and R ≡ dKC is the galactocentric radius. We are currently investigating the stability of MAGMA GMCs against
tidal forces and whether GMCs can avoid tidal destruction in this region of the LMC
disk (Thilliez et al., in preparation)
The angular distribution of MAGMA GMCs is more uniform, although the concentration of GMCs in the south-east of the LMC is evident as a peak at PA ∼ 150◦ in
Figure 3.11[b]. Both the number and, to a lesser degree, the mass of GMCs increase
in this direction; for PA ∈ [120◦ , 180◦ ], the combined GMC mass increases by a factor
of ∼ 2.5 above the LMC average (Figure 3.12[b]). The radial velocity distribution of
the MAGMA GMCs is not flat either, exhibiting two peaks at ∼ 230 and ∼ 280 km s−1
(Figure 3.11[c]). These peaks are also evident in the NANTEN catalogue (Fukui et al.,
2008): the peak at 230 km s−1 is due to GMCs in the molecular ridge and arc regions,
while the peak around 280 km s−1 is associated with GMCs in the N11 and N44 starforming regions (Henize, 1956).
Frequency distributions of the major-to-minor axis ratio and position angle of the GMC
major axis are presented in Figure 3.13. The frequency distribution of the major axis
position angle in Figure 3.13[a] suggests a slight tendency for the major axis of MAGMA
GMCs to be aligned in the north-south direction. Sixty per cent of the GMCs in the
MAGMA catalogue have major axis position angles < 45◦ or > 135◦ . This trend persists if GMCs with axis ratios less than 1.3 – i.e. round GMCs whose major axis may
not be well-determined – are excluded. The MAGMA GMCs tend to elongated, with
a median major-to-minor axis ratio of 1.7. The axis ratio distribution is quite skewed:
70% of clouds have axis ratios less than 2, but there are a few highly filamentary clouds
with axis ratios up to 4.6. We find no overall correlation between the size and axis
134
Chapter 3. Properties of MAGMA GMCs: I. Overview
60
[a]
50
Number of GMCs
Number of GMCs
60
40
30
20
10
0
0
1
2
[b]
50
40
30
20
10
0
3
Galactocentric radius [kpc]
0
60
Number of GMCs
100
200
300
Galactic Position Angle [degrees]
[c]
50
40
30
20
10
0
220
240
260
280
300
Radial velocity [LSR, km s−1]
Figure 3.11 Frequency distributions of the (a) distance to the LMC’s kinematic centre, (b)
galactic position angle and (c) radial velocity √
for the 125 GMCs in the MAGMA catalogue.
The error on each bin is calculated as σ = 1 + N + 0.75, where N is the number of clouds in
the bin. The histogram in panel [a] is constructed such that the annuli corresponding to the
dKC bins have equal area, assuming that the LMC’s disk is intrinsically circular.
3.3. Properties of GMCs in the LMC
135
[b]
log(Molecular Mass)
log(Molecular Mass)
[a]
7
6
5
4
7
6
5
4
0
1
2
3
Galactocentric radius [kpc]
4
0
100
200
300
Galactic Position Angle [degrees]
Figure 3.12 The (a) radial and (b) angular distribution of molecular mass for the MAGMA
GMCs. The dashed grey lines represent the combined molecular mass of the GMCs and the
solid black lines represent the median mass. As for Figure 3.11[a], the separation between points
along the x-axis in panel [a] correspond to annuli of equal area, assuming that the LMC’s disk
is intrinsically circular. We extrapolate over the region with zero clouds at dKC = 3.5 kpc. The
vertical error bars represent the RMS dispersion of the values in each bin.
ratio of the GMCs (Figure 3.14). There are no small, highly elongated GMCs in the
MAGMA catalogue, but this is likely to be a selection effect. As noted in Section 3.2.2,
our criteria are biased against small filamentary clouds, since the CPROPS method
for estimating the deconvolved cloud radius fails if the minor axis of the GMC is much
smaller than the width of the telescope beam. There is no evidence for systematic
variations in the axis ratio of the MAGMA GMCs with galactocentric radius, galactic
position angle or radial velocity.
In order to explore the connection between the morphology of the GMCs and the
large-scale structure of the LMC a little further, we define θ, the angle between the
GMC major axis and the tangent to a circle with origin at the LMC’s kinematic centre
(see also Fukui et al., 2008). A diagram illustrating how θ is defined is shown in Figure 3.15[a]. Note that for this comparison, we assume that the LMC’s disk is face-on
and circular, i.e. we do not attempt to ‘de-project’ the GMC position angles or the
angular separation between the GMC and the LMC’s kinematic centre. The distribution of θ values for MAGMA GMCs should deviate from a random distribution if
136
Chapter 3. Properties of MAGMA GMCs: I. Overview
50
40
30
20
10
0
60
[a]
Number of GMCs
Number of GMCs
60
0
50
100
50
40
30
20
10
0
150
Position angle [degrees]
[b]
1
2
3
4
Major−to−minor axis ratio
Major−to−minor axis ratio
Figure 3.13 Frequency distribution of (a) the major axis position angle and (b) the major-tominor axis ratio of MAGMA GMCs. The error on each bin is calculated as in Figure 3.11.
5
4
3
2
1
1.0
1.5
2.0
2.5
log(GMC Radius/[pc])
Figure 3.14 The major-to-minor axis ratio of the MAGMA GMCs plotted as a function of
their radius. GMCs belonging to the MAGMA cloud catalogue are represented by small open
squares, and GMCs in the high quality subsample are overplotted with filled grey circles.
3.3. Properties of GMCs in the LMC
137
60
e
]
Number of GMCs
]
]
[b]
50
40
30
20
10
0
0
20
40
60
θ [degrees]
80
Figure 3.15 (a) Diagram illustrating how θ is defined. (b) Histogram showing the frequency
distribution of θ values for MAGMA GMCs. The error on each bin is calculated as in Figure 3.11.
large-scale galactic processes such as shear or tidal-stretching have a strong influence on
GMC morphology. The distribution of θ for the MAGMA GMCs is presented in panel
[b] of Figure 3.15. The distribution is nearly uniform, although it is appears slightly less
common for GMCs to be elongated in the radial direction (i.e. along the line connecting
the GMC to the LMC’s kinematic centre, for which θ = 90◦ ). A Kolmogorov-Smirnov
test indicates that the observed θ distribution is consistent with a uniform random
distribution with 31% likelihood however, so we cannot exclude that the apparent lack
of GMCs with 75 < θ < 90◦ arises through stochastic variation. We find no evidence
that θ depends on location in the LMC, i.e. there is no correlation between θ and the
galactocentric radius, galactic position angle or radial velocity of the MAGMA GMCs.
3.3.3
Physical Properties of GMCs
CO Luminosity
The cloud mass distribution is an important property of GMC populations, describing
how the molecular gas within a galaxy is distributed across clouds of different mass. The
mass distribution is thought to be a signature of cloud formation and dispersal processes
(e.g. Kwan, 1979; Wada et al., 2000), with recent observational work suggesting that it
138
Chapter 3. Properties of MAGMA GMCs: I. Overview
varies between galaxies, and perhaps also within galactic disks (e.g. Rosolowsky, 2005;
Rosolowsky et al., 2007). The distribution is usually expressed in differential form, and
modelled as a power law:
dN
∝ Mγ .
dM
(3.4)
γ = −2 represents a critical value of the cloud mass distribution: for distributions with
γ > −2, the total molecular mass of a galaxy is dominated by massive GMCs, while
for distributions with γ < −2, most of the galaxy’s molecular mass is located in small
clouds. For galaxies with γ < −2, the total molecular mass derived by integrating the
mass spectrum diverges to infinity; in these galaxies, there must be a lower mass limit
for the molecular clouds or a turnover in the mass distribution at low cloud masses.
For GMCs in the inner Milky Way, the exponent of the mass spectrum is γ ∼ −1.5
(Solomon et al., 1987; Rosolowsky, 2005). Similar values for γ have been observed for
the clumpy structure within individual molecular clouds, which has been intepreted as
evidence for a hierarchical ISM (Kramer et al., 1998; Elmegreen & Falgarone, 1996).
The physical connection between the molecular clump mass spectrum and the stellar initial mass function also remains under investigation (e.g. Chabrier & Hennebelle, 2010).
The mass distributions of GMCs in the outer Milky Way, M31, IC10 and the LMC have
exponents ranging between −1.5 and −1.8 (Blitz et al., 2007). The GMC population is
M33 is unusual, exhibiting an overall mass spectrum with γ = −2.5±0.5 but with some
evidence that the value of γ depends on galactocentric radius (Rosolowsky et al., 2007).
The traditional method of estimating γ involves allocating the mass measurements into
logarithmically spaced bins, and dividing the number of clouds in each bin, Nbin , by
the width of each bin, ∆M : dN/dM ≈ Nbin /∆M . A simple power law is used to fit
the resulting differential distribution, assuming that the uncertainty in dN/dM arises
solely from counting errors. Two well-known problems with this technique are that i)
the derived value of γ is sensitive to the binning parameters and ii) errors in the cloud
mass measurements are neglected. Rosolowsky (2005) has demonstrated, for example,
that the binning procedure alone renders γ uncertain by ≥ 0.1 dex for molecular cloud
samples with fewer than 500 members. As an alternative to the traditional method for
3.3. Properties of GMCs in the LMC
139
log(MCO/[Msol])
log(N(L’>L)/Nclds)
4
5
6
7
γNAN = −1.9+/−0.1
γMAG = −2.0+/−0.2
0.0
0.0
−0.5
−0.5
−1.0
−1.0
−1.5
−1.5
−2.0
−2.0
−2.5
−2.5
3
4
5
6
log(LCO/[K km s−1 pc2])
Figure 3.16 The cumulative LCO distribution for GMCs in the MAGMA (black line) and
NANTEN (light grey line) catalogues (Fukui et al., 2008). The mass corresponding to the
LCO values, assuming XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 , is shown along the top axis. The
horizontal error√bars reflect the uncertainty in the GMC LCO measurements and vertical error
bars represent N counting errors. The red (blue) curve is the best-fitting truncated power
law to the NANTEN (MAGMA) distribution. The corresponding values of γ are indicated in
the top right corner.
estimating γ, Rosolowsky (2005) favours fitting a truncated power-law directly to the
cumulative mass distribution, and we follow his approach here. In this case,
′
N (M > M ) = N0
M γ+1
−1 ,
M0
(3.5)
where M0 is the maximum mass in the distribution, and N0 is the number of clouds
that are more massive than 21/(γ+1) M0 , the mass where the distribution begins to deviate significantly from a simple power law. Values of N0 significantly greater than one
indicate that there is an upper limit to the GMCs masses in a galaxy, and that the
dominant cloud formation mechanism is not scale-free.
140
Chapter 3. Properties of MAGMA GMCs: I. Overview
Although presentations of molecular cloud mass spectra are common in the literature,
we prefer to discuss the distribution of CO luminosities for the MAGMA GMCs, since
LCO is obtained directly from the observations, without making assumptions about the
correct value of XCO or the dynamical state of the clouds. The total CO luminosity of
GMCs in the MAGMA catalogue ranges from 103.5 to 105.5 K km s−1 pc2 . The cumulative LCO distribution of the MAGMA GMCs is shown in Figure 3.16, where we also
plot the LCO distribution for GMCs in the NANTEN catalogue. The vertical offset
between the MAGMA and NANTEN distributions arises because the MAGMA survey
only targeted bright GMCs for observation, i.e. the number of bright GMCs relative
to the “total” number of GMCs is higher for MAGMA simply because the LMC’s faint
cloud population is missing from the MAGMA catalogue. The shapes of the MAGMA
and NANTEN distributions are quite similar, however, even at low LCO values. This
is somewhat surprising, as we have seen that the current MAGMA catalogue is incomplete below 1.9 × 104 K km s−1 pc2 . Our analysis in Section 3.4 shows that most clouds
in the MAGMA catalogue demonstrate a one-to-one correspondence with a NANTEN
cloud, but that larger NANTEN clouds tend to appear as multiple GMCs at MAGMA’s
higher resolution. In this case it is difficult to judge the completeness of the MAGMA
catalogue correctly from a flattening of the spectrum, since the segmentation of large
clouds in the NANTEN catalogue raises the relative number of low luminosity clouds
in the MAGMA catalogue and steepens the observed spectrum. More generally, we
note that the slope of GMC mass distributions would therefore seem to depend on a
combination of the angular resolution, completeness limit and decomposition method
used to identify cloud structures.
To facilitate comparison with previous studies of GMC mass spectra, the mass corresponding to a given LCO value is indicated along the top axis of Figure 3.16, assuming
a constant CO-to-H2 factor of XCO = 2.0× 1020 cm−2 (K km s−1 )−1 . We fit a truncated
power-law to the NANTEN and MAGMA GMC mass spectra using the method recommended by Rosolowsky (2005). For the NANTEN data, we assume a completeness
limit of 1.4 × 104 M⊙ , which is equivalent to the completeness limit quoted by Fukui
et al. (2008) for the XCO factor that we have adopted. For the MAGMA data, we use a
3.3. Properties of GMCs in the LMC
141
Table 3.2 The best-fitting truncated power-law to the distribution of GMC masses in the LMC,
as measured by NANTEN and MAGMA. The results in columns 2 to 4 refer to the parameters
in Equation 3.5.
Survey
N0
M0
γ
[106 M⊙ ]
NANTEN
MAGMA
4.3 ± 3.6
1.8 ± 2.3
1.5 ± 0.9
1.6 ± 0.8
−1.85 ± 0.08
−2.02 ± 0.24
completeness limit of 8.3 × 104 M⊙ (see Section 3.2.2). The resulting fits to both mass
distributions are plotted in Figure 3.16, and are tabulated in Table 3.2. The derived
slopes are consistent with each other and with the fit derived independently by Fukui
et al. (2008) for the NANTEN GMCs. The slope of the mass spectra that we derive,
γ ∼ −1.9, indicates that molecular gas in the LMC is distributed more evenly across
high mass and low mass molecular clouds than in the inner Milky Way, where massive
GMCs appear to dominate the mass budget of the molecular ISM (e.g. Solomon et al.,
1987; Blitz et al., 2007). We do not find evidence for a break in the spectrum that
would indicate an upper limit to the mass of a GMC that can be formed in the LMC.
Radius
For resolved studies of GMCs, the cloud size spectrum is another tool for describing how
molecular gas in a galaxy is distributed across structures of different sizes. Features in
an otherwise smooth size spectrum may be a signature of physical processes – such as
cloud mergers or stellar feedback – that promote or suppress the formation of molecular
clouds at a characteristic spatial scale. In the inner and outer Milky Way, the cloud
size spectrum is smooth for clouds with radii between 10 and 100 pc, following a power
law of the form dN/dR ∝ Rm , where the derived values of m usually range between
−3.2 and −3.4 (e.g. Solomon et al., 1987; Heyer et al., 2001). The size spectrum of
structure within Galactic molecular clouds is also smooth, following dN/dR ∝ Rm down
to scales of a few tenths of a parsec (e.g. Elmegreen & Falgarone, 1996). Together,
these observations have been interpreted as evidence for the fractal structure of the
142
Chapter 3. Properties of MAGMA GMCs: I. Overview
γ = −3.9+/−0.4
log(N(R’>R)/Nclds)
0.0
−0.5
−1.0
−1.5
−2.0
−2.5
0.5
1.0
1.5
2.0
2.5
log(Radius/[pc])
Figure 3.17 The cumulative size distribution for GMCs in the MAGMA (black line) and
NANTEN (light grey line) catalogues (Fukui et al., 2008). The horizontal error bars
√ reflect the
uncertainty in the GMC radius measurements and vertical error bars represent N counting
errors. The best-fitting power law to the NANTEN size distribution is indicated with a red
line, and the corresponding slope is indicated in the top right corner. We do not attempt to fit
the MAGMA size distribution.
ISM, although self-similarity must eventually break down on the scale of an individual
star-forming core, where self-gravity dominates over other physical forces (e.g. Blitz &
Williams, 1997; Goodman et al., 2009).
The radii of the MAGMA GMCs range from 13 to 160 pc. The cumulative distribution
of the GMC radii is presented in Figure 3.17. The overall size distribution is relatively
featureless until R ∼ 50 pc, where it flattens slightly, before steepening sharply again
at R ∼ 80 pc. The size spectrum of GMCs in the NANTEN catalogue is also shown in
Figure 3.17; in contrast to the MAGMA data, the NANTEN size spectrum is relatively
smooth across the observed range of cloud sizes. Selection effects may therefore be
partially responsible for the kink in the MAGMA size spectrum, since the list of GMCs
that were not detected by CPROPS (or not targeted for observation) includes 7 clouds
with radii between 32 and 64 pc. An alternative interpretation is that the NANTEN
3.3. Properties of GMCs in the LMC
143
size spectrum may be artifically smooth, in the sense that its slope at large R reflects
the clustering of molecular clouds rather than the size distribution of individual GMCs.
The slope of the GMC size spectrum in the LMC is slightly steeper than in the Milky
Way, consistent with our previous conclusion that more of the molecular mass in the
LMC is located in small, low-mass structures.
Velocity Dispersion
The one-dimensional velocity dispersion of GMCs in the MAGMA catalogue ranges
from 1.0 to 6.1 km s−1 . The velocity dispersion is calculated over all the pixels within
a cloud, and hence includes fluctuations in the width of the individual line profiles as
well as variations in the velocity centroid across the projected cloud area. The velocity dispersion therefore reflects all the kinetic energy generated within a cloud by
dynamical processes such as rotation, turbulence and expansion. The velocity dispersion distribution for all 125 GMCs in the MAGMA catalogue is shown in Figure 3.18.
The MAGMA distribution is smooth over the observed range of σv values and appears
to be in good agreement with the distribution constructed from GMCs in the NANTEN
catalogue. While the velocity channels of the Mopra spectrometer are intrinsically narrow, the MAGMA velocity dispersion distribution is affected by incompleteness due
to a combination of the surface brightness criterion that was used to select MAGMA
targets (which is biased against large faint clouds) and the size-linewidth relation for
molecular clouds. The MAGMA catalogue may be missing GMCs with radii as large
as 64 pc: for a size-linewidth relation of the form σv ≈ 0.4R0.5 (Section 4.2), this implies that the MAGMA velocity dispersion distribution starts to be incomplete even at
σv = 3.2 km s−1 .
Peak CO Brightness
The maximum peak CO brightness, Tmax , of GMCs in the MAGMA catalogue ranges
from 1.2 to 7.1 K. As discussed in the preceding chapter, the CO emission in the LMC
is intrinsically weak. At the distance of the LMC, the peak CO brightness for the Orion
Chapter 3. Properties of MAGMA GMCs: I. Overview
log(N(σv’>σv)/Nclds)
144
0.0
−0.5
−1.0
−1.5
−2.0
−2.5
−0.5
0.0
0.5
1.0
log(σv/[km s −1])
Figure 3.18 The cumulative velocity dispersion distribution of GMCs in the MAGMA (black
line) and NANTEN (light grey line) catalogues (Fukui et al., 2008). The horizontal error bars
reflect
the uncertainty in the velocity dispersion measurements and vertical error bars represent
√
N counting errors.
3.4. Comparison with NANTEN GMCs
145
molecular cloud would be ∼ 20 K (Kutner et al., 1997), several times higher than what
we observe for any of the MAGMA GMCs. The Tmax distribution, which is shown in
Figure 3.19[a], is skewed towards lower values, peaking strongly around 2 K. The lack
of clouds with lower Tmax is not physical, but instead reflects our strategy of targeting
bright NANTEN GMCs for observation. The sensitivity limit of the MAGMA survey (see Section 2.4) and the signal-to-noise criteria that we impose for inclusion in the
MAGMA catalogue also contribute to the decreasing number of GMCs with Tmax < 2 K.
The maximum peak CO brightness is a measure of the emission from a single pixel
within a catalogued cloud. Although Tmax should trace conditions in the brightest
star-forming region within each GMC, it might not reflect the average conditions within
the GMC as a whole. The histogram in Figure 3.19[b] presents the distribution of the
average peak CO brightness, hTpk i, which we define as the average peak CO intensity
at the line centre for all the pixels within the projected area of the cloud. Overall, the
hTpk i values of the MAGMA clouds are ∼ 50 % lower than the corresponding values
of Tmax , and the upper tail of the hTpk i distribution is less pronounced. The hTpk i
and Tmax values for the MAGMA GMCs are well-correlated however (panel [c]), which
suggests that the hTpk i measurement is biased by the brightest pixels in the GMC. This
is not surprising since most MAGMA GMCs do not extend over an area larger than a
few resolution elements.
3.4 Comparison with NANTEN GMCs
In this section, we compare the properties of GMCs derived using the MAGMA data
with cloud property measurements for the same GMCs in the NANTEN catalogue
(Fukui et al., 2008).
We conduct this comparison using cloud properties derived
from the MAGMA data at 1.′ 0 and 0.53 km s−1 resolution, rather than convolving the
MAGMA data to the resolution of the NANTEN data (2.′ 6, 0.65 km s−1 ). Although
the latter approach would seem to constitute a fairer comparison between the datasets,
convolving the MAGMA data to the NANTEN resolution is not practical since the
146
Chapter 3. Properties of MAGMA GMCs: I. Overview
[a]
60
40
20
0
1
[b]
80
Number of GMCs
Number of GMCs
80
2
3
4
5
6
60
40
20
0
0.6
7
0.8
1.0
1.2
1.4
1.6
1.8
2.0
<Tpk> [K]
Tmax [K]
1.0
[c]
log(Tmax/[K])
0.8
0.6
0.4
0.2
0.0
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
log(<Tpk>/[K])
Figure 3.19 Frequency distributions of (a) the maximum peak CO brightness, Tmax , and (b)
the average peak CO brightness, hTpk i, of the MAGMA GMCs. In panel (c), Tmax is plotted
against hTpk i for all GMCs in the MAGMA catalogue (open squares) and GMCs in the high
quality subsample (filled grey circles). The vertical
√ error bars in panels [a] and [b] represent
counting errors. The error is calculated as σ = 1 + N + 0.75, where N is the number of clouds
in the bin.
3.4. Comparison with NANTEN GMCs
147
individual regions surveyed by MAGMA are small, and convolution with a Gaussian
smoothing kernel displaces emission beyond the boundaries of the MAGMA survey
region. Moreover, since CPROPS corrects the cloud property measurements for resolution and sensitivity bias, a comparison between the NANTEN and MAGMA datasets
provides an excellent opportunity to assess the accuracy of these corrections, using real
astronomical data rather than model cloud datasets.
Although the angular resolution of the MAGMA data is roughly five times higher than
the NANTEN data, approximately 75% of the NANTEN GMCs that were targeted
for observation demonstrate a one-to-one correspondence with a MAGMA cloud. Notable exceptions include the molecular ridge region, and the N11 and N44 star-forming
complexes (Henize, 1956). For both the MAGMA and NANTEN datasets, multiple
GMCs are identified in the molecular ridge and N11 regions, but the correspondence
between the identified objects is unclear. We therefore exclude GMCs in these regions
from our analysis in this Section. In the N44 region, by contrast, the single NANTEN
GMC LMC N J0522-6756 appears as nine individual clouds at MAGMA’s higher resolution. Typically, the NANTEN GMCs that resolve into multiple MAGMA structures
are large: the median radius of these NANTEN clouds is 64±17 pc (where 17 pc is the
median absolute deviation), compared to 34±11 pc for the NANTEN GMCs that show
a one-to-one correspondence with a MAGMA cloud.
In Figure 3.20[a], we plot the cloud radius as measured by MAGMA against the radius
as measured by NANTEN for all GMCs where there is a one-to-one correspondence between the catalogued clouds (filled circles). Cloud candidates that were excluded from
the MAGMA catalogue (i.e. the EERs) are also indicated in Figure 3.20 if they demonstrate an unambiguous correspondence to a NANTEN GMC. Equivalent plots for the
cloud velocity dispersion, CO luminosity, virial mass estimate, CO surface brightness
and CO-to-H2 conversion factor are shown in the other panels of Figure 3.20. For panels
[c] to [f], open square symbols represent NANTEN GMCs that are identified as multiple
GMCs in the MAGMA dataset. To calculate the equivalent MAGMA CO luminosity
and virial mass estimate of the resolved NANTEN GMCs, we sum the measurements
148
Chapter 3. Properties of MAGMA GMCs: I. Overview
1.0
log(σMAGMA/[km s−1])
log(RMAGMA/[pc])
[a]
2.0
1.5
1.0
[b]
0.5
0.0
0.5
0.5
1.0
1.5
2.0
0.0
[c]
6.5
log(MMAGMA/[Msol])
log(LMAGMA/[K km s−1 pc2])
5.5
5.0
4.5
4.0
3.5
1.0
[d]
6.0
5.5
5.0
4.5
4.0
3.0
3.5
3.0
3.5
4.0
4.5
5.0
3.5
5.5
log(LNANTEN/[K km s−1 pc2])
[e]
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
log(I(CO)NANTEN/[K km s−1])
4.0
4.5
5.0
5.5
6.0
6.5
log(MNANTEN/[Msol])
log(XMAGMA/[cm−2 (K km s−1)−1])
log(I(CO)MAGMA/[K km s−1])
0.5
log(σNANTEN/[km s−1])
log(RNANTEN/[pc])
[f]
21.5
21.0
20.5
20.0
20.0
20.5
21.0
21.5
log(XNANTEN/[cm−2 (K km s−1)−1])
Figure 3.20 Physical properties of NANTEN GMCs that have been observed by MAGMA,
plotted against the cloud properties derived from the MAGMA data. Panels [a] to [f] show the
GMC radius, velocity dispersion, CO luminosity, virial mass estimate, CO surface brightness
and CO-to-H2 conversion factor respectively. The filled grey circles indicate GMCs where
there is a one-to-one correspondence between a NANTEN GMC and a GMC in the MAGMA
catalogue. Open squares in panels [c] to [f] indicate NANTEN GMCs that are resolved into
multiple clouds at MAGMA’s higher resolution (see text). The small red squares indicate EERs,
i.e. objects identified in the MAGMA data that are excluded from the MAGMA catalogue due
to poor signal-to-noise and/or large measurements uncertainties. In each panel, the solid line
represents equality and the dashed lines indicate where the MAGMA measurement equals 50%
and 10% of the NANTEN value.
3.4. Comparison with NANTEN GMCs
149
of these quantities for the constituent MAGMA GMCs. The CO surface brightness and
CO-to-H2 conversion factor are estimated using a luminosity-weighted average of the
measurements for the constituent clouds.
Figure 3.20 shows that the NANTEN and MAGMA measurements of the GMC properties are remarkably consistent, despite the differences in resolution and sensitivity
between the two surveys. There is considerably more scatter between the NANTEN
and MAGMA measurements for the EERs, especially for the cloud radius. Many of
the EERs are intrinsically small, so it is possible that the NANTEN measurements
for these clouds are affected by beam dilution. By inspecting the CPROPS decomposition of the MAGMA data, however, we find that large discrepancies between the
MAGMA and NANTEN measurements for the total CO luminosity or cloud radius
usually indicate that a single NANTEN cloud has been resolved into two objects at
MAGMA’s higher resolution, one of which then fails to satisfy our criteria for inclusion
in the MAGMA catalogue. The NANTEN and MAGMA measurements also diverge
for a number of GMCs that exhibit extended low brightness emission surrounding a
compact high-brightness core. For these clouds, the CPROPS signal identification algorithm rejects the low brightness diffuse emission as being insufficiently distinct from
the background noise.
For GMCs where there is one-to-one correspondence between the NANTEN and MAGMA
cloud identification, the average ratio between the NANTEN measurement and the
MAGMA measurement is close to unity for all the cloud properties (see Table 3.3).
The cloud property that diverges most between the two datasets is the virial mass:
on average, the NANTEN estimates for Mvir are 40% higher than the corresponding
MAGMA values. For basic cloud properties – i.e. radius, velocity dispersion, CO luminosity – the dispersion in the ratio is ∼ 30%. For properties such as the CO surface
brightness that are calculated using a combination of these measurements, the dispersion increases to ∼ 50%. While the reported uncertainties are quite small for the GMCs
in both datasets, our analysis of model clouds in Section 3.2.2 suggests that a factor
of two variation is consistent with the accuracy of the CPROPS cloud identification
150
Chapter 3. Properties of MAGMA GMCs: I. Overview
Table 3.3 A comparison between the properties of GMCs in the LMC, as measured by NANTEN and MAGMA. The median ratio between the NANTEN measurement and the MAGMA
measurement, P , for each of the cloud properties is listed in the column 2. The quoted uncertainty is the median absolute deviation. The number of GMCs included in the comparison
is listed in the third column; only GMCs where there is one-to-one correspondence between a
NANTEN GMC and a MAGMA GMC are included. The duplicate entries for σv and LCO
include 9 extra NANTEN clouds that lack a measurement of their radius in the NANTEN
catalogue (i.e. they are unresolved by NANTEN).
Cloud Property
Radius [pc]
σv [ km s
−1
]
σv [ km s
−1
]
LCO [ K km s
LCO [ K km s
−1
C0 [ km s
XCO [ cm
−1
pc
−2
1.1 ± 0.2
53
1.1 ± 0.1
2
pc ]
1.3 ± 0.2
2
pc ]
1.2 ± 0.2
Mvir [M⊙ ]
−1
Nclds
1.2 ± 0.2
−1
ICO [ K km s
P
1.4 ± 0.4
]
−0.5
0.9 ± 0.3
]
(K km s
−1 −1
)
]
1.2 ± 0.3
1.2 ± 0.4
62
Notes
Includes unresolved NANTEN GMCs
53
62
Includes unresolved NANTEN GMCs
53
53
53
53
53
and decomposition methods. Finally, we note that our catalogue is generated from
MAGMA data that were obtained until the end of 2008, at which time a considerable
fraction of the survey fields had only been mapped once. Preliminary tests indicate
that the agreement between the MAGMA and NANTEN cloud property measurements
should improve for the final cloud catalogue, which will be generated from the complete
MAGMA dataset (Wong et al, in preparation).
3.5 Physical properties of GMCs without Star Formation
Molecular clouds have traditionally been modelled as quasi-equilibrium structures, but
recent theoretical work has also begun to explore whether molecular clouds might form
and disperse more rapidly as a consequence of large-scale dynamical events in the ISM,
such as turbulent flows or cloud collisions (e.g. Bergin et al., 2004; Tasker & Tan, 2008).
Observational constraints on the physical properties of recently formed GMCs would
be a useful contribution to the debate about GMC lifetimes, but it remains unclear
3.5. Physical properties of GMCs without Star Formation
whether observations of
12 CO(J
151
= 1 → 0) emission alone can distinguish between
younger and more evolved GMCs. While it is plausible that some potential characteristics of newly formed GMCs, such as colder gas temperatures, stronger bulk motions or
sparser CO filling factors, would have observational signatures, it is also possible that
the onset of widespread
12 CO(J
= 1 → 0) emission occurs late in the cloud assembly
process, or that physical conditions in the CO-emitting regions of GMCs are relatively
uniform and therefore insensitive to a cloud’s evolutionary state. In this section, we
investigate whether there are significant differences between the properties of young
GMC candidates and other GMCs in our catalogue.
We constructed a sample of young GMC candidates using the evolutionary classification scheme designed by Kawamura et al. (2009) for the 272 GMCs in the NANTEN
LMC catalogue (Fukui et al., 2008). Kawamura et al. (2009) classified GMCs on the
basis of their association with H II regions and young stellar clusters, finding 72 Type I
GMCs that show no association with massive star-forming phenomena. An important
assumption behind this approach is that all GMCs eventually form stars and are finally
dissipated by their stellar offspring; in this scenario, GMCs without signs of massive
star formation may be considered young. By the end of 2008, MAGMA had observed
30 Type I NANTEN GMCs, but there are only 17 MAGMA clouds associated with
these Type I GMCs that satisfy our criteria for inclusion in the MAGMA catalogue:
henceforth, we refer to these 17 MAGMA clouds as the “young GMC sample” or the
“non-star-forming GMCs”.
The 17 clouds in the young GMC sample correspond to 16 NANTEN GMCs: 15 of the
17 MAGMA clouds demonstrate a one-to-one correspondence with a Type I GMC in
the NANTEN catalogue, while the other NANTEN GMC divides into two clouds at
MAGMA’s finer resolution. CPROPS identifies 10 more objects in the MAGMA data
that are associated with a further 8 NANTEN Type I GMCs, but these objects either
have S/N < 5 and/or measurement errors that exceed 20%, and are therefore excluded
from the MAGMA catalogue. CPROPS does not identify any significant emission in
the MAGMA data for the remaining six NANTEN Type I GMCs. We do not attempt
152
Chapter 3. Properties of MAGMA GMCs: I. Overview
to re-classify the MAGMA clouds according to the criteria developed by Kawamura
et al. (2009), but simply ascribe the evolutionary classification of the NANTEN GMC
to any MAGMA cloud that is coincident in space and velocity. This classification should
be reliable for clouds in the young GMC sample since their projected areas are always
smaller than, and contained within, the corresponding NANTEN GMC boundary.
To verify that differences between the properties of star-forming and non-star-forming
GMCs are not due solely to variations in the cloud size, we constructed a control sample with the same size distribution as the young GMC sample by matching each of the
17 young GMC candidates with three star-forming clouds in the MAGMA catalogue
of a similar radius. The control sample therefore contains 51 clouds. Kawamura et al.
(2009) found that young GMCs in the NANTEN catalogue tend to be smaller than
star-forming GMCs, but here we wish to determine whether there are differences between star-forming and non-star-forming GMCs that persist even after variations in
cloud size are suppressed. This precaution is important because our experiments with
model clouds in Section 3.2.2 showed that the properties of small clouds may be systematically offset from the measurements for larger clouds, simply as a result of the
methods that we use to identify and parameterise GMCs. The average discrepancy
between the radius of a young GMC candidates and their three corresponding control
clouds is 2%, with a maximum discrepancy of 8%. The average properties of GMCs in
the MAGMA catalogue, the young GMC sample and the control sample are listed in
Table 3.4.
To test whether young GMCs have distinct physical properties, we conducted KolmogorovSmirnov (KS) tests between the young GMC sample and the control sample. The KS
test is a non-parametric test that compares the cumulative distribution functions of
two samples in order to determine whether there is a statistically significant difference
between the two populations. The test is reliable when the effective number of data
points, Ne ≡
N1 N2
N1 +N2 ,
is greater than 4, where N1 and N2 are the number of data
points in the first and second samples. The result of the KS test can be expressed as
a probability, P , that the sample distributions are drawn from the same underlying
3.5. Physical properties of GMCs without Star Formation
153
Table 3.4 Average physical properties of the MAGMA clouds and results of the KS tests for
the young GMC sample. Columns 2 to 4 list the median and median absolute deviation of the
cloud properties for GMCs in the MAGMA catalogue, the young GMC sample and the control
sample respectively. Column 5 lists the median P value obtained in the error trials, and column
6 lists the standard deviation of the P values in the trials (see text).
Cloud Property
R (pc)
σv ( km s−1 )
hTpk i (K)
Tmax (K)
LCO (104 K km s−1 pc2 )
Mvir (105 M⊙ )
Axis Ratio, Γ
ΣH2 (M⊙ pc−2 )
ICO (K km s−1 )
−1
XCO ( cm−2 (K km s−1 ) )
VLSR ( km s−1 )
Rgal (kpc)
N (H I) (1021 cm−2 )
Σ∗ (M⊙ pc−2 )
G0 /G0,⊙
Tpk (HI) (K)
Ph /kB (104 K cm−3 )
MAGMA
28±8
2.3±0.5
1.1±0.1
2.2±0.4
1.2±0.6
1.5±0.9
1.7±0.4
55±22
4.8±1.5
4.7±1.6
255±22
1.8±0.9
2.7±0.7
48±24
1.7±0.5
68±10
6.4±2.5
Young GMCs
30±8
2.4±0.7
1.0±0.1
1.7±0.2
1.2±0.5
1.7±1.0
1.5±0.2
73±21
4.3±0.8
6.9±2.3
248±18
2.3±0.9
2.7±0.4
50±16
1.3±0.5
51±10
6.4±0.9
Control
30±7
2.1±0.5
1.1±0.1
2.3±0.4
1.2±0.5
1.5±0.8
1.8±0.4
52±23
4.6±1.3
5.4±2.0
256±23
1.8±0.8
2.7±0.7
42±19
2.0±0.6
68±8
5.5±2.1
hP i
0.96
0.54
< 0.01
< 0.01
0.89
0.78
0.25
0.13
0.78
0.06
0.18
0.43
0.66
0.25
< 0.01
< 0.01
0.54
σ(P )
0.05
0.18
< 0.01
< 0.01
0.11
0.18
0.10
0.10
0.15
0.05
0.00
0.00
0.18
0.10
< 0.01
< 0.01
0.18
154
Chapter 3. Properties of MAGMA GMCs: I. Overview
distribution. As the traditional KS test does not account for uncertainties in the measurements of the cloud properties, we performed 1000 trials of each KS test. For each
trial, the value of each cloud property measurement was displaced by k∆x, where ∆x
is the absolute uncertainty in the cloud property measurement and k is a uniformly
distributed random number between -1 and 1. A summary of the KS test results is
shown in Table 3.4. If the results of the error trials are narrowly distributed around
zero – i.e. if hP i ≤ 0.05 and σ(P ) ≤ 0.05, where σ represents the standard deviation
– we consider that there is statistically significant evidence against the null hypothesis
that the cloud samples are drawn from the same underlying population.
Table 3.4 shows that the properties of both the young GMC and the control sample
show a large dispersion around their average value, and that differences between the
samples are not always obvious from measures of central tendency. The results of the
KS tests indicate that the null hypothesis cannot be rejected for many of the intrinsic
cloud properties. Both the maximum peak CO brightness (Tmax ) and the average peak
CO brightness (hTpk i) tend to be lower for young GMCs. Since this result holds for the
comparisons with the entire MAGMA catalogue and the control sample, we consider
this to be genuine difference, and not just the result of beam dilution for smaller clouds.
It is notable that there is no significant difference between the distributions of the total
CO luminosity (LCO ) or CO surface brightness (I(CO)), despite the differences in Tmax
and hTpk i.
The median XCO value for the young GMC sample is 6.9 × 1020 cm−2 (K km s−1 )−1 ,
∼ 50% greater than the median XCO value for the entire MAGMA catalogue. Some of
this variation may be due to cloud size, since the discrepancy is reduced once we restrict our comparison to the control sample. Yet some of the difference in XCO may be
genuine: our tests in Section 3.2.2 indicated that XCO measurements for small clouds
tend to biased towards lower, not higher, values. Our estimate of XCO for each GMC
is derived from the ratio between its virial mass and CO luminosity, assuming that the
GMCs achieve virial equilibrium. A higher mean value of XCO for non-star-forming
clouds could signify that their CO emission is underluminous compared to star-forming
log(ΣSFR/[Msol yr−1 kpc−2])
3.5. Physical properties of GMCs without Star Formation
155
1
0
−1
−2
−3
0.0
log(α =
0.5
1.0
5σ2R/GM
CO)
Figure 3.21 The star formation rate surface density of MAGMA GMCs, plotted as a function
of their virial parameter. GMCs belonging to the complete MAGMA catalogue are represented
by small open squares, and GMCs in the high quality subsample are indicated using filled
grey circles. The blue cross symbols represent GMCs without signs of active high-mass star
formation. The virial parameter is calculated using the mass estimate derived from a cloud’s
CO luminosity, assuming XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 .
GMCs, or that they are less virialised than their star-forming counterparts (or a combination of both effects). The KS test results indicate that the difference between XCO
for the young GMCs and the control sample is only marginally significant, but the
result merits attention since recent studies in the LMC molecular ridge (Indebetouw
et al., 2008) and M83 (Muraoka et al., 2009) have reported an anti-correlation between
the virial parameter, α ≡ 5σ 2 R/GM , and star formation activity on smaller (∼ 10 pc)
and larger scales (∼ 500 pc) than the GMCs studied here. We find no evidence of for
a general anti-correlation between α and ΣSF R for the MAGMA GMCs (Figure 3.21).
For properties of the local interstellar environment, young GMCs appear to be distributed throughout the LMC in a similar fashion as star-forming GMCs (i.e. across a
similar range of galactocentric radii and radial velocities), and they are detected across
a comparable range of stellar mass surface densities and H I column densities. There
156
Chapter 3. Properties of MAGMA GMCs: I. Overview
is a clear trend, however, for young GMCs to be located in regions where the H I peak
brightness (Tpk (HI)) is low, and the radiation field (G0 ) is weak. As discussed in the
previous chapter, lower values of Tpk (HI) may reflect sightlines with a higher filling
fraction of cold atomic gas, or an increased optical depth in the cold phase due to
higher densities and/or lower kinetic temperatures (Table 2.5). Lower G0 values for
non-star-forming GMCs may reflect the fact that young massive stars are a significant
source of dust heating in LMC molecular clouds (see also Section 3.7.3).
3.6 Velocity Gradients
Molecular clouds can present coherent velocity gradients over spatial scales up to several
tens of parsecs (see e.g. Phillips, 1999, and references therein). Mechanisms that could
be responsible for cloud velocity gradients include local events – e.g. stellar winds, infall
and non-uniform magnetic fields – and galactic scale processes, such as shear within
a differentially rotating disk. Previous studies have interpreted velocity gradients as a
signature of cloud rotation, which potentially plays a significant role in GMC stability
and evolution (Blitz, 1990). In the Milky Way and the few nearby galaxies where GMC
gradients have been systematically investigated, the typical magnitude of the gradients
is ∼ 0.1 km s−1 pc−1 (e.g. Rosolowsky et al., 2003; Koda et al., 2006). There is some
evidence for preferential alignment between the spin axes of molecular clouds and the
rotation axis of the host galaxy (e.g. Phillips, 1999; Rosolowsky et al., 2003), hinting
that the angular momentum of the cloud’s progenitor gas may be partially preseved
during the cloud formation process. However other analyses of cloud velocity gradients
have concluded that their rotation axes are randomly oriented (e.g. Koda et al., 2006).
To construct a map of the line-of-sight velocity field for each MAGMA GMC, we calculated the intensity-weighted velocity centroid at each (x, y) position within the projected
area of a cloud with I(CO) > 2 K km s−1 . As CO emission is usually only present in
a small number of velocity channels along any line-of-sight, we calculated the velocity
centroids using a masked version of the MAGMA data. More precisely, a blanking mask
was constructed using the smooth-and-mask technique described in Chapter 2, i.e. the
3.6. Velocity Gradients
157
MAGMA data cube is smoothed to 90′′ resolution, pixels with emission less than than
three times the RMS noise level of the smoothed cube are blanked, and the mask is then
transferred back to the original data cube. We verified that the velocity centroid maps
that we constructed using this procedure were similar to those obtained using other
common masking methods, e.g. extracting a narrow range of velocity channels around
the CO line peak or blanking pixels below a certain brightness threshold in the original
cube. Example velocity centroid maps for six MAGMA GMCs are shown in Figure 3.22.
Following Goodman et al. (1993), we estimate the uncertainty at each pixel in the
velocity centroid map ∆vc as
∆vc = 1.15
σRM S
Tpk
√
w∆V ,
(3.6)
where σRM S is the RMS noise of the (unmasked) spectrum, Tpk is the peak brightness
of the CO line profile, w = 0.53 km s−1 is the velocity resolution, and ∆V is the FWHM
linewidth. This estimate for ∆vc assumes that the CO line profiles are Gaussian, which
is usually the case. Across the MAGMA survey region, the average uncertainty in the
velocity centroid measurements is only ∼ 0.4 km s−1 , i.e. less than the width of a single
velocity channel. The masking process that we used to construct the velocity centroid
maps introduces an additional source of uncertainty to the vc values that is not easily
quantified. The true uncertainty is likely to be greater than the ∆vc values obtained
from Equation 3.6.
To estimate the velocity gradient across each cloud, we fit the velocity centroid map
with a function representing a plane, i.e.
vc = v0 + a∆x + b∆y .
(3.7)
In this equation, v0 is the systemic radial velocity of the cloud, ∆x and ∆y are the map
offsets in right ascension and declination expressed in arcseconds, and a and b are the
projections of the velocity gradient along the RA and Dec axes. The magnitude and
158
Chapter 3. Properties of MAGMA GMCs: I. Overview
Figure 3.22 Example velocity centroid maps for six MAGMA GMCs. The grey boxes indicate the regions that we use to calculate and verify the velocity gradient in the surrounding
atomic gas. The black contours represent the CO integrated intensity measured by MAGMA,
in 2 K km s−1 intervals.
3.6. Velocity Gradients
159
direction of the velocity gradient can then be written in terms of the coefficients a and
b,
G = |∇vc | = k
p
a2 + b2
(3.8)
a
.
b
(3.9)
and
Φ = tan−1
For this analysis, we assume that the disk of the LMC is viewed face-on and that the
map pixels have constant spatial dimensions across the LMC. The coefficient k = 0.243
in Equation 3.8 is the spatial scale corresponding to 1′′ at the distance of the LMC.
Φ represents the direction of increasing velocity and is measured anticlockwise from
North (Φ = 0◦ ).
For each velocity centroid map, we determined an outlier-resistant fit to Equation 3.7
using the routine rob mapfit from the IDL Astronomy Library. This procedure performs a regular least-squares fit to obtain an initial estimate, calculates the bisquare
weights, then iterates until the fit converges. We estimate the errors on the fitted
parameters using a bootstrap technique, generating 500 trial versions of each velocity
centroid map. The trial maps are constructed by sampling f × N pixels of the original
map, where f is a uniform random number between 0.3 and 1.0, and N is the original
number of map pixels. We obtain the best-fitting plane to each of the trial maps using
rob mapfit, and use the variance of the parameters obtained from the trial fits to estimate the uncertainty in our original fit. The final uncertainty on each fitted parameter
√
is the standard deviation of the trial values multiplied by the oversampling factor n,
where n = 50 is the number of pixels per resolution element in our velocity centroid
maps. The advantages of a robust regression method in our case is that the velocity
centroid maps often contain a small but non-negligible fraction of pixels with highly
discrepant values that would bias a classical least-squares estimator. The disadvantages
are that measurement uncertainties in the velocity centroid values are not taken into
account, and that errors on the fitted parameters cannot be derived analytically. As
a check on our results, we performed a Leverberg-Marquardt least-squares fit to the
velocity centroid maps, as implemented in the mpfit2dfun IDL routine (Markwardt,
160
Chapter 3. Properties of MAGMA GMCs: I. Overview
2009). The mpfit2dfun procedure was quite sensitive to outliers, and failed to converge for ∼ 50% of the MAGMA velocity centroid maps. For maps where mpfit2dfun
terminated successfully, the best-fitting parameters agreed with the rob mapfit results
to within 15% for the magnitude and 10% for the direction of the derived velocity
gradients.
In addition to the magnitude and direction of the best-fitting velocity gradient and
their uncertainties, we calculated the reduced χ2 and a robust estimate for the standard deviation of the fit residuals σres in order to evaluate goodness-of-fit. We found
that a low value for the fit residuals, σres ≤ 1.5 km s−1 , in combination with a minimum number of map pixels used to calculate the fit (Npix ≥ 100), were efficient criteria
for identifying credible velocity gradients. For the MAGMA clouds that satisfy these
criteria, the reduced χ2 values that we obtained were rather high (hχ2 i ∼ 12). This
is probably due to the presence of outliers in the velocity centroid maps that are not
accurately reflected in our estimate for the uncertainty (Equation 3.6).
For over half the GMCs in the MAGMA catalogue with velocity maps containing more
than 100 pixels, the fit residuals are large (σres > 1.5 km s−1 ), and visual inspection
confirms that a plane is not a good representation of the velocity field. Several of the
poor fits correspond to faint clouds where the velocity centroid map is dominated by
artefacts. However, the majority of poor fits are caused by genuine complex structure
in the velocity centroid maps that is not well-represented by a plane; examples are
shown in panels [c] and [e] of Figure 3.22. For these clouds, it seems likely that the
line-of-sight velocity field reflects localised rather than large-scale processes. The large
percentage of MAGMA GMCs that do not exhibit a linear gradient should be kept in
mind when interpreting the velocity gradients that are detected.
The results of fitting Equation 3.7 to the velocity centroid maps of the 54 MAGMA
GMCs and 11 EERs where a velocity gradient was detected are presented in Appendix 3.C (Table 3.9). A histogram of the G values is shown in Figure 3.23[a]. The
magnitude of the velocity gradients range between 0.01 and 0.64 km s−1 pc−1 with a
3.6. Velocity Gradients
161
median value of 0.09 km s−1 pc−1 , comparable to the results obtained for Milky Way
molecular clouds (e.g. Blitz, 1993; Phillips, 1999). Seventy percent of the observed
velocity gradients are significant in the sense that the relative uncertainty in the fitted magnitude is less than 40%. The steeper velocity gradients that we detect (i.e.
& 0.3 km s−1 pc−1 ) tend to be associated with smaller clouds and have larger uncertainties (Figure 3.23[b]). We note that a velocity gradient of only 0.1 km s−1 pc−1
will contribute 1.5 km s−1 of line broadening within a 1.′ 0 beam at the distance of the
LMC. Figure 3.23[c] shows that the systematic shift in the velocity centroid of the
CO emission line across the MAGMA GMCs contributes a significant fraction of their
measured velocity dispersion, especially for large clouds. This implies that the process
that is responsible for the observed velocity gradient makes a dominant contribution
to the cloud’s total kinetic energy, although we argue in Section 3.7.4 that it is unclear
whether cloud gradients in the LMC are due to uniform rotation or whether they are
a signature of a different physical process such as large-scale gas flows.
The cloud velocity gradients are distributed through all directions on the sky (Figure 3.23[d]). There is some suggestion that the velocity gradients tend to be aligned
along the north-south axis (Φ = 0 or 180◦ ) rather than the east-west axis (Φ = 90 or
270◦ ). To test this, we generated 500 realisations of a uniform random distribution,
and conducted a KS test between the observed distribution of the velocity gradient
orientations and each trial distribution. A probability that they were drawn from the
same parent population of less than 0.1 (P < 0.1) occurred for only 18 trials, indicating
that a random orientation for the velocity gradients is not strongly excluded.
If the observed velocity gradients are due to cloud rotation, then the direction of the
velocity gradient is related to the rotation axis of the GMC Φω via Φ = Φω + 90◦ . The
magnitude of the velocity gradient reflects the angular velocity of the GMC ω projected
onto the plane of the sky, i.e.
G = |ω| sin i ,
(3.10)
where i is the inclination of the rotation axis relative to the line-of-sight. If the spin
Chapter 3. Properties of MAGMA GMCs: I. Overview
Number of GMCs
30
[a]
25
20
15
10
5
Gradient [km s−1 pc−1]
162
[b]
0.8
0.6
0.4
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
2.0
1.0
0.5
0.0
3.5
[d]
25
20
15
10
5
−0.5
−0.2
3.0
30
[c]
1.5
2.5
log(Number of map pixels)
Number of GMCs
log(G x R / [km s−1])
Gradient [km s−1 pc−1]
0.0
0.2
0.4
0.6
0.8
log(σv / [km s−1])
1.0
0
100
200
300
Gradient Direction [degrees]
Figure 3.23 (a) Frequency distribution of the magnitudes of the velocity gradients determined
for MAGMA GMCs. (b) The magnitude of the velocity gradient plotted as a function of the
number of pixels in the velocity centroid map for each GMC. Our gridding strategy corresponds
to ∼ 50 map pixels per resolution element for the reduced MAGMA data subcubes. (c) Velocity shift across each GMC, plotted as a function of its velocity dispersion. (d) Frequency
distribution of the position angles of the velocity gradients. For panels (a) and (d), the open
black histogram indicates the distribution for all the measured velocity gradients; the filled grey
histogram indicates clouds where the relative uncertainty in the gradient magnitude is less than
40%. In panels (b) and (c), filled (open) circles represent clouds where the uncertainty in the
velocity gradient magnitude is less (more) than 40%.
3.6. Velocity Gradients
163
axes of all the GMCs were perpendicular to the plane of the LMC’s gas disk, which is
inclined to the line of sight by ∼ 55◦ (van der Marel et al., 2002), then the observed
G values should be increased by a factor of 1.7 to obtain the intrinsic angular velocity of the GMCs. This configuration might be expected if the rotation of individual
clouds were determined solely by galactic shear, but it is likely that the orientations
of the rotation axes are altered to some degree by e.g. magnetic field irregularities
and/or local dynamical processes during a cloud’s evolution. If the cloud spin axes are
randomly oriented, then G provides only a lower limit to the angular velocity of any individual cloud but for the GMC ensemble we would expect < G/ sin i >= (4/π) < G >
(e.g. Chandrasekhar & Münch, 1950). Lacking any empirical constraints on the orientation of the GMC rotation axes, we assume sin i = 1 for all the clouds in our sample.
We do not find a correlation between the magnitude of the velocity gradient and the
axis ratio of the clouds, nor a correlation between the direction of the velocity gradient
and the position angle of the GMC major axis (see Figure 3.24). Correlations between
these properties might have been expected if rotation played an important role in determining cloud shapes, e.g. if molecular clouds were deformed through centrifugal stress.
The absence of such correlations suggests that only a small fraction of a cloud’s total
energy is associated with rotation, and is at odds with the contribution of the velocity
gradients to the cloud linewidths that we measure. The histogram in Figure 3.24[b]
gives the impression that velocity gradients are less likely to be aligned with the minor axis of a GMC. As before, we tested the significance of this result by conducting
KS tests between random uniform distributions and the observed distribution of the
difference between the morphological and velocity gradient position angles. P < 0.1
was obtained for 65 out of 500 trials, suggesting that the deficit of clouds at ∼ 90◦ in
Figure 3.24[b] is not highly significant.
The location of GMCs with measured velocity gradients and the orientation of their
gradients are shown in Figure 3.25. Although we do not detect a globally preferred
orientation for the GMC velocity gradients, Figure 3.25 suggests some coherence of
the velocity gradients on smaller scales, especially within the stellar bar, the molecular
164
Chapter 3. Properties of MAGMA GMCs: I. Overview
0.8
Number of GMCs
Gradient [km s−1 pc−1]
25
0.6
0.4
0.2
20
15
10
5
0.0
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Major−to−minor axis ratio
0
20
40
60
80
| PA(Major Axis) − φ | [degrees]
Figure 3.24 (a) The magnitude of the cloud velocity gradient, plotted as a function of the
cloud’s major-to-minor axis ratio. Filled (open) circles represent clouds where the uncertainty
in the velocity gradient magnitude is less (more) than 40%. (b) Frequency distribution of
the difference between the position angle of the cloud’s major axis and the direction of its
velocity gradient. The open black histogram indicates the distribution for all the measured
velocity gradients; the filled grey histogram indicates clouds where the relative uncertainty in
the gradient magnitude is less than 40%.
arc and in the north-west of the LMC. This may be a sign that the velocity gradients
within molecular clouds are connected to the kinematics of the local ISM. To explore
this possibility further, we compare the magnitude and direction of the GMC velocity
gradients to the velocity gradient in the surrounding atomic gas using the H I survey of
the LMC by Kim et al. (2003a). We calculate the intensity-weighted velocity centroid
of the H I emission at each pixel within a 2R × 2R box centred on each GMC (see e.g.
Figure 3.22), where R is the radius of the GMC. We then determine the magnitude
and direction of the velocity gradient in the local atomic gas using the same procedure
that we applied to the MAGMA CO data. The fitted gradients are sensitive to the size
of the area that is used to derive the best-fitting plane to the local H I velocity field: in
particular, we note that the average magnitude of the gradients decreases by a factor
of two when the width of the box is increased from 2R to 6R. To ensure that our
estimates for the local atomic gas gradient are reliable, we reject gradients where the
magnitude varies by more than 100% or the direction varies by more than 90◦ when
the size of the box width is increased from 2R to 4R.
3.6. Velocity Gradients
165
Figure 3.25 A map of the H I column density in the LMC, overlaid with vectors representing
the direction of cloud velocity gradients. The blue (grey) vectors represent clouds where the
uncertainty in the velocity gradient magnitude is less (more) than 40%. The dark grey ellipse
indicates the stellar bar region.
166
Chapter 3. Properties of MAGMA GMCs: I. Overview
There are 32 catalogued GMCs and 5 EERs where the velocity gradient in both the
molecular cloud and local atomic gas are well-determined. The distribution of the difference between the position angles of the H I and CO velocity gradients (|ΦHI − ΦCO |)
is presented as a histogram in Figure 3.26[a], revealing a weak tendency for the velocity
gradients in the two gas phases to be aligned. 89 of 500 KS tests between the observed
distribution and different realisations of a uniform random distribution return P < 0.1;
this is not highly significant, but it is more than we obtain when comparing two random distributions (for which 35 of 500 trials return P < 0.1). Figure 3.26[b] shows that
the magnitudes of the cloud velocity gradients are comparable to the gradient in the
surrounding gas. This is distinct from the situation in M31, where the GMC velocity
gradients are greater than the local gradient by a factor of ∼ 3 on average (Rosolowsky,
2007).
Figure 3.26[b] suggests that the magnitudes of the H I and CO velocity gradients tend
to converge when the gradients are aligned within ∼ 50◦ . We find that steeper CO
and H I velocity gradients are preferentially associated with larger |ΦHI − ΦCO | values
(panels [c] and [d] of Figure 3.26): since steeper cloud velocity gradients tend to occur
for smaller clouds and larger uncertainties, we might therefore expect less scatter in
GHI − GCO for larger clouds. It is not immediately obvious, however, why the alignment
of the H I and CO velocity gradients should also be correlated with the cloud size (see
Figure 3.27). We discuss possible explanations for this result in Section 3.7.4. At minimum, our analysis provides evidence that GMCs in the LMC are not entirely decoupled
from the kinematics of the local interstellar gas.
3.7 Discussion
3.7.1
The CO-to-N(H2 ) Conversion Factor
Line emission of CO is a common and practical tracer of molecular hydrogen H2 , the
major chemical constituent of GMCs. Observations of GMCs in the Milky Way suggest
that there is a good correlation between their average
12 CO(J
= 1 → 0) integrated
167
[a]
Number of Clouds
20
15
10
GHI − GCO [km s−1 pc−1]
3.7. Discussion
1.0
[b]
0.5
0.0
−0.5
5
−1.0
0
50
100
150
0
| φCO − φHI | [degrees]
[c]
1.0
0.8
0.6
0.4
0.2
0.0
−0.2
100
150
1.2
[d]
1.0
GHI [km s−1 pc−1]
GCO [km s−1 pc−1]
1.2
50
| φCO − φHI | [degrees]
0.8
0.6
0.4
0.2
0.0
0
50
100
150
| φCO − φHI | [degrees]
−0.2
0
50
100
150
| φCO − φHI | [degrees]
Figure 3.26 (a) Frequency distribution of the difference between the position angle of the
velocity gradient in a molecular√
cloud and the surrounding atomic gas (see text). The error on
each bin is calculated as σ = 1+ N + 0.75, where N is the number of clouds in the bin. (b) The
difference between the magnitudes of the CO and H I velocity gradients, plotted as a function
of the difference in their orientation |ΦHI − ΦCO |. (c) Correlation between the magnitude of
the molecular cloud (i.e. CO) velocity gradient and |ΦHI − ΦCO |. (d) Correlation between the
magnitude of the local atomic velocity gradient and |ΦHI − ΦCO |.
Chapter 3. Properties of MAGMA GMCs: I. Overview
| φCO − φHI | [degrees]
168
rcat = (−0.53,<0.01)
rall = (−0.41,0.01)
150
100
50
0
1.0
1.2
1.4
1.6
1.8
2.0
log(Radius/[pc])
Figure 3.27 The difference in position angle between the cloud velocity gradient and the velocity
gradient in the surrounding atomic gas, plotted as a function of the cloud radius. GMCs in the
MAGMA catalogue are plotted with filled circles, and EERs are plotted as open circles. The
Spearman correlation coefficient and its significance is shown in the upper left for all clouds
(rall ) and for catalogued GMCs (rcat ).
intensity, I(CO), and mean H2 column density, N (H2 ):
N (H2 ) [ cm−2 ] = XCO I(CO) [ K km s−1 ] ,
(3.11)
where XCO is the CO-to-H2 factor to be empirically calibrated. Since H2 in GMCs
cannot be observed directly, several methods have been used to infer N (H2 ) for nearby
GMCs, including measurements of the γ-ray flux produced by interactions between
cosmic rays and protons (e.g. Strong & Mattox, 1996), excitation analyses of multiple molecular line transitions (e.g. Carpenter et al., 1990), and observations of the
emission from dust in GMCs (e.g. Schloerb et al., 1987). The values of XCO derived by these methods are generally in good agreement with those obtained by assuming that GMCs are in virial equilibrium, so it has become common to estimate
XCO for GMCs in more distant systems using the ratio between their virial mass
estimate and their CO luminosity.
Recent studies that have used a virial analy-
sis to estimate XCO for extragalactic GMC populations have obtained XCO values
3.7. Discussion
169
between 4.0 and 7.0 × 1020 cm−2 (K km s−1 )−1 , (e.g. B08, Blitz et al., 2007; Fukui
et al., 2008), which are quite close to the values estimated for Galactic clouds (XCO =
1.8 − 3.5 × 1020 cm−2 (K km s−1 )−1 , e.g. Strong & Mattox, 1996).
The median XCO factor of all the MAGMA GMCs, derived using the virial theorem, is
4.7±1.4×1020 cm−2 (K km s−1 )−1 , where the quoted uncertainty is the median absolute
deviation. Strictly, the virial mass estimate Mvir = 1040Rσv2 that we have used only
applies to spherical clouds with a truncated ρ ∝ R−1 density profile, so some variation
in XCO may be due to differences in the shape and internal density distribution of the
GMCs. The magnitude of the corresponding XCO variations should be small however.
For cloud with a uniform density profile, the true virial mass will be greater than our
estimate by 10%, while the virial mass of a cloud with a ρ ∝ R−2 density profile will be
lower than our estimate by 30%. The shape-dependent correction factor to the virial
mass for the range of major-to-minor axis ratios exhibited by the MAGMA GMCs (1.0
to 4.6) also diverges from unity by . 10% (see figure 2 of Bertoldi & McKee, 1992).
Empirically, the most reliable estimates for XCO will be obtained for the well-resolved,
round clouds. For MAGMA GMCs with R > 25 pc and major-to-minor axis ratios
less than 2, the median XCO is 4.3 ± 0.8 × 1020 cm−2 (K km s−1 )−1 , consistent with the
value obtained from the entire GMC sample.
Despite the agreement between the XCO values obtained for GMCs in the Milky Way
and other nearby galaxies using the virial theorem, it should be noted that cloud property measurements of extragalactic GMCs using alternative techniques often obtain
masses (and hence XCO values) that diverge significantly from the results of a virial
analysis. Studies in the Magellanic Clouds that have measured cloud properties using
far-infrared or sub-millimetre dust continuum emission, for example, have yielded H2
masses that are much higher than the virial mass derived from the velocity dispersion
and spatial extent of the CO emission (e.g. Israel, 1997; Rubio et al., 2004; Leroy et al.,
2007a). The most common physical interpretation of these results is that the CO emission arises from dense clumps that are embedded within a much more extensive H2
cloud. Selective photodissociation of CO molecules should be more effective in environ-
170
Chapter 3. Properties of MAGMA GMCs: I. Overview
7.0
[a] m = 1.0
log(Mvir/[Msol])
log(Mvir/[Msol])
7.0
6.5
6.0
5.5
5.0
4.5
[b] m = 0.7
6.5
6.0
5.5
5.0
4.5
3
4
5
log(LCO/[K km
6
s−1
pc2])
3
4
5
log(LCO/[K km
6
s−1
pc2])
Figure 3.28 The correlation between LCO and Mvir for 100 model clouds with randomly generated radii and velocity dispersions. We generate a (R,σv ) pair for each ‘cloud’ by drawing from
uniform random distributions of R and σv values. The values of LCO and Mvir are then calculated according to common approximations, Mvir = 1040Rσv2 and LCO = π(2π)1/2 hTpk iR2 σv ,
assuming hTpk i = 2 K. The dashed line in each panel represents a linear relationship, and the
solid line represents an ordinary least squares fit to the data. The slope of the fit m is indicated
in the top left corner of each panel. In panel [a], the R values are selected from a random
distribution with a lower (upper) limit of 15 pc (50 pc); in panel [b], the upper limit of the R
values is extended to 150 pc. The range of σv values in both panels is 1 to 6 K km s−1 . Strong
correlations between LCO and Mvir arise due to their mutual dependence on R and σv , i.e. we
have made no assumptions about the dynamical state of the model clouds, nor have we imposed
any relationship between R and σv .
ments where the dust-to-gas ratio is low, so the size of the CO-dark H2 envelope relative
to the CO-emitting regions should increase for GMCs in low-metallicity environments
such as the Magellanic Clouds (e.g. Bolatto et al., 1999). Observational confirmation
of the presence and size of CO-dark H2 envelopes remains an active area of research
(e.g. Leroy et al., 2009a; Roman-Duval et al., 2010).
For extragalactic GMC populations, it therefore remains uncertain whether a correlation between the CO luminosity and virial mass estimate of molecular clouds provides
a reliable estimate for XCO . In particular, we note that LCO (≈ π(2π)1/2 hTpk iR2 σv )
and Mvir are both functions of R and σv , so even random distributions of R and σv
values will yield a strong correlation between log(LCO ) and log(Mvir ), with a slope that
depends on the dynamic range in R and σv (Figure 3.28). Under these circumstances,
there would seem to be no guarantee that Mvir traces the underlying H2 mass, so the
3.7. Discussion
171
physical significance of an XCO value determined solely from a virial analysis is not
clear.
3.7.2
Comparison with Previous Results
It is well-established that star formation in galaxies is intimately connected to the
surface density of neutral interstellar gas (e.g. Kennicutt, 1998). Recent studies have
indicated that the Kennicutt-Schmidt Law – a correlation between the star formation
rate surface density and the total (i.e. H I + H2 ) gas surface density – is driven by the
molecular gas component (e.g. Wong & Blitz, 2002; Bigiel et al., 2008), and that the
star formation efficiency of molecular gas (defined as the star formation rate surface
density per unit molecular gas surface density SF EH2 ≡ ΣSFR /ΣH2 ) is approximately
constant in normal spiral galaxies, SF EH2 = 5.25 ± 2.5 × 10−10 yr−1 (Leroy et al.,
2008). As noted by the authors, this result could arise if the star-forming efficiency
of an individual GMC is determined by its intrinsic properties, and if the properties
of GMCs are independent of their interstellar environment (e.g. Krumholz & McKee,
2005). In galaxies with star formation rates similar to the solar neighbourhood, it is
likely that star formation proceeds as it does locally, i.e. within the dense substructure
of molecular clouds. For extreme environments, on the other hand, there is some evidence that the physical conditions and star formation efficiency of molecular gas depart
significantly from local Galactic values (e.g Oka et al., 2001; Bouché et al., 2007). From
these results, we might expect GMCs to exhibit a continuum of properties, such that
GMCs become denser and more massive as the density and pressure of the ambient
ISM increase (see also Rosolowsky, 2007).
Deep, high resolution, wide-field 12 CO(J = 1 → 0) surveys remain technically challenging with current facilities, but the heterogeneity of existing datasets and the lack of
consistent analysis techniques have also hindered efforts to determine whether GMCs
have similar properties throughout the Local Group. To generate the MAGMA cloud
catalogue, we purposely used identical parameters for the CPROPS signal detection
and cloud decomposition algorithms as B08. While resolution effects cannot be entirely surmounted (Section 3.4), this choice was motivated by our goal of comparing
172
Chapter 3. Properties of MAGMA GMCs: I. Overview
the properties of MAGMA GMCs and the extragalactic GMC populations studied by
B08. In Table 3.5, we list the median and range for the mass, CO-to-H2 conversion
factor, mass surface density and CO surface brightness of GMCs in the LMC, SMC,
and in the galaxies studied by B08. Galaxy parameters are tabulated in Table 3.6.
Results from resolved observations of the GMC populations in NGC 6822 (Gratier
et al., 2010) and M64 (Rosolowsky & Blitz, 2005) are also shown at the bottom of
Table 3.5. These studies used CPROPS (or CPROPS-like methods) to identify and
parameterise GMCs, but the cloud property measurements are not strictly consistent
with the data for other galaxies as distinct decomposition parameters were used. For
NGC 6822, the reported Tpk and inferred XCO measurements have been scaled to account for a
12 CO(J
M64, we assume a
= 2 → 1)/12 CO(J = 1 → 0) ratio of 0.7 (Sawada et al., 2001). For
12 CO(J
= 1 → 0)/13 CO(J = 1 → 0) ratio of 6.7 (Polk et al., 1988).
In his analysis of the M64 dataset, Rosolowsky (2005) adopts this conversion factor
and reports an excellent match between the properties of M64 GMCs identified using
12 CO(J
= 1 → 0) and
13 CO(J
= 1 → 0) emission line data. For the SMC clouds, we
constructed a GMC sample by applying CPROPS to the MAGMA
12 CO(J
= 1 → 0)
data cubes for the north and south-west of the SMC. These data were presented by
Muller et al. (2010), although a different method was used to measure molecular cloud
properties in that analysis.
It is difficult to draw a strong conclusion from the data in Tables 3.5 and 3.6. There
are order of magnitude differences in the range and average values of the GMC mass
surface density (ΣH2 ) and peak CO brightness (Tpk ) among galaxies, yet these variations are not clearly linked to the galaxy’s metallicity or mass. The GMCs in the
Magellanic Clouds and NGC 6822 appear to have lower ΣH2 values than the GMCs in
the other galaxies by a factor of a few. It is possible that the lower ΣH2 values in the
Magellanic Clouds and NGC 6822 have a physical origin: selective photodissociation of
CO molecules might confine the CO emission to the GMC’s dense interior (where the
clump-clump velocity dispersion is correspondingly lower) in the low metallicity and
strong radiation field environments of these galaxies. In this case, the CO linewidth –
3.7. Discussion
Table 3.5 Average properties of resolved GMCs in the LMC and other nearby galaxies. The columns list the number of GMCs
in the galaxy sample (3), and the median and interquartile range of: the GMC virial masses (4); CO-to-H2 conversion factor (5);
mass surface density (6); and peak CO brightness. For each parameter, the interquartile range is only shown if there are more than
five GMCs in the galaxy sample. The third row lists NANTEN measurements for GMCs that show a one-to-one correspondence
with GMCs in the MAGMA catalogue. References: (1) this work (2) B08 (3) Gratier et al. (2010) (4) Rosolowsky & Blitz (2005)
(5) Fukui et al. (2008).
Galaxy
LMC (MAGMA)
LMC (NANTEN, all)
LMC (NANTEN, subsample)
SMC (SEST)
SMC (MAGMA)
M31
M33
NGC 205
IC 10
NGC 1569
NGC 4214
NGC 2976
NGC 3077
NGC 4605
NGC 6822
M64
N
125
194
53
4
7
44
15
1
10
1
3
7
4
4
10
23
Mvir
[105 M⊙ ]
1.5 [0.7,3.3]
1.4 [0.6,3.5]
2.5 [1.6,4.6]
0.1
0.2 [0.1,0.5]
5.5 [2.3,8.7]
2.4 [1.8,3.6]
10.2
2.4 [0.7,3.2]
2.0
6.0
25.7 [6.6,35.5]
15.5
26.7
0.5 [0.2,1.7]
60.9 [3.6,185.1]
XCO
−1
[1020 cm−2 (K km s−1 ) ]
4.7 [3.6,7.6]
7.7 [5.3,11.2]
6.0 [5.0,8.6]
5.8
6.6 [4.2,9.7]
3.6 [2.5,5.8]
3.1 [1.7,4.2]
19.5
2.8 [1.7,5.1]
6.6
1.5
6.2 [4.9,29.6]
2.4
4.2
8.5 [7.3,16.8]
3.1 [2.2,4.9]
ΣH2
[M⊙ pc−2 ]
55 [38,87]
45 [25,73]
66 [41,88]
23
27 [18,40]
161 [127,265]
156 [88,341]
450
113 [90,130]
171
82
103 [49,206]
138
67
14 [5.5,23]
365 [239,599]
2.3
0.8
0.7
2.5
3.3
2.8
0.4
0.3
Tpk
[K]
[1.9,2.8]
···
···
[0.7,0.9]
[0.6,0.8]
[1.9,3.0]
[2.0,4.0]
1.0
[2.6,3.7]
0.4
1.2
[0.3,0.5]
4.4
0.6
[0.2,0.4]
···
Refs.
1
1,5
1,5
2
1
2
2
2
2
2
2
2
2
2
3
4
173
Chapter 3. Properties of MAGMA GMCs: I. Overview
174
Table 3.6 Summary of the survey parameters and general properties of the galaxies listed in Table 3.5. The reference for
the galaxy types and magnitudes is de Vaucouleurs et al. (1991). For consistency, we quote the galaxy distance that was
used by the studies listed in Table 3.5. References for galaxy metallicity: (1) Marble et al. (2010) (2) Lee et al. (2006) (3)
Kobulnicky & Skillman (1997) (4) Garnett (1990) (5) Rosolowsky & Simon (2008) (6) B08 (7) Kennicutt et al. (1998) (8)
Richer & McCall (1995)
Galaxy
LMC (MAGMA,NANTEN)
SMC (SEST,MAGMA)
M31
M33
NGC 205
IC 10
NGC 1569
NGC 4214
NGC 2976
NGC 3077
NGC 4605
NGC 6822
M64
Resolution
[pc]
15,40
17,17
27
30
28
19
45
80
94
41
109
36
75
Vel. Resolution
[ km s−1 ]
0.53,0.65
0.25,0.53
2
2
3
0.7
1.6
3
3
1.3
3
0.41
4.3
Distance
[Mpc]
0.05
0.06
0.79
0.84
0.85
0.95
2.2
2.94
3.45
3.9
4.26
0.49
4.1
Morphology
SB(s)m
SB(s)m pec
SA(s)b4
SA(s)cd
E5 pec
IBm
IBm
IAB(s)m
SAc pec
I0 pec
SB(s)c pec
IB(s)m
(R)SA(rs)ab
Metallicity
[12 + log(O/H)]
8.26
7.96
8.98
8.36
8.6
8.26
8.19
8.25
8.7
8.64
8.64
8.11
9.09
MB
[mag]
-18.0
-16.7
-21.1
-18.9
-15.9
-16.7
-17.3
-17.2
-17.4
-17.5
-17.9
-15.8
-20.2
Refs.
1
1
7
5
7
4
3
1
6
1
1
2
1
3.7. Discussion
175
which is used to calculate Mvir and ΣH2 – would only reflect the kinematics of the CObright core and not the gravitational potential of an entire molecular (i.e. H2 ) cloud.
Insofar as it reflects a low covering factor of CO emission relative to Galatic clouds
(e.g Israel, 2000), the low peak CO brightness of Magellanic GMCs would be consistent
with this scenario. Further supporting evidence is the determination of the H2 mass
surface density in the SMC by Leroy et al. (2007a), who found ΣH2 = 180 ± 30 M⊙ pc−2
on ∼ 45 pc scales using far-infrared dust emission, rather than CO, to trace molecular
gas. If selective photodissociation were the explanation, however, it is surprising that
the GMC population in IC 10, another low metallicity galaxy, does not follow a similar
trend as the Magellanic Clouds.
As noted by B08, the data in Table 3.5 reveal a correlation between the minimum
observed cloud mass and galaxy distance that is simply due to the finite sensitivity
of the observations. In principle, incompleteness and a dependence between ΣH2 and
cloud mass could then produce variations in the mean ΣH2 between galaxies. More
specifically, if the mass surface density of GMCs were not constant but increased with
increasing cloud mass, then observations that only sampled the high mass GMC population would also tend to exhibit higher average values of ΣH2 . We do not consider
this incompleteness effect to be dominant, however, since the trends in the median ΣH2
values that we observed are mirrored by a shift for the entire ΣH2 distribution. In
the scenario just described, the maximum observed ΣH2 value would remain constant,
which is not observed.
Comparing the NANTEN and MAGMA measurements for LMC clouds shows that a
modest improvement in angular resolution tends to decrease the maximum observed
cloud mass but has little effect on ΣH2 . If the larger GMC masses observed in NGC 3077,
M31 and M33 are due to spatially unresolved cloud complexes, then we would expect
future higher resolution observations to reveal a lower maximum observed cloud mass,
higher Tpk measurements (since beam dilution would be less severe) and similar or
higher values of ΣH2 . In other words, the ‘cost’ of better agreement between the distribution of Mvir among these galaxies might be a larger discrepancy between their Tpk
176
Chapter 3. Properties of MAGMA GMCs: I. Overview
measurements and relatively little change in the difference between their ΣH2 values.
While spatial resolution effects therefore seem an unlikely origin for the differences in
ΣH2 for this subsample of galaxies, variations in spectral resolution could be significant.
In particular, if there were two physically-distinct GMCs with similar radial velocities
along the line-of-sight, then low spectral resolution observations would be more likely to
misclassify them as a single cloud with a relatively high velocity dispersion, and hence
a large ΣH2 . The spectral resolution of the observations in the Magellanic Clouds
and NGC 6822 are better by a factor of ∼ 4 than the observations in M31, M33 and
NGC 3077. The latter group of galaxies are also more inclined to the plane of the
sky (i ∈ [45, 77]◦ ) than the LMC (i ∼ 35◦ ), although the increase in the probability
of velocity blending, and its ultimate effect on the observed mean and range of ΣH2
values still needs to be calculated. For M31, the galaxy with the greatest inclination,
Rosolowsky (2007) argue that the probability of significant blending is low. NGC 6822
is inclined (i ∼ 60◦ , Weldrake et al., 2003) and its GMCs exhibit low ΣH2 values, so it
seems unlikely that blending alone can explain the variation in ΣH2 between different
galaxies.
A final important caveat is that many of the galaxies in the B08 sample were observed
with interferometers whereas the LMC, SMC and NGC 6822 datasets were obtained
using single-dish telescopes. Interferometers are less sensitive to diffuse emission than
filled aperture telescopes, so another possible explanation for the variation in ΣH2 between the datasets is that interferometers act as a spatial filter. An extended region of
low CO brightness will contribute significantly to the measured size of a GMC, but not
to the total CO luminosity. As an extreme example, Rosolowsky (2007) report that
BIMA observations of GMCs in M33 by Rosolowsky et al. (2003) recover only 20%
of the CO luminosity obtained by FCRAO 14 m observations (Heyer et al., 2004). If
this effect is important, the good agreement between ΣH2 values in Table 3.5 with the
average value of ΣH2 for Galactic GMCs (170 M⊙ pc−2 , B08) may be misleading.1 A
lack of sensitivity to extended emission cannot explain the large Mvir and ΣH2 values
1
In addition, we note that Heyer et al. (2009) have recently argued that the Galactic average should
be revised downwards to 100 M⊙ pc−2 .
3.7. Discussion
177
for the M64 GMC population, since these measurements were derived from a combined
single-dish (FCRAO) and interferometer (BIMA) dataset.
In summary, there would seem to be sufficient uncertainty regarding the combined effect
of differences in resolution, instrument configuration and physical conditions between
galaxies that the uniformity (or diversity) of extragalactic GMC populations cannot be
established from Table 3.5 alone. Comparing estimates for the H2 mass of GMCs in
low- and high-metallicity environments using methods based on the dust and CO emission (e.g Leroy et al., 2007a; Roman-Duval et al., 2010) will be an important project
for Herschel, and should provide crucial insight into whether the CO linewidth is accurately tracing the total mass of molecular material. This comparison will be key to
determining whether the lower ΣH2 values obtained in the Magellanic Clouds are due
to selective photodissociation of CO molecules, or if there are genuine variations in the
internal mass distribution of GMCs in different interstellar environments.
In light of the uncertainties that hinder comparisons between GMC samples constructed
from heterogeneous datasets, another way to make progress would be to investigate
whether GMC properties vary within a single galaxy for which a relatively complete
census of the GMC population has been obtained. To date, most of the discussion
regarding GMC properties has focussed on galaxy-wide averages, neglecting the fact
that measurements for individual GMCs can vary by more than an order of magnitude.
Indeed, a recent re-analysis of the S87 GMC sample by Heyer et al. (2009) argues
that the mass surface density of Galactic GMCs is not constant, but instead increases
with the amplitude of the non-thermal motions within GMCs (i.e. the velocity dispersion measured over a fixed spatial scale). These authors propose that GMCs may be
magnetically supported, such that ΣH2 adjusts to the magnetic critical surface density,
Σc = B/(63G)0.5 , where B is the strength of the local magnetic field (e.g. Mouschovias,
1987). While we cannot explicitly test this hypothesis with the MAGMA data, we address the possibility of an environmental dependence for ΣH2 in Chapter 4.
178
3.7.3
Chapter 3. Properties of MAGMA GMCs: I. Overview
Properties of non-star-forming GMCs
In Section 3.5, we investigated the physical properties of the non-star-forming GMC
in the MAGMA cloud catalogue, finding that sightlines through these clouds tend to
have lower Tmax and hTpk i than sightlines through star-forming GMCs of equivalent
size. Models of the
12 CO(J
= 1 → 0) emission from GMCs indicate that the emission
arises from a large number of optically thick clumps that are not self-shadowing (e.g.
Wolfire et al., 1993). For each independent sightline through a GMC, the observed
peak CO brightness is then a measure of the total projected area of the optically thick
clumps within the beam area, weighted by their brightness temperature, which should
correspond to the kinetic temperature of the CO-emitting gas if emission in the clumps
is optically thick (e.g Maloney & Black, 1988). The usual assumption is that the distribution of clump sizes and the brightness temperature do not vary significantly between
sightlines, and that the observed CO brightness measures the number of clumps – and
hence the total amount of molecular gas – within the telescope beam. While this assumption may be justified for clouds in the inner disk of the Milky Way (S87), it is
worth noting that the peak CO brightness results from a combination of the brightness
temperature, the number of CO-emitting clumps within the beam, and their average
size. A possible interpretation for the different average peak CO brightness of starforming and non-star-forming GMCs is that there are fewer CO-emitting clumps in
GMCs without star formation, leading to a lower angular filling factor of CO emission. Alternatively, colder gas temperatures in the dormant CO-emitting substructures
within non-star-forming GMCs could lead to a lower average brightness temperature
for the clump ensemble.
As non-star-forming GMCs tend to have a lower hTpk i and Tmax values than starforming GMCs of comparable size, it might be expected that their total CO luminosity
would also be fainter. However, the KS tests reveal no systematic differences between
the distributions of LCO and ICO for the various cloud samples, which suggests that the
regions of high CO brightness in the star-forming GMCs are restricted to a relatively
small number of pixels in the MAGMA data subcubes. This is consistent with the
3.7. Discussion
179
view of star formation as a highly localised process: occupying only a small fraction of
the total cloud volume, star-forming clumps have temperatures and densities that are
much higher than in the bulk of the GMC, most of which does not participate directly
in star formation. The lower hTpk i and Tmax of non-star-forming GMCs would seem
to provide some preliminary evidence that the general characteristics of substructure
within non-star-forming GMCs in the Milky Way – i.e. cooler clumps that are less massive and more diffuse than in star-forming GMCs (e.g. Williams et al., 1994; Williams
& Blitz, 1998) – will also be found to apply in the LMC.
Finally, we found a clear trend for non-star-forming GMCs to be located in regions
where G0 is relatively weak. A straightforward explanation for this result is that once
young massive stars begin to form, they are an important source of dust-heating within
LMC molecular clouds. Importantly, this would mean that G0 is not strictly tracing the
ambient (i.e. external) radiation field incident on a GMC, but instead contains a signficant contribution from the massive stars that are within – or have recently emerged
from – their GMC progenitor. A strong correlation between G0 and H α surface brightness for all the MAGMA LMC clouds (see Fig. 3.29[a]) indicates a strong connection
between dust heating and star-formation activity, which would seem to support this
interpretation. There is no overall correlation between G0 and the stellar mass surface
density (Fig. 3.29[b]), which we interpret as evidence that old stars make a relatively
small contribution to dust-heating in GMCs. However, there are no GMCs with low
G0 and high Σ∗ : this could indicate that dust-heating by old stars becomes significant
at high stellar densities, but could also be a sign that stellar gravity plays a role in
bringing the molecular gas to high densities, and increasing the star formation activity
of GMCs in those regions.
3.7.4
Rotation and MAGMA GMCs
Due to the twin requirements of high spatial resolution and wide-field coverage, the
velocity fields in extragalactic GMC populations have not been widely investigated
(studies of GMCs in M33 and M31 by Rosolowsky et al. (2003) and Rosolowsky (2007)
180
Chapter 3. Properties of MAGMA GMCs: I. Overview
1.0
log(G0/G0,sol)
log(G0/G0,sol)
1.0
[a] rall = (0.73,<0.01)
rhq = (0.76,<0.01)
0.5
0.0
[b] rall = (0.25,<0.01)
rhq = (0.16,0.21)
0.5
0.0
−0.5
−0.5
1
2
3
log(ΣHα/[dR])
4
0.5
1.0
1.5
log(Σ*/[Msol
2.0
2.5
pc−2])
Figure 3.29 The radiation field at the location of the MAGMA clouds, plotted as a
function of (a) the H α surface brightness, as observed by SHASSA (Gaustad et al.,
2001), and (b) the stellar mass surface density. Plot symbols are the same as in Fig. 4.1.
The Spearman correlation coefficient and corresponding p-value for all 125 MAGMA
GMCs and the high quality subsample are indicated at the top left of each panel.
are notable exceptions). Although their interpretation can be ambiguous, velocity gradients potentially contain important information regarding cloud rotation and angular
momentum, properties that should influence the stability and evolution of GMCs. In
the absence of external forces, shear within a differentially rotating galactic disk will
impart angular momentum to a gas cloud, causing it to rotate (e.g. Field, 1978). Rotation, in turn, may affect a cloud’s internal mass distribution, the fragmentation process
and its stability against global gravitational collapse. Since angular momentum is a
conserved quantity, velocity gradients provide valuable empirical evidence about the
relationship between individual clouds and the ISM, and to evaluate cloud formation
theories. A large discrepancy between the angular momentum predicted from galactic shear and the value measured in the GMC populations provides good motivation
to investigate the influence of magnetic fields on GMC evolution, for example, since
magnetic braking is one of the few mechanisms that can dissipate angular momentum
efficiently (e.g Mouschovias & Paleologou, 1979; Kim et al., 2003b).
The dynamical significance of rotation in a molecular cloud can be quantified through
the parameter, β, which is defined as the ratio of the rotational to gravitational energy.
3.7. Discussion
181
More specifically,
β=
p ω 2 R3
0.5Iω 2
=
0.5
,
qGM 2 /R
q GM
(3.12)
where q = 3/5 for a spherical cloud, I = pM R2 is the moment of inertia, and p is a
constant that depends on the cloud’s shape and density distribution. For a spherical
cloud with constant density, p = 2/5, while for a spherical cloud with a ρ(r) ∝ r −2 density profile, p = 2/15 (e.g. Mulholland, 1980). By combining Equations 3.12 and 3.10,
we see that β is related to the observed velocity gradient according to
β=
3p
1
G2
,
2 q 4πGhρi sin2 i
(3.13)
where hρi is the average volume density of the cloud.
The β values for MAGMA clouds with a measured velocity gradient are listed in Table 3.9. These are presented as a range: the lower limit is calculated for a uniform
cloud density profile and XCO = 4.7 × 1020 cm−2 (K km s−1 )−1 , and the upper limit is
calculated for a ρ(r) ∝ r −2 density profile and XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 .
In both cases, we assume that the angular velocity vectors are orthogonal to the lineof-sight (i.e. sin i = 1); inclinations less than 90◦ for the cloud rotation axes would
lead to produce higher values of β. Using our upper estimates, the median value of β
is 0.18 ± 0.15, where the quoted uncertainty is the median absolute deviation. This is
lower than early estimates for rotation in Galactic molecular clouds (0.4 . β . 1.2,
Arquilla & Goldsmith, 1986), but comparable to the median values that we derive for
GMCs in M31 (β = 0.07 ± 0.06) and M33 (β = 0.06 ± 0.08) using the data presented
in Rosolowsky (2007) and Rosolowsky et al. (2003).
In Table 3.9, we also tabulate the specific angular momentum for each GMC, which we
calculate according to j = ηGR2 (i.e. assuming solid-body rotation). The constant of
proportionality η ranges between 0.33 and 0.5, and depends on the assumed cloud density profile (Phillips, 1999). We adopt η = 0.4. The median specific angular momentum
for the MAGMA GMCs is 20 ± 13 pc km s−1 . This is comparable to the average specific angular momentum of GMCs in M33 (19 pc km s−1 ) and M31 (36 pc km s−1 ). On
182
Chapter 3. Properties of MAGMA GMCs: I. Overview
small scales, Burkert & Bodenheimer (2000) have shown that turbulent compression
can produce line-of-sight gradients in molecular cloud cores of similar magnitude to
those that arise due to solid body rotation. Our estimates for the angular momentum
of MAGMA clouds assume that the velocity gradients are due entirely to rotation, and
should therefore be regarded as upper limits.
The absence of linear gradients for nearly half the MAGMA sample, low β values, and
the poor alignment between the orientation of the velocity gradients and the position
angle of the GMC major axes each suggest that rotation is not dynamically significant
for the majority of GMCs in the LMC. Contrary to GMCs in M33 and M31, which
have velocity gradients that are significantly greater than the local galactic gradient,
the MAGMA GMCs exhibit velocity gradients that are comparable in magnitude to the
gradients that are measured for the surrounding ISM (e.g. Figure 3.26). This suggests
that it may be inappropriate to interpret the observed velocity gradients as a signature
of uniform rotation, and that GMCs in the LMC may instead be participating in larger
scale interstellar flows. Conceivably, a correlation between GMC size and the alignment
of the cloud velocity gradient with respect to the local ISM might arise if GMCs form
with a chaotic velocity field at the site of collisions between H I flows and then evolve towards the average galactic gradient through the combined action of turbulence and/or
tides. We are not aware of numerical simulations that model the formation of individual GMCs via colliding flows in a system experiencing an external torque, but our
analysis indicates that predictions for the velocity field structure within GMCs and in
the surrounding atomic gas for different cloud formation mechanisms would be valuable.
Although we have proposed that velocity gradients may not be a sign of cloud rotation in
the LMC, we should for completeness check whether the measured angular momentum
for these clouds is similar to what we would expect if they were formed from atomic gas
orbiting at their location in the LMC’s disk. The angular momentum of gas rotating
in the galactic disk is given by Rosolowsky (2007):
jgal = ψr 2
1 d
(Rc V )|R=Rc .
Rc dRc
(3.14)
183
log(j [km s−1 pc])
3.7. Discussion
jgal
jgmc
3
2
1
0
0
1
2
3
Galactocentric Radius [kpc]
Figure 3.30 The specific angular momenta of MAGMA GMCs as inferred from their velocity
gradients, jGMC , plotted against galactocentric radius (black circles). The error bars represent
1σ measurement uncertainties, derived using error propagation. Systematic errors are likely to
dominate the true uncertainty. The predicted specific angular momenta of the MAGMA GMCs
if they had formed from atomic gas orbiting at their location in the LMC’s disk, jgal , are also
shown (grey triangles). The median value of jGMC and jgal are indicated using a solid and
dashed line respectively.
184
Chapter 3. Properties of MAGMA GMCs: I. Overview
In this equation, R is the radial distance from the LMC’s kinematic centre, V (R) is
the galactic rotation curve, Rc is the galactocentric radius of the GMC, and r = ∆R
is the range of galactocentric radii from which the progenitor atomic gas originated. ψ
depends on the assumed shape of the contracting region: following Rosolowsky (2007),
we set ψ = 1/4, which is appropriate for a uniform cylinder with radius r that extends
to infinity in the direction orthogonal to the galactic plane. In our calculations, we
adopt the galactic rotation curve derived by Wong et al. (2009) and we estimate r from
the mass of the GMC and a suitable estimate for the surface density for the progenitor
atomic gas, MGM C = πΣHI r 2 with ΣHI = 10 M⊙ pc−2 .
The angular momenta predicted by Equation 3.14 and those inferred from the GMC
velocity gradients are plotted in Figure 3.30. On average, jgal is 50% less than jGM C ,
but the measurement and prediction are consistent within the scatter (∼ 1 dex). This
is distinct to the situation in M31 and M33 where the GMC angular momenta are
lower than the value predicted from galactic rotation by an order of magnitude or
more. It is a not surprising result, however, since the shearing force due to differential
rotation is significantly lower in the gaseous disks of dwarf galaxies than in massive
spirals. While Figure 3.30 complicates rather than clarifies the origin of the cloud velocity gradients in the LMC, an important corollary is that there is no need to invoke a
braking mechanism to dissipate angular momentum during the cloud formation process.
3.8 Conclusions
In this chapter, we presented a catalogue of GMCs in the Large Magellanic Cloud.
We discussed the inherent limitations and uncertainties that are associated with our
cloud property measurements, and examined whether GMCs in the LMC are similar to
molecular clouds in the Milky Way and other nearby galaxies. We report the following
results and conclusions:
1. The observed GMCs have radii ranging between 13 and 160 pc, velocity disper-
3.8. Conclusions
185
sions between 1.0 and 6.1 km s−1 , peak CO brightnesses between 1.2 and 7.1 K, CO
luminosities between 103.5 and 105.5 K km s−1 pc2 , and virial masses between 104.2 and
106.8 M⊙ . The clouds tend to be elongated, with a median major-to-minor axis ratio of
1.7. These values are comparable to the measured properties of Galactic GMCs. The
average mass surface density of the observed clouds is ∼ 50 M⊙ pc−2 , approximately
half the value determined for GMCs in the inner Milky Way catalogue of Solomon et al.
(1987).
2. The observed GMCs are distributed irregularly across the gas disk of the LMC. The
number surface density of GMCs increases by a factor of two in the inner 1.5 kpc of the
LMC compared to the outer disk, producing corresponding variations in the molecular
mass surface density. There is a deficit of GMCs at galactocentric radii between 1.5
and 2 kpc, the origin of which is uncertain.
3. Physical properties of star-forming GMCs are very similar to the properties of GMCs
without signs of massive star formation. Sightlines through non-star-forming GMCs
tend to have lower peak CO brightness, suggesting that the filling fraction and/or
brightness temperature of the CO-emitting substructure is lower for clouds without
star formation.
4. Linear velocity gradients are observed for ∼ 50% of MAGMA GMCs, with a median
value of 0.1 km s−1 pc−2 . The magnitude of the observed gradients are comparable to
those measured for GMCs in the Milky Way, M31 and M33 (Rosolowsky et al., 2003;
Koda et al., 2006; Rosolowsky, 2007). For GMCs where velocity gradients are detected,
the gradient contributes significantly to cloud’s measured velocity dispersion.
5. There is no clear relationship between the morphology of individuals GMCs and
their velocity gradients. On larger scales, the gradients appear spatially organized in
relation to the structure in the LMC’s disk, although a random distribution of gradient
orientations cannot be strongly excluded.
186
Chapter 3. Properties of MAGMA GMCs: I. Overview
6. The velocity gradient in GMCs is similar in magnitude to the velocity gradient
in the surrounding ISM. There is also weak evidence for preferential alignment of the
velocity gradients traced by the CO and H I emission, especially for larger clouds. We
propose that GMCs remain kinematically coupled to the local interstellar gas, and that
the velocity field may be a useful discriminant for evaluating models of GMC formation.
3.A. Data for Excluded Emission Regions
187
3.A Data for Excluded Emission Regions
Table 3.7: Position and Peak CO Brightness of Excluded Emission Regions. The final column
contains a letter code that indicates why the cloud was excluded from the MAGMA catalogue:
a = insufficient signal to noise; b = uncertainty in radius measurement greater than 20%; c =
uncertainty in velocity dispersion greater than 20%; d = deconvolution from telescope beam
results in an undefined value for cloud radius.
Cloud ID
RA (J2000)
Dec (J2000)
VLSR
Tmax
Criteria
1
05:12:32.6
-67:44:21
272.9
1.6
-b–
2
05:12:37.8
-68:13:15
283.3
1.7
-b–
3
05:12:42.9
-68:09:50
282.7
1.5
-bc-
4
05:10:44.5
-68:59:23
236.1
1.3
-bcd
5
05:12:34.1
-69:03:55
237.0
1.4
-bc-
6
05:08:11.1
-69:02:46
242.3
1.5
-b–
7
05:09:35.6
-68:45:38
266.5
1.8
-bc-
8
05:09:38.2
-69:10:17
239.8
2.0
-b–
9
05:25:36.4
-69:49:39
250.0
1.7
-bc-
10
05:22:08.8
-68:34:37
250.2
1.5
-bc-
11
05:22:36.3
-68:33:42
250.8
1.3
-bc-
12
05:22:40.4
-68:22:39
253.4
1.8
-b–
13
05:23:27.5
-68:18:36
257.8
1.2
ab–
14
05:20:46.5
-68:36:50
257.4
1.6
–c-
15
05:21:17.9
-68:41:59
270.8
1.3
-bc-
16
05:26:53.6
-68:53:34
239.7
1.9
-b–
17
05:42:00.4
-70:49:47
213.2
2.4
-bcd
18
05:38:53.9
-70:13:41
224.8
4.5
-b–
19
05:40:05.5
-69:57:37
225.5
1.6
abcd
20
05:40:18.3
-70:41:32
227.9
2.1
-b-d
21
05:40:33.8
-70:37:33
232.4
1.6
abc-
22
05:41:04.8
-70:54:05
234.6
1.7
-bc-
23
05:39:59.9
-69:37:20
232.9
1.9
-bcd
24
05:38:52.5
-69:04:04
248.8
1.9
-b–
25
05:38:55.0
-69:34:47
250.4
1.8
-b–
26
05:38:41.1
-69:25:26
249.9
1.6
abcd
Continued on next page . . .
188
Chapter 3. Properties of MAGMA GMCs: I. Overview
Table 3.7 – Continued
Cloud ID
RA (J2000)
Dec (J2000)
VLSR
Tmax
Criteria
27
05:34:59.4
-69:04:55
256.2
3.7
-bcd
28
05:38:08.5
-69:34:46
261.5
2.2
-b–
29
05:20:08.6
-66:52:17
290.9
1.9
abc-
30
05:21:22.7
-68:02:05
272.8
1.7
-b–
31
05:22:15.7
-67:36:33
279.6
1.8
-bcd
32
05:22:26.1
-68:04:59
285.2
1.4
-bc-
33
05:21:26.1
-67:47:52
298.1
1.4
-bc-
34
05:23:06.0
-67:06:24
268.1
1.4
-b–
35
05:22:43.3
-67:07:27
294.1
1.7
-b–
36
05:27:27.3
-70:36:16
238.7
2.2
-b–
37
05:35:18.6
-67:35:09
284.4
1.1
abc-
38
04:52:39.7
-69:11:44
247.0
1.8
-b–
39
05:35:48.9
-69:12:54
239.5
2.1
-bc-
40
05:35:52.4
-68:44:23
249.7
1.7
-bc-
41
05:35:29.2
-70:45:35
268.2
1.5
-b–
42
05:45:43.1
-69:20:57
226.7
1.2
-bc-
43
05:43:09.9
-69:20:24
247.7
1.5
-bc-
44
05:45:30.3
-67:07:55
285.7
1.2
a—
45
05:47:30.5
-69:58:42
224.4
1.4
-b–
46
04:56:28.9
-66:32:01
276.3
1.4
-bc-
47
04:57:12.1
-68:26:45
257.6
1.3
ab–
48
04:56:52.9
-66:24:13
283.9
1.6
-b–
49
04:58:59.4
-66:13:21
280.6
1.6
-b–
50
04:57:47.2
-66:18:19
284.9
1.1
-b–
51
04:58:39.0
-66:15:31
284.2
1.6
-bcd
52
05:17:19.4
-71:13:23
223.1
1.8
abc-
53
05:17:36.0
-66:42:09
289.5
2.1
-b–
3.B. The MAGMA GMC catalogue
189
3.B The MAGMA GMC catalogue
Table 3.8: The MAGMA GMC catalogue
Cloud
RA
Dec.
VLSR
Radius
σv
Tpeak
LCO
Number
(J2000)
(J2000)
( km s−1 )
(pc)
( km s−1 )
(K)
(104 K km s−1 pc2 )
1
05:12:15.9
-70:28:07
232.9
35
2.1
2.6
2.0
2
05:11:45.2
-67:48:47
276.1
26
2.3
1.5
0.9
3
05:14:23.4
-70:11:30
236.2
30
1.9
3.0
1.7
4
05:11:46.4
-69:00:56
233.0
30
2.0
1.7
1.0
5
05:10:13.7
-68:53:22
241.1
48
2.2
2.5
3.2
6
05:08:57.8
-68:43:50
244.5
16
2.0
2.0
0.7
7
05:11:18.2
-68:52:07
248.1
44
2.9
3.1
2.3
8
05:07:47.7
-68:59:14
255.2
28
5.2
1.2
1.8
9
05:14:37.8
-68:47:23
266.0
33
2.1
1.9
1.4
10
05:13:08.6
-69:36:54
234.8
64
3.1
3.2
7.0
11
05:08:36.2
-69:23:31
225.4
26
1.9
5.0
2.5
12
05:09:24.1
-69:23:36
231.1
18
3.2
4.1
1.1
13
05:10:04.2
-69:26:10
227.5
23
1.3
1.7
0.6
14
05:13:22.2
-69:22:39
236.1
19
2.5
7.1
2.4
15
05:16:28.4
-68:13:45
278.5
42
3.2
3.1
1.8
16
05:15:56.1
-68:02:09
282.1
75
2.9
2.8
7.7
17
05:16:46.4
-68:21:11
279.5
37
2.1
2.2
1.9
18
05:17:42.1
-68:48:52
260.3
30
3.8
2.1
1.4
19
05:16:35.5
-68:48:39
264.8
17
2.0
1.8
0.6
20
05:19:27.0
-69:08:44
267.2
25
2.6
3.8
1.9
21
05:16:38.2
-69:23:11
240.7
14
1.0
2.6
0.5
22
05:17:34.1
-69:15:06
257.3
13
2.0
2.2
0.6
23
05:25:35.0
-69:18:41
259.6
18
1.8
2.0
0.5
24
05:24:38.5
-69:14:53
259.7
17
1.5
1.7
0.6
25
05:22:03.4
-69:41:37
240.9
32
4.5
3.9
3.4
26
05:19:19.6
-69:39:10
240.5
39
3.5
2.9
2.4
27
05:24:05.4
-69:38:53
250.4
27
2.8
3.2
2.1
28
05:24:48.3
-69:40:53
263.7
28
2.6
4.2
2.8
29
05:21:08.0
-70:13:15
226.0
20
1.7
3.3
1.2
30
05:21:05.3
-70:01:06
240.9
47
2.9
3.6
7.1
31
05:18:16.7
-70:02:15
248.4
22
1.5
1.9
0.7
32
05:22:04.1
-68:27:41
243.5
29
2.4
3.1
1.3
33
05:24:16.8
-68:29:05
249.5
26
1.6
2.1
0.8
34
05:24:29.6
-68:26:40
258.9
45
2.6
3.9
4.7
35
05:21:29.8
-68:47:55
279.4
46
2.4
2.1
1.9
36
05:20:07.3
-68:38:09
255.7
28
1.5
2.0
0.9
Continued on next page. . .
190
Chapter 3. Properties of MAGMA GMCs: I. Overview
Table 3.8 – Continued
Cloud
RA
Dec.
VLSR
Radius
σv
(pc)
( km s−1 )
Tpeak
(K)
LCO
(104
K km s−1 pc2 )
Number
(J2000)
(J2000)
( km s−1 )
37
05:21:03.9
-68:40:59
265.9
13
1.3
1.8
0.4
38
05:26:07.5
-68:35:29
254.6
29
1.5
2.3
1.0
39
05:26:22.9
-68:48:36
256.1
22
1.5
1.6
0.6
40
05:28:15.2
-69:53:00
249.7
17
1.3
4.2
1.1
41
05:32:58.1
-68:58:11
252.4
25
2.4
2.4
1.2
42
05:32:17.7
-68:39:36
253.2
37
1.6
1.7
1.1
43
05:31:26.9
-68:31:34
258.6
75
3.5
3.0
5.7
44
05:34:24.6
-68:12:35
276.9
32
1.6
1.9
0.7
45
04:49:23.5
-68:27:26
249.2
94
2.0
3.1
6.9
46
04:47:27.3
-67:13:08
256.4
54
5.7
1.7
3.3
47
04:47:57.1
-67:20:45
257.3
40
1.7
1.4
1.2
48
05:26:53.2
-71:19:47
226.2
80
2.1
3.3
8.4
49
04:52:12.2
-66:55:06
275.4
23
3.1
2.3
1.3
50
04:52:12.4
-66:59:23
274.1
23
2.6
2.2
0.8
51
04:51:56.4
-67:08:20
275.3
82
2.1
2.5
3.8
52
05:47:31.8
-70:41:23
217.4
77
4.5
2.7
8.0
53
05:43:54.0
-71:07:54
221.2
30
3.2
2.2
1.9
54
05:44:20.7
-71:02:50
220.2
18
2.0
1.4
0.5
55
05:32:27.0
-66:26:56
289.0
25
1.7
2.1
0.6
56
05:30:57.6
-71:07:09
228.2
45
2.4
3.0
4.7
57
05:38:41.1
-70:17:44
219.5
19
1.7
2.0
0.5
58
05:40:11.8
-70:15:30
230.8
160
6.1
4.5
28.8
59
05:39:50.5
-69:36:27
228.1
26
1.4
2.1
0.7
60
05:39:50.3
-69:48:19
235.5
80
3.5
5.6
16.1
61
05:40:49.8
-70:44:03
237.2
16
2.3
2.9
1.0
62
05:39:44.7
-69:59:07
237.6
24
2.0
2.5
1.1
63
05:39:38.7
-69:39:34
238.7
35
3.1
2.4
1.3
64
05:37:06.5
-69:47:53
251.7
15
2.4
2.3
0.8
65
05:39:13.0
-69:30:54
255.9
24
1.8
1.9
0.7
66
05:35:45.3
-69:02:35
258.5
18
1.9
2.5
1.1
67
04:50:50.0
-69:18:56
236.1
33
1.9
2.4
1.1
68
05:23:16.8
-68:01:48
278.8
66
3.8
5.6
10.7
69
05:22:03.2
-67:58:44
282.9
46
2.9
5.2
4.3
70
05:23:47.3
-67:52:45
278.9
21
2.6
1.3
0.4
71
05:20:20.8
-67:50:07
279.7
15
1.6
1.8
0.4
72
05:21:35.4
-67:48:17
280.5
53
2.7
2.5
4.0
73
05:21:49.6
-67:40:13
284.4
25
1.4
1.9
0.6
74
05:23:41.3
-68:04:28
289.4
23
1.6
2.2
0.6
75
05:22:47.0
-65:40:42
295.0
28
1.6
2.6
1.2
76
05:23:05.1
-66:41:56
293.4
32
2.3
2.5
1.8
Continued on next page. . .
3.B. The MAGMA GMC catalogue
191
Table 3.8 – Continued
Cloud
RA
Dec.
VLSR
Radius
σv
(pc)
( km s−1 )
Tpeak
(K)
LCO
(104
K km s−1 pc2 )
Number
(J2000)
(J2000)
( km s−1 )
77
05:23:16.2
-71:38:42
222.6
16
2.0
2.0
0.7
78
05:25:27.4
-66:13:41
291.0
58
4.8
2.6
5.3
79
05:26:18.4
-66:02:04
286.3
20
2.3
4.0
2.1
80
05:26:04.8
-66:09:13
285.3
20
1.5
1.9
0.6
81
05:26:26.9
-66:10:27
297.4
15
2.6
1.6
0.4
82
04:51:54.9
-69:22:41
232.8
22
2.4
3.6
1.5
83
05:28:10.4
-71:40:22
225.0
38
3.3
1.3
1.6
84
05:29:34.7
-71:03:28
225.5
21
2.5
2.4
0.7
85
05:32:09.9
-67:43:06
285.9
58
2.4
1.6
2.1
86
05:32:15.1
-71:13:57
224.9
25
1.8
4.2
2.0
87
05:32:42.0
-69:46:04
265.3
13
1.7
2.1
0.5
88
04:52:55.3
-68:04:34
267.5
25
2.8
2.6
1.5
89
05:35:21.4
-67:36:46
280.5
17
1.6
1.4
0.4
90
04:53:52.2
-69:09:45
245.8
48
3.0
2.3
3.9
91
05:36:00.0
-70:43:25
238.6
33
2.6
1.9
1.1
92
05:40:23.1
-71:12:49
216.1
18
2.7
1.6
0.5
93
05:39:47.2
-71:09:39
229.7
36
3.5
4.0
3.6
94
05:40:04.4
-71:32:57
212.0
21
4.0
1.5
0.7
95
05:42:25.5
-71:20:38
216.9
33
2.1
1.8
1.3
96
05:41:21.2
-71:17:54
219.0
35
2.3
1.8
1.0
97
05:44:25.4
-71:28:17
219.9
33
2.7
1.7
1.3
98
05:44:29.5
-69:24:43
229.7
72
4.4
4.2
16.2
99
05:43:31.6
-69:26:36
249.3
37
2.3
2.2
1.5
100
05:45:22.8
-69:49:33
227.6
31
2.3
2.3
2.1
101
05:46:21.2
-69:36:38
235.5
40
3.8
1.6
2.3
102
05:47:50.8
-69:53:32
222.8
47
2.2
2.4
2.6
103
05:48:16.6
-70:07:16
224.4
48
2.8
2.2
1.7
104
04:55:35.0
-66:32:10
279.8
37
2.9
2.7
1.7
105
04:56:17.8
-66:37:23
278.1
27
1.6
2.4
1.0
106
05:55:42.2
-68:10:05
284.5
27
2.0
2.1
1.2
107
04:57:05.5
-69:11:40
236.8
22
1.9
2.1
0.7
108
04:57:17.2
-68:56:15
258.7
21
1.8
1.7
0.6
109
04:58:40.6
-66:18:42
276.0
81
4.2
2.1
4.8
110
04:57:49.6
-66:28:53
279.3
22
2.7
2.3
1.0
111
04:58:49.9
-66:08:24
276.3
33
1.9
2.5
1.2
112
05:00:45.1
-66:22:28
276.3
32
1.2
2.1
0.8
113
04:57:22.2
-66:22:34
279.6
29
2.6
1.4
0.7
114
04:57:17.5
-66:18:01
279.2
20
2.6
1.3
0.5
115
05:03:04.9
-65:53:39
279.1
17
2.2
1.4
0.6
116
04:49:01.8
-69:10:29
240.1
40
1.9
2.3
1.6
Continued on next page. . .
192
Chapter 3. Properties of MAGMA GMCs: I. Overview
Table 3.8 – Continued
Cloud
RA
Dec.
VLSR
Radius
σv
(pc)
( km s−1 )
Tpeak
(K)
LCO
(104
K km s−1 pc2 )
Number
(J2000)
(J2000)
( km s−1 )
117
05:03:49.9
-67:19:47
274.0
22
3.4
2.7
1.8
118
05:03:37.2
-67:10:50
274.5
27
1.3
2.0
0.7
119
05:04:50.8
-70:06:49
229.6
17
1.3
1.6
0.4
120
05:04:45.8
-70:56:17
231.3
32
2.7
2.2
1.0
121
05:04:48.2
-66:49:26
281.0
14
2.2
2.3
0.7
122
05:05:24.6
-66:54:25
280.9
15
1.7
2.1
0.6
123
05:12:06.4
-67:10:18
288.9
21
1.8
2.8
1.2
124
05:13:51.3
-67:23:46
283.3
31
1.5
1.6
0.5
125
05:14:34.3
-67:26:33
295.4
19
1.2
1.9
0.3
3.C. Velocity Gradients of MAGMA GMCs
193
3.C Velocity Gradients of MAGMA GMCs
Table 3.9: Results of velocity gradient fits for MAGMA GMCs
Cloud ID
Gradient
−1
( km s
−1
pc
Direction
)
(Degrees)
G×R
−1
( km s
β
j
km s−1 pc
)
E
0.31±0.08
75 ±17
9.1
[0.19,1.30]
26.8
4
0.13±0.05
66 ±59
7.5
[0.11,0.75]
44.5
E
0.25±0.04
65 ±18
6.5
[0.07,0.47]
16.8
9
0.02±0.01
325±75
1.4
[< 0.01,0.02]
9.4
10
0.07±0.01
132±6
9.4
[0.05,0.36]
120.6
14
0.08±0.02
115±13
3.3
[0.01,0.04]
12.5
18
0.13±0.10
27 ±27
7.8
[0.08,0.58]
46.9
19
0.06±0.01
251±33
1.9
[0.01,0.05]
6.4
20
0.07±0.02
50 ±17
3.4
[0.01,0.07]
16.9
22
0.64±0.20
173±11
16.9
[0.37,2.60]
44.4
23
0.48±0.13
111±22
17.0
[0.67,4.74]
60.6
25
0.18±0.01
239±7
11.1
[0.07,0.52]
70.7
26
0.11±0.01
118±20
8.3
[0.07,0.51]
65.8
29
0.04±0.01
334±12
1.7
[< 0.01,0.02]
6.9
30
0.06±0.01
244±10
5.6
[0.01,0.09]
52.0
32
0.05±0.02
290±17
3.1
[0.01,0.09]
18.0
33
0.22±0.02
34 ±14
11.4
[0.26,1.82]
59.3
36
0.08±0.01
236±12
4.3
[0.04,0.26]
24.3
37
0.11±0.07
134±17
3.0
[0.02,0.15]
8.4
39
0.03±0.04
85 ±100
1.3
[< 0.01,0.03]
5.8
40
0.15±0.04
142±15
5.4
[0.03,0.21]
18.8
41
0.06±0.02
69 ±21
2.9
[0.01,0.07]
14.1
43
0.04±0.00
32 ±27
5.2
[0.02,0.16]
78.3
44
0.05±0.01
314±19
3.2
[0.03,0.22]
21.0
45
0.01±0.00
349±25
2.7
[0.01,0.04]
50.2
46
0.15±0.02
64 ±7
16.3
[0.27,1.95]
176.6
48
0.02±0.00
37 ±30
3.8
[0.01,0.06]
60.5
53
0.14±0.02
122±8
8.4
[0.07,0.51]
51.3
55
0.04±0.01
230±33
1.9
[0.01,0.06]
9.3
59
0.15±0.03
141±30
8.0
[0.16,1.11]
41.3
60
0.04±0.00
299±6
5.7
[0.01,0.08]
90.5
Continued on next page. . .
194
Chapter 3. Properties of MAGMA GMCs: I. Overview
Table 3.9 – Continued
Cloud ID
Gradient
−1
( km s
−1
pc
Direction
)
(Degrees)
G×R
−1
( km s
β
j
km s−1 pc
)
E
0.16±0.03
26 ±12
4.4
[0.03,0.19]
12.2
E
0.10±0.02
50 ±8
4.7
[0.04,0.29]
21.9
E
0.13±0.02
123±23
···
···
···
61
0.04±0.03
120±33
1.4
[< 0.01,0.01]
4.3
63
0.11±0.02
235±8
8.1
[0.11,0.79]
57.6
E
0.10±0.02
174±19
2.9
[0.01,0.06]
8.3
64
0.09±0.01
28 ±18
2.7
[0.01,0.07]
8.3
66
0.04±0.30
59 ±85
1.3
[< 0.01,0.01]
4.8
E
0.06±0.01
240±34
1.9
[0.01,0.04]
5.9
73
0.02±0.02
266±30
0.9
[< 0.01,0.02]
4.7
75
0.05±0.01
338±12
2.9
[0.01,0.09]
15.8
79
0.06±0.01
28 ±9
2.3
[< 0.01,0.02]
9.3
80
0.06±0.01
18 ±11
2.5
[0.01,0.10]
10.2
E
0.11±0.01
347±11
1.3
[< 0.01,0.01]
1.6
83
0.13±0.02
172±31
10.2
[0.16,1.14]
78.6
84
0.09±0.02
169±21
3.9
[0.03,0.22]
16.5
88
0.11±0.01
318±6
5.5
[0.03,0.23]
27.6
E
0.22±0.02
357±6
6.3
[0.12,0.86]
18.0
90
0.08±0.01
287±9
7.4
[0.04,0.29]
70.2
94
0.17±0.08
297±29
7.4
[0.10,0.73]
31.2
95
0.09±0.03
235±17
5.6
[0.05,0.36]
37.3
96
0.08±0.03
142±84
3.3
[0.02,0.17]
23.3
97
0.06±0.01
45 ±13
4.0
[0.02,0.18]
26.8
98
0.09±0.00
286±2
13.0
[0.05,0.33]
186.6
101
0.13±0.02
250±10
10.3
[0.12,0.83]
83.0
E
0.07±0.02
313±21
2.5
[0.02,0.12]
9.8
105
0.07±0.01
16 ±13
3.5
[0.02,0.14]
18.4
106
0.06±0.00
315±18
3.1
[0.01,0.09]
16.9
112
0.12±0.03
148±53
7.6
[0.16,1.11]
49.5
E
0.28±0.17
218±26
6.7
[0.07,0.53]
16.2
117
0.13±0.02
34 ±17
5.8
[0.03,0.18]
25.3
118
0.03±0.39
233±52
1.8
[0.01,0.06]
10.2
119
0.02±0.03
56 ±176
0.7
[< 0.01,0.01]
2.5
123
0.03±0.01
229±20
1.5
[< 0.01,0.02]
6.4
3.C. Velocity Gradients of MAGMA GMCs
195
4
Properties of MAGMA GMCs: II. Scaling
Relations and Environmental Trends
In this chapter, we investigate scaling relations between the physical properties of giant
molecular clouds (GMCs) in the MAGMA LMC cloud catalogue. The observed clouds
exhibit relationships that are similar to those determined for Galactic GMCs, although
LMC clouds have narrower linewidths and lower CO luminosities than Galactic clouds
of a similar size. The average mass surface density of the LMC clouds is 50 M⊙ pc−2 ,
approximately half that of GMCs in the inner Milky Way. The intrinsic scatter in the
observed size-linewidth relation is larger than the measurement uncertainties, which
motivates us to examine whether GMC properties are sensitive to variations in local
interstellar conditions. Specifically, we investigate whether there are correlations between GMC properties and the H I column density, radiation field, stellar mass surface
density, external pressure and location within the LMC. Very few cloud properties
demonstrate a clear dependence on environment. The exceptions are significant positive correlations between i) the GMC velocity dispersion and the H I column density,
ii) the stellar mass surface density and the average peak CO brightness, and iii) the
stellar mass surface density and the CO surface brightness. The mass surface density
of GMCs without signs of massive star formation shows no dependence on the local
radiation field, which is inconsistent with the photoionization-regulated star formation theory proposed by McKee (1989). We find some evidence that the mass surface
197
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
198
Trends
density of the MAGMA clouds increases with the interstellar pressure, as proposed
by Elmegreen (1989), but the detailed predictions of this model are not fulfilled once
estimates for the local radiation field, metallicity and GMC envelope mass are taken
into account. On the scale of individual GMCs, we find no correlation between the
star formation rate surface density ΣSF R and the mass surface densities of atomic ΣHI ,
molecular ΣH2 and neutral (i.e. atomic+molecular) gas ΣHI+H2 . Consistent with re1.0 and
solved observations of nearby galaxies, however, relations of the form ΣSF R ∝ ΣH
2
ΣSF R ∝ Σ1.8
HI+H2 emerge if the GMC data are averaged over ∼ 0.5 kpc scales.
4.1 Introduction
The formation of GMCs and the transformation of molecular gas into stars are key
processes in the life cycle of galaxies. Models of galactic evolution often assume that
GMCs are sufficiently similar across different galactic environments that a galaxy’s star
formation rate can be parameterised as the product of the GMC formation rate and the
star formation efficiency of molecular gas (e.g. Ballesteros-Paredes & Hartmann, 2007;
Blitz & Rosolowsky, 2006). This approach was initially justified by studies of Galactic
molecular clouds, which found that the basic physical properties of GMCs in the Milky
Way’s disk obeyed well-defined scaling relations, often referred to as “Larson’s laws”
(e.g. Larson, 1981; Solomon et al., 1987; Heyer et al., 2001). Recently, considerable
effort has been devoted to determining whether GMCs in other galaxies also follow the
Larson relations (e.g. Rosolowsky et al., 2003; Rosolowsky & Blitz, 2005; Rosolowsky,
2007), since empirical evidence that GMC properties are uniform – or at least exhibit
well-behaved correlations with a parameter such as metallicity or pressure – would provide valuable information for developing models of star formation and galaxy evolution
through cosmic time.
As well as furnishing galaxy evolution models with empirical inputs, studies of extragalactic GMC populations aspire to resolve long-standing questions about the physical
processes that are important for the formation and evolution of molecular clouds. Are
GMCs quasi-equilibrium structures, for example, or transient features in the turbulent
4.1. Introduction
199
interstellar medium (ISM)? Do all GMCs form stars, and if not, why not? What is
the physical origin of Larson’s scaling relations? Although a number of different theories to explain molecular cloud properties and the Larson relations have been proposed
(Chieze, 1987; Fleck, 1988; McKee, 1989; Elmegreen, 1989), there are few extragalactic
GMC samples that are comparable to the catalogue of Solomon et al. (1987, henceforth
S87), which contains 273 clouds in the inner Milky Way disk. A survey of the LMC by
NANTEN provided the first complete inventory of GMCs in any galaxy (Fukui et al.,
2008), but could not resolve molecular cloud structures smaller than ∼40 pc. Thorough testing of molecular cloud models will require deep, unbiased, wide-field surveys
of molecular clouds at high angular resolution across a range of interstellar conditions.
Extensive surveys of this kind are only just feasible with current instrumentation, and
hence the number of molecular cloud samples that can be used to falsify molecular
cloud models remains frustratingly small.
To date, studies of the CO emission in nearby galaxies have concluded that extragalactic GMCs are alike. For a sample of ∼ 70 resolved GMCs located in five galaxies (M31,
M33, IC10, and the Magellanic Clouds), Blitz et al. (2007) found that extragalactic
GMCs not only follow the Galactic Larson relations, but also that different galaxies
have similar GMC mass distributions. Similar conclusions were reached by Bolatto
et al. (2008, henceforth B08), although these authors also noted that molecular clouds
in the SMC have low CO luminosities and narrow linewidths compared to Galactic
GMCs of a similar size. By comparing tracers of star formation and neutral gas on
∼ 1 kpc scales for galaxies in The H I Nearby Galaxy Survey (THINGS, Walter et al.,
2008), Leroy et al. (2008) found that the star formation efficiency of molecular gas,
defined as SF EH2 ≡ ΣSF R /ΣH2 , was constant in spiral galaxies. More precisely, these
authors found SF EH2 = 5.25± 2.5× 10−10 yr−1 , a result that is consistent with uniform
GMC properties (Krumholz & McKee, 2005).
While the existing observational evidence has so far been interpreted in favour of GMCs
constituting a homogeneous population, a dependence of GMC properties on the local
interstellar environment is by no means ruled out. A constant SF EH2 on kiloparsec
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
200
Trends
scales indicates that the properties of GMC ensembles are alike on those scales; whether
this conclusion can be applied to individual GMCs is far less certain. Neither B08 nor
Blitz et al. (2007) pursued the origin of the scatter in the extragalactic Larson relations
that they observed, even though the mean GMC mass surface density among galaxies
in their respective samples varies by more than an order of magnitude, and the mass
surface densities of individual GMCs varies between ∼ 10 and 1000 M⊙ pc−2 . Heyer
et al. (2009) have recently presented evidence that the mass surface density of Galactic
GMCs increases with the velocity dispersion normalised over a fixed spatial scale. This
result would be expected if GMCs were magnetically supported, but could also indicate
that GMCs with large mass surface densities must be strongly turbulent if they are to
maintain rough virial balance. A resolved survey of a large number (& 100) of GMCs
located in a single galaxy is a valuable resource to address this issue, since it eliminates
the uncertainties inherent in combining heterogeneous datasets and provides a sample
that is large enough to investigate both the average properties and scaling relations of
an extragalactic GMC population, as well as the dispersion around overall trends and
average quantities.
In this chapter, we examine the Larson relations for GMCs in the LMC and investigate
whether the properties of the GMCs depend on conditions in the local environment.
The rest of this chapter is structured as follows: in Section 4.2, we discuss scaling
relations between the cloud properties. Section 4.3 presents a comparison between the
physical properties of the GMCs and properties of their local interstellar environment.
In Section 4.4, we discuss whether our results are consistent with i) the photoionizationregulated theory of star formation proposed by McKee (1989, henceforth M89) and ii)
a dominant role for interstellar gas pressure in the determination of molecular cloud
properties, as suggested by Elmegreen (1989, henceforth E89). In this Section, we also
examine whether a Kennicutt-Schmidt correlation, i.e. a relationship between the star
formation rate and gas surface densities, is evident for the LMC on scales between 0.05
and 0.5 kpc. We conclude with a summary of our key results in Section 4.5.
4.2. The Larson Scaling Relations
201
4.2 The Larson Scaling Relations
Empirical scaling relations between the basic physical properties of molecular clouds
have become a standard test for assessing differences between molecular cloud populations. Larson’s initial work identified the three well-known “laws” obeyed by Galactic
molecular clouds: i) a power-law relationship between the size of a cloud and its velocity dispersion, ii) a nearly linear correlation between the virial mass of a cloud and
mass estimates based on other tracers of the H2 column density, which seemed to imply
that molecular clouds are self-gravitating and in approximate virial balance, and iii) an
inverse relationship between the size of a cloud and its average density (Larson, 1979,
1981). S87 were subsequently able to measure the coefficients and exponents of the
power-law relationships between the properties of 273 GMCs in the inner Milky Way,
establishing the empirical expressions for Larson’s Laws that have become the yardstick
for studies of GMCs in other galaxies and in different interstellar environments (see e.g.
B08, Blitz et al., 2007).
Most famously, the analysis by S87 showed that inner Milky Way clouds follow a sizelinewidth relation of the form σv = 0.72R0.5±0.05 km s−1 , and that there is a strong,
approximately linear correlation between a cloud’s virial mass and its CO luminosity,
M⊙ . These two relations can be combined to provide expressions for
Mvir = 39L0.81±0.03
CO
the relationship between a cloud’s luminosity and size, and luminosity and linewidth:
LCO ≈ 25R2.5 K km s−1 pc2 and LCO ≈ 130σv5 K km s−1 pc2 . As noted by S87, virialised
clouds (for which M ∝ Rσv2 ) with σv ∝ R0.5 will follow a mass-size relation of the form
M ∝ R2 . This implies constant average mass surface density for molecular clouds,
√
hΣH2 i, which is related to the coefficient of the size-linewidth relation, C0 ≡ σv / R,
via hΣH2 i ≈ 331C02 M⊙ pc−2 for clouds with a ρ ∝ R−1 density profile. S87 found
C0 = 0.72 km s−1 pc−0.5 and hΣH2 i ∼ 170 M⊙ pc−2 for molecular clouds in the inner
Milky Way, slightly higher than the median surface density of the extragalactic GMCs
analysed by B08, who found hΣH2 i ∼ 130 M⊙ pc−2 . Heyer et al. (2009) have recently
argued that the S87 estimate should be revised downwards to ∼ 100 M⊙ pc−2 , and we
adopt this as our reference value in the remainder of this chapter.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
202
Trends
4.2.1
The Size-Linewidth Relation
Figure 4.1[a] presents a plot of velocity dispersion versus radius for GMCs in the
MAGMA cloud list. The LMC clouds are clearly offset towards lower velocity dispersions compared to the R − σv relations derived by S87 and B08: some of the larger
0.6±0.1 )
LMC clouds fall under the R − σv relation determined by B08 (σv ≈ 0.44+0.18
−0.13 R
by a factor of ∼ 3 in velocity dispersion. The discrepancy between the LMC clouds
and the R − σv relation derived by B08 should not be the result of cloud decomposition techniques, as we have identified cloud and parameterized GMC properties using
the same algorithms as those authors. The offset towards lower velocity dispersion at
a given radius would suggest that the turbulent bulk motions within LMC molecular clouds are more quiescent than in the B08 GMCs. If GMCs in the LMC manage
to achieve rough dynamic equilibrium, then this would imply that they require lower
mass surface densities to be stable against gravitational collapse than the B08 clouds.
A further possibility is that CO molecules are photodissociated in the outer parts of
GMCs in the LMC and that the CO linewidth only reflects gas motions within the
dense CO-bright core. In this case, however, we would expect that the spatial extent
of the CO emission, and hence the measured radius, also to decrease.
To fit the R − σv relationship for the MAGMA data, we used the BCES bisector linear
regression method presented by Akritas & Bershady (1996), which is designed to take
measurement errors in both the dependent and independent variable, and the intrinsic
scatter of a dataset into account.1 For our analysis of the Larson relations, we use the
bisector method because our goal is to estimate the intrinsic relation between the cloud
properties (e.g. Babu & Feigelson, 1996). The best-fitting relation for all 125 clouds in
the MAGMA cloud list, illustrated with grey shading in Figure 4.1[a], is:
log σv = (−0.73 ± 0.08) + (0.74 ± 0.05) log R (BCES bisector) .
1
(4.1)
’BCES’ stands for bivariate, correlated errors and intrinsic scatter. Software that implements this
method is available from: http://www.astro.wisc.edu/∼mab/archive/stats/stats.html. For our
analysis, we assume that measurement errors are uncorrelated.
4.2. The Larson Scaling Relations
[a]
7
log(Mvir/[Msol])
log(σv/[km s−1])
1.0
203
0.5
7
S8
0.0
8
B0
rall = (0.49,<0.01)
rhq = (0.39,<0.01)
1.0
1.5
2.0
[b]
6
00
5
10
0
4
10
rall = (0.79,<0.01)
rhq = (0.80,<0.01)
10
2.5
1.0
10
0
[c]
10
7
.0
5.5
1
5.0
4.5
S8
7
4.0
rall = (0.81,<0.01)
rhq = (0.79,<0.01)
8
3.5
3.0
1.0
1.5
2.0
log(Radius/[pc])
1.5
2.0
2.5
log(Radius/[pc])
2.5
log(Mvir/[Msol])
6.0
B0
log(LCO/[K km s−1 pc2])
log(Radius/[pc])
21
[d]
20
4e
4e
19
4e
6
5
4
7
S8
8
B0
3.0
rall = (0.82,<0.01)
rhq = (0.81,<0.01)
3.5
4.0
4.5
5.0
5.5
6.0
log(LCO/[K km s−1 pc2])
Figure 4.1 Plots of (a) radius versus velocity dispersion; (b) radius versus virial mass; (c)
radius versus CO luminosity; and (d) CO luminosity versus virial mass for the GMCs identified
in the MAGMA LMC survey. In each panel, the light grey shaded area represents our BCES
bisector fit to the 125 GMCs in the MAGMA cloud list and the 1σ uncertainty in the fit (see
text). The black dotted line in each panel shows the standard relation for the S87 inner Milky
Way data, while the black dashed line represents the relation determined for extragalactic
GMCs by B08. The dot-dashed grey lines represent constant values of CO surface brightness
(I(CO) = 1, 10, 100 K km s−1 , panel [b]); mass surface density (ΣH2 = 10, 100, 1000 M⊙ pc−2 ,
−1
panel [c]); and CO-to-H2 conversion factor (XCO = 0.4, 4.0, 40 × 1020 cm−2 (K km s−1 ) , panel
[d]). GMCs belonging to the complete MAGMA LMC cloud list are represented by small open
squares, and GMCs in the high quality subsample are indicated using filled grey circles. The
blue cross symbols represent GMCs without signs of active star formation. For comparison
with the correlations presented in Figure 4.2 to 4.6, Spearman’s rank correlation coefficent and
corresponding p-value for all clouds and the high quality subsample are indicated at the bottom
right of each panel.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
204
Trends
Here, and for all other relations presented in this chapter, the errors in the regression
coefficients are derived using bootstrapping techniques; for relations determined using
a BCES estimator, they are consistent with the standard deviation of the regression coefficients derived according to equation 30 in Akritas & Bershady (1996). Although the
errors in best-fitting relation that we derive are small, the form of the relation depends
on the linear regression method (for a discussion of this issue in other astronomical contexts, see e.g. Tremaine et al., 2002; Kelly, 2007; Blanc et al., 2009). For comparison
with other work, the best-fitting relations determined using the BCES ordinary least
squares (henceforth OLS(Y|X)) and BCES orthogonal methods are:
log σv = (−0.24 ± 0.09) + (0.40 ± 0.06) log R (BCES OLS(Y|X)), and
(4.2)
log σv = (−0.46 ± 0.12) + (0.56 ± 0.08) log R (BCES orthogonal) .
(4.3)
The best-fitting relation derived using the FITEXY estimator (Press et al., 1992) is:
log σv = (−0.37 ± 0.17) + (0.50 ± 0.11) log R (FITEXY) .
(4.4)
The intrinsic scatter of the MAGMA GMCs around the best-fitting R − σv relation
is greater than the measurement errors in R and σv across the observed range of
cloud radii. The C0 values of individual MAGMA GMCs vary between 0.21 and
0.98 km s−1 pc−0.5 . Although LMC clouds may be said to follow the same R − σv
relation as other extragalactic GMCs in the sense that the slope and amplitude of the
derived best-fitting relations are similar, their mass surface density is not strictly constant, but instead varies between 15 and 320 M⊙ pc−2 (see Figure 4.1[b]). This is larger
than the variation in ΣH2 that we would expect from our GMC identification and decomposition methods (cf. Figure 3.9). An outstanding question, which we investigate
further in Section 4.3, is whether the variation in ΣH2 is stochastic or whether it is
related to changes in the environment of the GMCs.
4.2. The Larson Scaling Relations
4.2.2
205
The Size-Luminosity Relation
Figure 4.1[c] presents a plot of CO luminosity versus radius for GMCs in the MAGMA
cloud list. Although the LCO − R relation determined for extragalactic clouds by B08
2.54±0.20 ) overlaps with the smaller MAGMA clouds, the slope of the
(LCO ≈ 7.8+6.9
−3.7 R
LCO − R relation in the LMC is clearly shallower, such that the CO emission in large
LMC molecular clouds is up to an order of magnitude fainter than for the B08 GMCs.
A BCES bisector fit yields:
log LCO = (1.39 ± 0.12) + (1.88 ± 0.08) log R ,
(4.5)
for the LCO − R relation. The relations determined using the BCES OLS(Y|X), BCES
orthogonal and FITEXY methods are also shallower than the B08 fit, with slopes of
1.67±0.09, 2.02±0.10 and 2.17±0.29 respectively.
The median CO surface brightness of GMCs in the MAGMA cloud list is 4.8 K km s−1 ,
and the median absolute deviation of the GMCs around this value is ∼ 30%. This
corresponds to an average mass surface density of only hΣH2 i ∼ 20 M⊙ pc−2 for the
MAGMA clouds if we adopt the Galactic XCO value (2 × 1020 cm−2 (K km s−1 )−1 , e.g.
Strong & Mattox, 1996) and hΣH2 i ∼ 50 M⊙ pc−2 if we use the average XCO value of
GMCs in the MAGMA cloud list (XCO = 4.7 × 1020 cm−2 (K km s−1 )−1 , see Table 3.4).
Individual GMCs have I(CO) values between 1.8 and 20.4 K km s−1 . Some of the
variation in I(CO) is related to the location of the GMCs: for clouds that are coincident
with the stellar bar (defined as regions where Σ∗ > 100 M⊙ pc−2 , see Figure 2.2), the
median CO surface brightness is 9.1 K km s−1 . We examine the relationship between
the CO emission in LMC molecular clouds and the stellar mass surface density more
closely in Section 4.3.3.
4.2.3
The Calibration between Virial Mass and CO Luminosity
Figure 4.1[d] presents a plot of the virial mass estimate versus the CO luminosity for
the MAGMA clouds. The LMC clouds appear to be in reasonable agreement with
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
206
Trends
the slope of the relation determined for the B08 extragalactic GMC data (Mvir ≈
1.00±0.04
), although offset slightly to higher Mvir values. A BCES bisector fit
7.6+3.2
−2.6 LCO
to the Mvir − LCO relation for the complete MAGMA LMC cloud list yields:
log Mvir = (0.50 ± 0.25) + (1.13 ± 0.06) log LCO .
(4.6)
The slopes of the relations determined using the BCES OLS(Y|X), BCES orthogonal
and FITEXY methods are 0.99±0.06, 1.16±0.07 and 0.97±0.17 respectively. While
the correlation between the virial mass and CO luminosity of the MAGMA clouds is
tight, the slope of the best-fitting relation that we derive is at least linear, and perhaps
slightly greater than unity. Even for the steepest BCES fit, however, the systematic
variation in XCO with mass is small, corresponding to only a factor of two increase in
XCO for GMC masses between 3 × 104 and 3 × 106 M⊙ .
The median value of XCO for the MAGMA LMC clouds, derived by comparing the CO
luminosity to the virial mass estimate for each GMC, is 4.7 × 1020 cm−2 (K km s−1 )−1 .
The median absolute deviation of the XCO estimates for individual clouds is about
30%. This is in excellent agreement with the values derived by B08 and Blitz et al.
(2007) for their extragalactic GMCs, and the LMC value obtained by the SEST Large
Programme (Israel et al., 2003b), but lower than the value derived from the NANTEN
LMC survey (7 × 1020 cm−2 (K km s−1 )−1 , Fukui et al., 2008). While the CPROPS
cloud decomposition algorithm aims to minimize instrumental effects, part of this discrepancy may be due to the difference in angular resolution between the two surveys.
GMCs are constituted by dense (n ≈ 103 cm−3 ) CO-bright clumps embedded in more
diffuse gas with lower CO brightness. As noted in previous studies (e.g. Pineda et al.,
2009; Bolatto et al., 2003), observations with coarser resolution trace larger physical
structures and hence derive larger values for XCO . In principle, the discrepancy could
also arise from MAGMA’s observational strategy, which excluded clouds in the NANTEN catalogue with low CO surface brightness (recall that XCO ≡ ΣH2 /2.2I(CO)). In
practice, however, we do not expect that our target selection has a significant impact
on the average MAGMA XCO value, since there are only five NANTEN clouds with
4.3. GMC Properties and Environment
207
LCO > 7000 K km s−1 pc2 and peak I(CO) < 1 K km s−1 . GMCs without signs of massive star formation appear to lie along the upper envelope of the points in Figure 4.1[d],
reflecting their slightly higher XCO factors.
4.3 GMC Properties and Environment
In this section, we explore the variation of the physical properties of the MAGMA
LMC clouds in response to local interstellar conditions. We estimate the H I column
density, stellar mass surface density, interstellar radiation field and external pressure
at the location of each GMC using the maps described in Section 2.5, taking the mean
value of all independent pixels with integrated CO emission greater than 1 K km s−1 .
In addition to the physical properties of the GMCs, we also examine whether their
star formation rate surface density and the ratio between their molecular and atomic
gas surface densities (Rmol ≡ ΣH2 ,CO /ΣHI ) depend on environmental parameters. On
1.0±0.2
and that Rmol increases
kiloparsec scales, recent work has shown that ΣSF R ∝ ΣH
2
with the hydrostatic pressure at the disk midplane Ph according to Rmol ∝ Phγ with
γ ∈ [0.8, 1.0] (e.g. Wong & Blitz, 2002; Blitz & Rosolowsky, 2006; Bigiel et al., 2008;
Leroy et al., 2008). Here we are interested to determine whether these relations hold
on the scale of individual GMCs in the LMC, since the size scale on which these trends
break down should provide a valuable clue as to their physical origin. Following the
methods used in extragalactic studies where individual GMCs cannot be resolved, we
use the molecular mass surface density inferred from the CO luminosity ΣH2 ,CO to estimate Rmol .
We measure the strength of correlations between the GMC and interstellar properties
using the Spearman rank correlation coefficient r. The statistical significance of r is
assessed by calculating the corresponding p-value, which is the two-sided significance
level of r’s deviation from zero. We consider p-values less than 0.01 to provide statistically significant evidence against the null hypothesis. We regard |r| values greater than
0.6 as strong correlations (or anti-correlations if r < 0), |r| values between 0.4 and 0.6
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
208
Trends
as moderate correlations, and |r| values between 0.2 and 0.4 as weak correlations. We
regard correlations with |r| values less than 0.2 to be very weak and therefore unlikely
to have practical significance, even if their p-value is small.
Each correlation test was repeated for the complete MAGMA LMC cloud list and for
the high quality subsample. Since the Spearman rank correlation test does not account for measurement uncertainties, we performed 500 trials of each correlation test
in which we offset each cloud property measurement by a fraction of its uncertainty.
The value of a cloud property measurement in each trial was displaced by k∆x, where
∆x is the absolute uncertainty in the cloud property measurement and k is a uniformly
distributed random number between -1 and 1. We consider our correlation result to be
robust and significant if i) the correlation coefficients obtained in the trials are narrowly
distributed around the original (i.e. unperturbed) value of r, ii) the corresponding pvalues are narrowly distributed around zero, i.e. hpi ≤ 0.01 and σp ≤ 0.01, and iii)
|r| ≥ 0.2 for both the complete MAGMA cloud list and the high quality subsample.
The results of all the correlation tests are presented in Table 4.1.
As a reference for the values obtained in these comparisons, we conducted Spearman
rank correlation tests for the Larson scaling relations shown in Figure 4.1, and present
the results in Table 4.2. We note that the size-linewidth relation is only a weak to
moderate correlation: for all 125 GMCs in the MAGMA cloud list hri = 0.48, while for
the high quality GMCs hri = 0.39. The results for the other scaling relations indicate
strong correlations. This is not surprising, since the these relations involve quantities
that are not independent, i.e. Mvir ∝ σv2 R and LCO ∝ σv R2 hT i, where hT i is the
average CO brightness.
4.3. GMC Properties and Environment
209
Table 4.1 Results of the correlation tests between properties of the MAGMA GMCs and
properties of the interstellar environment. The properties used in the comparison are listed in
columns 1 and 2. The results of the correlation tests for the complete MAGMA cloud list are
shown in columns 3 to 5; the results for the 57 high quality GMCs are shown in columns 6 to
8. The results list hri, hpi and σp , where hri is the median Spearman correlation coefficient
obtained in the error trials (see text), hpi is the median of the corresponding p-values, and σp
is the standard deviation of the p-values.
Environment
Rgal
G0
Σ∗
N (HI)
Ph
GMC
R
σv
hTpk i
I(CO)
ΣH2
XCO
Rmol
ΣSF R
R
σv
hTpk i
I(CO)
ΣH2
XCO
Rmol
ΣSF R
R
σv
hTpk i
I(CO)
ΣH2
XCO
Rmol
ΣSF R
R
σv
hTpk i
I(CO)
ΣH2
XCO
Rmol
ΣSF R
R
σv
hTpk i
I(CO)
ΣH2
XCO
Rmol
ΣSF R
hri
0.12
0.16
-0.30
-0.19
0.12
0.26
-0.28
-0.05
-0.16
-0.02
0.18
0.17
0.06
-0.06
0.17
0.79
-0.12
0.00
0.34
0.35
0.06
-0.18
0.32
-0.01
0.12
0.30
-0.08
-0.05
0.25
0.29
-0.58
0.22
0.04
0.26
0.13
0.17
0.26
0.14
-0.30
0.23
All GMCs
hpi
σ(p)
0.22
0.40
0.10
0.20
< 0.01 < 0.01
0.05
0.11
0.22
0.42
0.01
0.02
< 0.01 < 0.01
0.40
0.57
0.11
0.23
0.48
0.55
0.07
0.16
0.09
0.20
0.38
0.57
0.44
0.56
0.09
0.19
< 0.01 < 0.01
0.21
0.42
0.49
0.54
< 0.01 < 0.01
< 0.01 < 0.01
0.39
0.60
0.07
0.16
< 0.01 < 0.01
0.50
0.56
0.23
0.45
< 0.01 < 0.01
0.34
0.53
0.40
0.59
0.01
0.03
< 0.01 < 0.01
< 0.01 < 0.01
0.03
0.06
0.46
0.57
< 0.01
0.02
0.19
0.39
0.09
0.17
< 0.01
0.02
0.17
0.33
< 0.01 < 0.01
0.02
0.05
hri
0.06
-0.05
-0.49
-0.29
-0.02
0.20
-0.35
0.02
-0.27
0.13
0.28
0.38
0.28
-0.03
0.34
0.81
-0.09
0.07
0.56
0.43
0.10
-0.23
0.42
-0.07
0.28
0.42
-0.13
-0.03
0.26
0.30
-0.49
0.26
0.19
0.48
0.26
0.25
0.34
0.14
-0.12
0.27
HQ GMCs
hpi
σ(p)
0.55
0.52
0.46
0.56
< 0.01 < 0.01
0.05
0.11
0.44
0.52
0.18
0.36
0.01
0.04
0.49
0.57
0.07
0.15
0.32
0.56
0.06
0.13
0.01
0.02
0.06
0.13
0.46
0.54
0.02
0.05
< 0.01 < 0.01
0.43
0.59
0.46
0.61
< 0.01 < 0.01
< 0.01 < 0.01
0.39
0.58
0.13
0.28
< 0.01 < 0.01
0.45
0.63
0.07
0.14
< 0.01 < 0.01
0.32
0.60
0.45
0.56
0.08
0.16
0.05
0.10
< 0.01 < 0.01
0.08
0.17
0.20
0.38
< 0.01 < 0.01
0.09
0.18
0.10
0.21
0.02
0.05
0.32
0.50
0.36
0.56
0.07
0.16
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
210
Trends
Table 4.2 Results of the Spearman rank correlation tests for Larson’s scaling relations in
the LMC. The relation is listed in column 1. The results of the correlation tests for the
complete MAGMA cloud list are shown in columns 2 to 4; the results for the 57 high quality
GMCs are shown in columns 5 to 7. hri is the median Spearman correlation coefficient
obtained in the error trials (see text), hpi is the median of the corresponding p-values, and
σp is the standard deviation of the p-values.
4.3.1
Relation
hri
All GMCs
hpi
σ(p)
hri
R − σv
R − LCO
LCO − Mvir
0.48
0.80
0.81
< 0.01
< 0.01
< 0.01
0.39
0.80
0.80
< 0.01
< 0.01
< 0.01
HQ GMCs
hpi
σ(p)
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
Comparison with Galactocentric Radius
In Figure 4.2, we plot properties of the MAGMA clouds as a function of the separation
between the GMC and the LMC’s kinematic centre, dKC . We derive dKC for each GMC
using the same geometric assumptions as in Chapter 3, i.e. a disk inclination of 35◦ ,
a position angle of 340◦ for the receding line-of-nodes, and a kinematic centre of RA
05h19m30s, Dec -68d53m (J2000) (Wong et al., 2009). The plots in Figure 4.2 are highly
scattered, with little evidence that the properties of MAGMA GMCs vary systematically with galactocentric radius. As noted in Chapter 3, there is an obvious gap at
dKC ∼ 1.5 kpc where relatively few GMCs are located. The Spearman correlation tests
indicate a weak but significant anti-correlation between the average peak CO brightness
Tpk and dKC . This trend is not apparent for GMCs located within dKC . 1.5 kpc but
becomes more pronounced at larger galactocentric radii, and is likely to be responsible
for the lower average I(CO) and Rmol values for GMCs beyond dKC ∼ 2 kpc.
4.3.2
Comparison with G0
In Figure 4.3, we plot properties of the MAGMA clouds as a function of the local interstellar radiation field, G0 . There is an excellent correlation between G0 and ΣSF R ,
which arises because star formation makes a significant contribution to dust-heating
locally. Otherwise none of the correlations satisfy our criteria for significance. Contrary
to what might be expected from classic photodissociation models (e.g. van Dishoeck &
4.3. GMC Properties and Environment
1.0
[a] rall = (0.12,0.18)
rhq = (0.08,0.56)
log(σv/[km s−1])
2.5
log(Radius/[pc])
211
2.0
1.5
0.8
0.6
0.4
0.2
0.0
1.0
0
0.4
1
2
−0.2
3
log(ICO/[K km s−1])
[c] rall = (−0.32,<0.01)
rhq = (−0.49,<0.01)
0.3
log(<Tpk>/[K])
[b] rall = (0.16,0.07)
rhq = (−0.05,0.73)
0.2
0.1
0.0
−0.1
0
1
2
3
[d] rall = (−0.20,0.02)
rhq = (−0.31,0.02)
1.5
1.0
0.5
0.0
0
1
2
3
log(ΣH2/[Msol pc−2])
3.0
[e] rall = (0.13,0.14)
rhq = (−0.03,0.84)
2.5
2.0
1.5
1.0
2
1.0
0.5
0.0
−0.5
1
2
3
[f] rall = (0.27,<0.01)
rhq = (0.23,0.09)
1.5
1.0
0.5
0.0
0
3
[g] rall = (−0.29,<0.01)
rhq = (−0.36,<0.01)
1.5
log(ΣH2,CO/ΣHI)
1
log(SFR/[Msol yr−1 kpc−2])
0
0
log(XCO/[1020 cm−2 (K km s−1)−1])
−0.2
1
2
3
[h] rall = (−0.05,0.68)
rhq = (0.00,0.98)
1
0
−1
−2
−3
0
1
2
3
Gal. Radius [kpc, W09]
0
1
2
3
Gal. Radius [kpc, W09]
Figure 4.2 Properties of the MAGMA GMCs versus their spatial separation from the LMC’s
kinematic centre: (a) R; (b) σv ; (c) Tpk ; (d) I(CO); (e) ΣH2 ; (f) XCO ; (g) Rmol ; and (h) ΣSFR .
The plot symbols are the same as in Figure 4.1. The horizontal dotted lines in panels [e] and
[f] indicate ΣH2 = 100 M⊙ pc−2 and XCO ∼ 2 × 1020 cm−2 (K km s−1 )−1 . The Spearman rank
correlation coefficient and corresponding p-value for the complete MAGMA cloud list and high
quality subsample are indicated at the top left of each panel.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
212
Trends
Black, 1988), there is no general trend between the G0 and XCO , even for GMCs without signs of active star formation (i.e. where G0 is dominated by the external field).
An earlier analysis of the MAGMA data for the molecular ridge region also found that
XCO was insensitive to variations in the radiation field strength (Pineda et al., 2009).
4.3.3
Comparison with the Interstellar Pressure
In this subsection, we investigate whether the physical properties of the MAGMA clouds
vary with the interstellar pressure, which we estimate according to Equation 2.6. In
the following, we first compare the cloud properties to two independent components of
Ph for which we have an empirical tracer: i) the stellar mass surface density, Σ∗ ; and
ii) the atomic gas surface density, Σg .
Comparison with Σ∗
In Figure 4.4, we plot the properties of the MAGMA clouds versus Σ∗ . The correlation tests indicate weak but significant correlations between Σ∗ and Tpk (panel [c]),
I(CO) (panel [d]) and Rmol (panel [g]); these correlations are stronger if we only consider GMCs in the high quality subsample. The existence of trends between GMC
properties and Σ∗ suggests that the GMCs in the LMC do respond to the presence of
the galaxy’s stellar population, despite evidence that the stellar bar may be physically
offset from the gas disk (e.g. Zhao & Evans, 2000; Nikolaev et al., 2004).
The plot in Figure 4.4[g] is interesting since it suggests that the stellar surface density
plays a role in determining the balance between the atomic and molecular gas phases,
even on small scales. Rmol is not correlated with G0 (Figure 4.3[g]), however, which
suggests that it may be the gravitational potential of the stars (e.g. Yang et al., 2007;
Elmegreen & Parravano, 1994), rather than stellar feedback (e.g. Hunter et al., 1998),
that promotes the formation of molecular gas. The Rmol values are scattered around
Rmol ∼ 1 for GMCs with Σ∗ ∈ [10, 100] M⊙ pc−2 , but appear to increase more sharply
for higher Σ∗ values. Leroy et al. (2008) determined a linear correlation between Rmol
and Σ∗ for galaxies in their sample (indicated in Figure 4.4[g] by a dashed line), with
4.3. GMC Properties and Environment
1.0
[a] rall = (−0.17,0.06)
rhq = (−0.27,0.04)
log(σv/[km s−1])
log(Radius/[pc])
2.5
213
2.0
1.5
−0.5
0.0
0.5
0.6
0.4
0.2
−0.2
1.0
[c] rall = (0.19,0.04)
rhq = (0.26,0.05)
log(ICO/[K km s−1])
log(<Tpk>/[K])
0.3
0.8
0.0
1.0
0.4
[b] rall = (−0.03,0.75)
rhq = (0.12,0.36)
0.2
0.1
0.0
−0.1
1.5
−0.5
0.0
0.5
1.0
0.5
1.0
[d] rall = (0.17,0.05)
rhq = (0.37,0.01)
1.0
0.5
0.0
−0.5
0.0
0.5
1.0
log(ΣH2/[Msol pc−2])
3.0
[e] rall = (0.06,0.50)
rhq = (0.27,0.05)
2.5
2.0
1.5
1.0
log(ΣH2,CO/ΣHI)
1.5
0.0
0.5
1.5
[g] rall = (0.17,0.05)
rhq = (0.34,0.01)
1.0
0.5
0.0
−0.5
0.0
[f] rall = (−0.06,0.51)
rhq = (−0.04,0.78)
1.0
0.5
0.0
−0.5
1.0
log(SFR/[Msol yr−1 kpc−2])
−0.5
−0.5
log(XCO/[1020 cm−2 (K km s−1)−1])
−0.2
1
0.0
0.5
1.0
[h] rall = (0.80,<0.01)
rhq = (0.83,<0.01)
0
−1
−2
−3
−0.5
0.0
0.5
log(G0/G0,sol)
1.0
−0.5
0.0
0.5
1.0
log(G0/G0,sol)
Figure 4.3 Properties of the MAGMA GMCs, plotted as a function of the local interstellar radiation field, G0 /G0,⊙ . The panels, plot symbols and annotations are the same as in Figure 4.2.
The blue crosses in panel [e] represent GMCs without signs of massive star formation.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
214
Trends
no evidence for a threshold or break in the relation for Σ∗ values between 10 and
103 M⊙ pc−2 ; we note, however, that these authors estimated Rmol in dwarf galaxies
from measurements of ΣSF R and ΣHI by assuming a fixed star formation efficiency in
molecular gas, rather than CO observations. Finally, we caution that an increase in
the H2 mass surface density is not the only possible explanation for the plots in panels
[c], [d] and [g]; variations in the CO excitation temperature and/or abundance of CO
relative to H2 in regions with high Σ∗ could produce similar trends (see Section 4.4.2).
Comparison with N (H I)
In Figure 4.5, we plot the cloud properties as a function of the atomic gas surface
density, Σg , which is estimated from the total H I column density along the line-ofsight. We find a weak but robust correlation between Σg and σv (panel [b]). There
is some indication that ΣH2 (panel [e]) and XCO (panel [f]) also increase with the H I
column density – as would be expected if σv increases without a corresponding increase
in cloud size or CO luminosity – but the correlations are not significant if only high
quality GMCs are considered. As Σg ≡ ΣHI by definition, the anti-correlation in panel
[g] is not particularly meaningful, although it demonstrates that most of the variation
in Rmol is due to variations in the atomic, rather than molecular, mass surface density
of the MAGMA GMCs.
An important caveat for interpreting Figure 4.5 is that H I line profiles in the LMC are
complex, exhibiting two well-defined velocity components in some parts of the LMC’s
disk (especially in the south-east, e.g. Luks & Rohlfs, 1992). The CO emission is
almost invariably associated with only one H I velocity component (Wong et al., 2009),
so the H I column density that is physically associated with a GMC is almost certainly
overestimated by the total N (H I) along the line-of-sight in these regions. Excluding
GMCs located in the south-east of the LMC (i.e. clouds with right ascension above
05h38m and declination below -68d30m (J2000)) from our comparisons between the
cloud properties and Σg suggests that the correlation between Σg and σv is not severely
contaminated by the contribution of a secondary H I velocity component to N (H I).
4.3. GMC Properties and Environment
1.0
[a] rall = (−0.13,0.15)
rhq = (−0.12,0.38)
log(σv/[km s−1])
log(Radius/[pc])
2.5
215
2.0
1.5
log(<Tpk>/[K])
0.3
1.0
1.5
2.0
0.6
0.4
0.2
−0.2
0.5
2.5
[c] rall = (0.35,<0.01)
rhq = (0.55,<0.01)
log(ICO/[K km s−1])
0.4
0.8
0.0
1.0
0.5
[b] rall = (−0.01,0.94)
rhq = (0.06,0.64)
0.2
0.1
0.0
−0.1
1.5
1.0
1.5
2.0
2.5
2.0
2.5
2.0
2.5
2.0
2.5
[d] rall = (0.35,<0.01)
rhq = (0.39,<0.01)
1.0
0.5
0.0
1.0
1.5
2.0
2.5
log(ΣH2/[Msol pc−2])
3.0
[e] rall = (0.06,0.50)
rhq = (0.08,0.56)
2.5
2.0
1.5
1.0
log(ΣH2,CO/ΣHI)
1.5
1.0
1.5
2.0
[g] rall = (0.32,<0.01)
rhq = (0.41,<0.01)
1.0
0.5
0.0
−0.5
0.5
1.0
1.5
2.0
log(Σ*/[Msol pc−2])
2.5
1.5
1.0
1.5
[f] rall = (−0.20,0.03)
rhq = (−0.24,0.08)
1.0
0.5
0.0
0.5
2.5
log(SFR/[Msol yr−1 kpc−2])
0.5
0.5
log(XCO/[1020 cm−2 (K km s−1)−1])
−0.2
0.5
1
1.0
1.5
[h] rall = (−0.02,0.86)
rhq = (−0.09,0.51)
0
−1
−2
−3
0.5
1.0
1.5
log(Σ*/[Msol pc−2])
Figure 4.4 Properties of the MAGMA clouds, plotted as a function of the stellar mass surface
density, Σ∗ . The panels, plot symbols and annotations are the same as in Figure 4.3. The
shaded region indicates Σ∗ ≥ 100 M⊙ pc−2 , corresponding to the the region denoted by the
ellipse in Figure 2.2. The dashed line in panel [g] represents Rmol = Σ∗ /[81M⊙ pc−2 ], which
is the relation determined by Leroy et al. (2008) for galaxies in the THINGS survey (Walter
et al., 2008).
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
216
Trends
1.0
[a] rall = (0.12,0.18)
rhq = (0.29,0.03)
log(σv/[km s−1])
log(Radius/[pc])
2.5
2.0
1.5
1.0
1.2
1.4
1.6
1.8
0.6
0.4
0.2
−0.2
2.0
[c] rall = (−0.08,0.37)
rhq = (−0.15,0.26)
log(ICO/[K km s−1])
log(<Tpk>/[K])
0.3
0.8
0.0
1.0
0.4
[a] rall = (0.30,<0.01)
rhq = (0.44,<0.01)
0.2
0.1
0.0
−0.1
1.5
1.0
1.2
1.4
1.6
1.8
2.0
1.6
1.8
2.0
1.6
1.8
2.0
1.6
1.8
2.0
[d] rall = (−0.06,0.53)
rhq = (−0.02,0.88)
1.0
0.5
0.0
1.0
1.2
1.4
1.6
1.8
2.0
log(ΣH2/[Msol pc−2])
3.0
[e] rall = (0.26,<0.01)
rhq = (0.26,0.05)
2.5
2.0
1.5
1.0
log(ΣH2,CO/ΣHI)
1.5
1.2
1.4
1.6
1.8
1.5
[g] rall = (−0.60,<0.01)
rhq = (−0.50,<0.01)
1.0
0.5
0.0
−0.5
1.2
1.4
[f] rall = (0.29,<0.01)
rhq = (0.30,0.02)
1.0
0.5
0.0
1.0
2.0
log(SFR/[Msol yr−1 kpc−2])
1.0
1.0
log(XCO/[1020 cm−2 (K km s−1)−1])
−0.2
1
1.2
1.4
[h] rall = (0.22,0.01)
rhq = (0.27,0.04)
0
−1
−2
−3
1.0
1.2
1.4
1.6
1.8
log(Σg/[Msol pc−2])
2.0
1.0
1.2
1.4
log(Σg/[Msol pc−2])
Figure 4.5 Properties of the MAGMA clouds, plotted as a function of the atomic gas surface
density, Σg . The panels, plot symbols and annotations are the same as in Figure 4.2.
4.4. Discussion
217
Comparison with Ph
The comparison between properties of the MAGMA clouds and Σg is helpful for interpreting the plots in Figure 4.6. In particular, both σv and ΣH2 increase in regions
with higher Ph , following their behaviour in regions with high H I column density. The
dominant physics underlying these correlations may therefore be the importance of an
atomic shielding layer for the survival of H2 molecules, rather than pressure regulation.
ΣH2 is more strongly correlated with Ph than with Σg however, and we observe that
there are few clouds with low I(CO) or ΣH2 in regions with high Σ∗ (panels [d] and [e] of
Figure 4.4). Insofar as I(CO) and ΣH2 are reliable tracers of the H2 surface density, this
provides some indication that shielding alone may not regulate the H2 surface density
in regions of the LMC where the interstellar gas pressure is high. There is no significant
correlation between Rmol and Ph (Figure 4.6[g]), in contrast to the good correlation
between these quantities that is observed on kiloparsec scales in nearby spiral galaxies
(Leroy et al., 2008).
4.4 Discussion
4.4.1
The Origin of Larson’s Laws
Despite the longevity of Larson’s scaling relations, a complete theoretical explanation
for the origin of the size-linewidth relation is still lacking. Considerable effort has been
devoted to demonstrating that the observed size-linewith relationship can be reproduced by realistic models of interstellar turbulence (e.g. Mac Low & Klessen, 2004;
Ballesteros-Paredes et al., 2007, and references therein), and that turbulence in the
cold gas phase is both universal and nearly invariant (e.g. Heyer & Brunt, 2004), but
differences between the working variables and descriptive tools available to theory and
observation represent a significant obstacle to making turbulent models empirically falsifiable. In many instances, however, older explanations for the origin of Larson’s laws
have not been thoroughly tested, since there are few extragalactic datasets that are
comparable to the Milky Way molecular cloud samples that guided the development of
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
218
Trends
1.0
[a] rall = (0.03,0.74)
rhq = (0.18,0.18)
log(σv/[km s−1])
log(Radius/[pc])
2.5
2.0
1.5
4.0
4.5
5.0
0.6
0.4
0.2
−0.2
5.5
[c] rall = (0.13,0.16)
rhq = (0.24,0.07)
log(ICO/[K km s−1])
log(<Tpk>/[K])
0.3
0.8
0.0
1.0
0.4
[b] rall = (0.27,<0.01)
rhq = (0.49,<0.01)
0.2
0.1
0.0
−0.1
1.5
4.0
4.5
5.0
5.5
5.0
5.5
5.0
5.5
5.0
5.5
[d] rall = (0.16,0.07)
rhq = (0.26,0.06)
1.0
0.5
0.0
4.0
4.5
5.0
5.5
log(ΣH2/[Msol pc−2])
3.0
[e] rall = (0.28,<0.01)
rhq = (0.34,<0.01)
2.5
2.0
1.5
1.0
log(ΣH2,CO/ΣHI)
1.5
4.5
5.0
1.5
[g] rall = (−0.32,<0.01)
rhq = (−0.14,0.31)
1.0
0.5
0.0
−0.5
4.5
[f] rall = (0.14,0.13)
rhq = (0.14,0.29)
1.0
0.5
0.0
4.0
5.5
log(SFR/[Msol yr−1 kpc−2])
4.0
4.0
log(XCO/[1020 cm−2 (K km s−1)−1])
−0.2
1
4.5
[h] rall = (0.23,0.01)
rhq = (0.29,0.03)
0
−1
−2
−3
4.0
4.5
5.0
log(Ph/kB [cm−3 K])
5.5
4.0
4.5
log(Ph/kB [cm−3 K])
Figure 4.6 Properties of the MAGMA clouds, plotted as a function of the interstellar pressure,
Ph . The panels, plot symbols and annotations are the same as in Figure 4.2. The dashed line
in panel [g] represents Rmol = (Ph /[1.7 × 104 kB cm−3 K])0.8 , which is the relation determined
by Leroy et al. (2008) for galaxies in the THINGS survey (Walter et al., 2008); the dotted line
is the relation determined by Leroy et al. (2008) for dwarf galaxies only.
4.4. Discussion
219
these early models. In this section, we therefore consider whether the MAGMA data are
consistent with two analytic models for the origin of Larson’s laws: the photoionizationregulated star formation theory proposed by M89 and the model of molecular clouds
as virialized polytropes proposed by E89.
Comparison with McKee (1989)
The photoionization-regulated theory of star formation proposed by M89 provides one
possible explanation for the origin of Larson’s laws. In this theory, molecular clouds
evolve towards an equilibrium state where energy injection from newborn low-mass
stars halts the clouds’ gravitational contraction. Equilibrium depends on the level of
photoionization by the interstellar far-ultraviolet (FUV) radiation field because ambipolar diffusion governs the rate of low-mass star formation in the cloud; in turn, the
rate of ambipolar diffusion is regulated by the ionization fraction, which depends on
the interstellar FUV radiation field in the bulk of the molecular cloud. A second factor
that determines the equilibrium state of the GMCs is the local dust abundance, since
dust shields H2 molecules against photodissociation. Notably, the M89 theory predicts
that molecular clouds in equilibrium should have uniform extinction, rather than constant column density: clouds in environments with low dust-to-gas ratios and/or strong
radiation fields will require larger column densities to attain the equilibrium level of
extinction, and should therefore follow a R − σv relation with a higher coefficient than
the Milky Way relation. Recent measurements of the surface densities of extragalactic
GMCs contradict this prediction, instead showing that molecular cloud surface densities in low metallicity environments are similar to, or even lower than, the average mass
surface density of Milky Way clouds (e.g. B08, Leroy et al., 2007a). The median mass
surface density of the MAGMA clouds is ∼ 50 M⊙ pc−2 , in line with these results.
It is worth noting, however, that low mass surface densities (i.e. less than ∼ 100 M⊙ pc−2
for GMCs in subsolar metallicity environments) are not necessarily inconsistent with the
M89 model: the complete prediction by M89 is that the velocity dispersion of molecular
clouds should increase as the dust-to-gas ratio decreases, provided that the densities of
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
220
Trends
the CO-emitting clumps within GMCs are comparable to the densities of the clumps
in Galactic molecular clouds, and that appropriate corrections for the angular filling
fraction of the CO-emitting clumps, C, have been applied. If the CO-emitting clumps
within GMCs have C ∼ 1, densities of nH = 103 cm−3 , and clump-to-cloud extinction
ratios of Āc /A¯v ∼ 0.3 – values that M89 regards as typical for molecular clouds in
the inner Milky Way disk – then the photoionization-regulated star formation theory
predicts that equilibrium is achieved for visual extinctions between A¯v ∼ 4 and 8 mag.
Equations 5.5 to 5.7 in M89 show that an equilibrium extinction value of A¯v ∼ 1 can
none the less be obtained in an environment with the LMC’s typical dust-to-gas ratio
(∼ 0.3, Dobashi et al., 2008) if the CO-emitting clumps within GMCs have an angular
filling fraction of C = 0.25 and a typical density of nH = 104.5 cm−3 , and if the fraction
of the total cloud mass residing in these dense clumps is ∼ 45 per cent. While agreement
with the M89 model is theoretically possible, it requires the density contrast in GMCs
in the LMC to be more extreme than in Milky Way clouds. C values less than unity
have previously been invoked to explain the low Tpk measurements for LMC clouds
(e.g. Wolfire et al., 1993; Kutner et al., 1997; Garay et al., 2002), but average densities
of nH ∼ 104.5 cm−3 for the CO-emitting clumps seem less plausible. Excitation analyses of millimetre and submillimetre spectral line observations (e.g. Heikkilä et al., 1999;
Pineda et al., 2008; Minamidani et al., 2008) have reported clump densities between 104
and 106 cm−3 , but as these studies targeted the LMC’s brightest star-forming regions
it remains uncertain whether similar clump densities would be common in molecular
clouds throughout the LMC.
A further problem for the photoionization-regulated star formation theory is that there
is no sign of a correlation between G0 and ΣH2 or I(CO) for GMCs without signs of
high-mass star formation (blue crosses in panels [d] and [e] of Figure 4.3). In the scenario postulated by M89, equilibrium is only achieved prior to the onset of high-mass
star formation: after this, young stars rapidly disrupt their natal clouds, destroying the
relationship between the gas column density, dust abundance and ambient radiation
field. The GMCs that are designated as star-forming in the MAGMA sample contain
at least one O star (Kawamura et al., 2009) and their young stellar content makes a sig-
4.4. Discussion
221
nificant contribution to the radiation field within the cloud (see Table 3.4). For GMCs
without star formation, however, ΣH2 and I(CO) should show a correlation with G0
if their column density is regulated by the ambient radiation field, assuming that the
dust-to-gas ratio is roughly constant in the environments of non-star-forming GMCs
across the LMC. No such correlation is apparent in panel [d] or [e] of Figure 4.3.
Finally, we note that a correlation between the internally-generated radiation field and
the H2 mass surface density would be expected if the star formation efficiency of molecular gas were constant (Leroy et al., 2008), since GMCs with higher H2 column densities
– and presumably higher volume densities – should have a higher surface density of
star formation. The correlation tests in Section 4.3 indicated that ΣH2 for star-forming
GMCs in the high quality subsample are associated with higher values of G0 , but the
trend is not significant if we consider all the GMCs in the MAGMA cloud list, or if
we use I(CO) rather than ΣH2 to trace the H2 mass surface density. As we discuss in
Section 4.4.3, evolutionary effects might also make the correlation difficult to detect on
the scale of individual GMCs.
Comparison with Elmegreen (1989)
Another explanation for the origin of Larson’s laws was put forward by E89, who
proposed that molecular clouds and their atomic envelopes are virialized, magnetic
polytropes (i.e. with internal pressure P that varies with the density ρ according to
P = Kρn , where K is a constant and n is the polytropic index) and with external pressure that is determined by the kinetic pressure of the ISM. In this theory, the radius
and density of a molecular cloud complex adjust so that the pressure at the boundary of
the atomic envelope equals the ambient kinetic pressure. In this case, all the molecular
clouds within a galaxy have a similar mass surface density because the ambient pressure
throughout the galaxy is also roughly uniform. While the notion that molecular clouds
can achieve dynamical equilibrium within their lifetime has been disputed (e.g. Hartmann et al., 2001), recent work has highlighted the potential importance of pressure
for the formation of molecular gas (e.g. Wong & Blitz, 2002; Blitz & Rosolowsky, 2004,
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
222
Trends
2006).
The molecular cloud model proposed by E89 predicts that C0 and ΣH2 should scale with
the total mass of the atomic+molecular cloud complex, due to the increasing weight
of the atomic gas layer surrounding large molecular clouds. In Sections 4.2.1 and 4.3,
we saw that the scatter in the Larson-type scaling relations for the MAGMA clouds
implies order of magnitude variations in C0 and ΣH2 , and also evidence for a weak
correlation between ΣH2 and the interstellar pressure (Figure 4.6[e]). These trends
motivate us to examine more closely whether the MAGMA clouds are consistent with
the E89 theory for the origin of Larson’s Laws, once variations in the local radiation
field, metallicity and mass of atomic gas surrounding the GMCs are taken into account.
In lieu of Larson’s third law, E89 predicts that the total (i.e. atomic+molecular) mass
surface density of molecular cloud complexes will vary according to
Mt
≈ 190 ± 90
Rt2
Pe
4
10 kB cm−3 K
1/2
M⊙ pc−2 ,
(4.7)
where Pe is the external pressure on a molecular+atomic cloud complex, Mt is the
total mass of the atomic+molecular complex and Rt is the radius of the complex. This
equation can be written in terms of observed molecular cloud properties:
Mm
≈ 380±250
2
Rm
Pe
4
10 kB cm−3 K
−1/24 Mt
105 M⊙
1/4 G0 /G⊙,0
Z/Z⊙
1/2
M⊙ pc−2 , (4.8)
where Rm and Mm are the radius and mass of the molecular part of the cloud complex.
The range of coefficients in these equations arise from solutions to the virial theorem
for plausible values of the adiabatic index and variations in the ratio of the magnetic
field pressure to the kinetic pressure (see figure 3 in E89).
To explore the relative importance of the parameters that contribute to the right hand
side of Equation 4.8, we defined six basic models that use different estimates for the
total mass, metallicity and external radiation field of the molecular cloud complexes.
4.4. Discussion
223
Table 4.3 A summary of the model parameters which are substituted into Equation 4.8 in
order to produce the plots in Figure 4.7. The second column describes the metallicity, and the
third column lists the factor k (see text). The fourth column describes the relationship between
the total atomic+molecular mass, Mt , and the molecular mass, Mm ≡ Mvir , that we adopt for
the clouds.
Model Identifier
M1
M2
M3
M4
M5
M6
Z/Z⊙
0.5
0.5
Gradient
Gradient
Gradient
Gradient
k
1.0
2.0
1.0
2.0
1.0
1.0
Mass Dependency
Mt = 2Mm
Mt = 2Mm
Mt = 2Mm
Mt = 2Mm
Mt /[M⊙ ] = (Mm /21.45 M⊙ )1.5
Mt /[M⊙ ] = (Mm /141.42 M⊙ )2.0
For all models, Pe is assumed to be the same as the kinetic pressure of the ambient ISM,
i.e. Pe = Ph /(1 + α + β) where α ∼ 0.4 and β ∼ 0.25 are the relative contribution by
cosmic-rays and the magnetic field to the total pressure, and Ph is estimated according
to Equation 2.6. The metallicity is either held constant at Z/Z⊙ = 0.5, or allowed to
follow a shallow radial gradient of −0.05 dex kpc−1 (e.g. Cole et al., 2004). We also
select a value of 1.0 or 2.0 for the parameter k, which is the factor by which we reduce
the measured value of G0 /G0,⊙ for GMCs with signs of high-mass star formation. We
introduce k to account for the fact the radiation field in Equation 4.8 is the external
field incident on the molecular cloud, i.e. it does not include the contribution from
stars within the cloud. We test three relationships for the dependence between the
total and molecular mass of a cloud complex. For four of the models, we use the linear
relationship adopted by E89, Mt = 2Mm . The mass dependencies for the remaining
models (M5 and M6) are constructed such that the total mass of the cloud complex
increases more rapidly than the molecular mass; the coefficient of the mass dependence
for these models is chosen such that Mt ≥ Mm for the observed range of MAGMA
GMC masses. The model parameters are summarized in Table 4.3.
In Figure 4.7, we plot the observed values of ΣH2 for the MAGMA clouds against the
values predicted by Equation 4.8 for each of the six models. Figure 4.7 shows that the
measured values for ΣH2 for the MAGMA clouds are significantly lower than predicted
by E89, regardless of which model we adopt. The average mass surface density is sen-
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
224
Trends
sitive to variations in the metallicity and radiation field, but the LMC would need to
have Z ≥ Z⊙ and G0 ≤ G0,⊙ for the MAGMA clouds to be consistent with the closest
line of equality in Figure 4.7 (which corresponds to the lowest value of the coefficient
in Equation 4.8). The models in which the total complex mass increases faster than
the molecular mass (M5 and M6) demonstrate a better agreement with the slopes predicted by E89, but these models are not physically realistic since they imply that the
combined mass of the H I envelopes surrounding the MAGMA clouds is almost an order
of magnitude greater than the total H I mass of the LMC (5 × 108 M⊙ , Staveley-Smith
et al., 2003). Reducing the coefficient of the mass dependency in these models would
lower the total H I envelope mass and also shift the data towards the line of equality in
Figure 4.8, but it leads to the unphysical solution that Mt < Mm for low mass MAGMA
clouds.
The total atomic+molecular mass of the cloud complex is perhaps the most important source of uncertainty in the present comparison, and we are currently undertaking
an analysis of the H I and MAGMA CO datasets that should place empirical constraints on the mass of the H I gas that is associated with individual MAGMA clouds.
However, two further comments regarding the H I data and its potential to constrain
the E89 model are worth noting here. First, visual inspection of the CO and H I
LMC maps shows that the majority of GMCs are not isolated, but are instead located
within a group of molecular clouds that appear to share a common H I envelope (see
Figure 2.3). This possibility is not explicitly addressed by E89, but it is important
because neighbouring molecular clouds will partially shield each other, reducing the
total amount of H I required for the shielding layer. Second, we note that CO emission
is detected in regions where the total H I column density through the LMC is only
N (HI) ≈ 1 − 2 × 1021 cm−2 (refer figure 2 of Wong et al., 2009). This is problematic
insofar as the H2 self-shielding theory invoked by E89 requires a uniform shielding layer
with N (HI) = 1.2 × 1021 cm−2 for a molecular cloud situated in an ambient radiation
field G0 /G0,⊙ = 1.5 and metallicity Z/Z⊙ = 0.5, assuming a density of n ≈ 60 H cm−3
in the atomic layer (Federman et al., 1979). N (HI) = 1.2 × 1021 cm−2 is probably a
lower limit: if the gas in the shielding layer is clumpy, then the required column density
2.0
1.5
1.0
log(ΣH2/[Msol pc−2])MAGMA
2.5
3.0
[c]
M3
2.0
1.5
1.0
2.5
3.0
[e]
M5
2.0
1.5
1.0
2.5
3.0
3.5
log(ΣH2/[Msol pc−2])E89
M2
2.0
1.5
1.0
2.0
2.5
3.0
[d]
3.5
M4
2.5
2.0
1.5
1.0
3.5
2.5
2.0
[b]
2.5
3.5
2.5
2.0
log(ΣH2/[Msol pc−2])MAGMA
M1
log(ΣH2/[Msol pc−2])MAGMA
[a]
2.5
2.0
log(ΣH2/[Msol pc−2])MAGMA
225
2.0
log(ΣH2/[Msol pc−2])MAGMA
log(ΣH2/[Msol pc−2])MAGMA
4.4. Discussion
2.5
3.0
[f]
3.5
M6
2.5
2.0
1.5
1.0
2.0
2.5
3.0
3.5
log(ΣH2/[Msol pc−2])E89
Figure 4.7 The observed values of ΣH2 for the MAGMA clouds versus the values predicted by
E89 for the models of the metallicity, external radiation field and total cloud mass presented
in Table 4.3. Plot symbols are the same as in Figure 4.1. The solid line represents equality
between the observed and predicted values for the coefficients adopted by E89. The dashed
lines indicate the potential shift in the line of equality for the maximum range of the coefficients
in Equation 4.8.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
226
Trends
increases by a factor f /f⊙ , where f = hni2 /hn2 i is the volume filling factor. Part of
this discrepancy may be because sightlines towards GMCs in the LMC have significant
optical depth: H I absorption studies indicate peak optical depths between τ = 0.5 and
1.5 near regions with CO emission, implying that the true H I column density is a factor
of τ /[1 − exp(−τ )] = 1.3 − 2.0 greater than the observed value (Dickey et al., 1994;
Marx-Zimmer et al., 2000). A recent study of the LMC’s far-infrared emission has also
proposed a widespread cold atomic gas component with significant optical depth in the
LMC in order to explain an excess of emission at 70 µm (Bernard et al., 2008).
More generally, we note that plausible variations in the interstellar pressure due to e.g.
a widespread ionized gas component or a high rate of cosmic-ray escape would not have
a significant impact on the plots in Figure 4.7, since the exponent of the pressure term
in Equation 4.8 is small. A significant mass of H2 without CO emission associated
with each GMC would tend to rather magnify than reduce the discrepancy between
the MAGMA clouds and the E89 model, moreover, except in a physically improbable
scenario where the CO-dark H2 gas has a greater average density than the CO-emitting
region of the GMC. One possible resolution may be the porosity of the LMC’s ISM: as
noted above, the calculations in E89 assume a uniform gas layer which provides more
effective shielding than gas that is highly clumped. A comparison between the volume
filling factor of H I in the solar neighbourhood and in the LMC, plus the inclusion of
clumpy cloud structure in the E89 theory, would be required to test the influence of
ISM porosity on the dynamical structure of molecular clouds.
4.4.2
GMC Properties: Trends with Environment
Previous comparative studies of the Milky Way and nearby extragalactic GMC populations have found that GMC properties are relatively uniform, and mostly insensitive
to variations in environmental parameters such as the radiation field and dust abundance (e.g. B08, Rosolowsky et al., 2003; Rosolowsky, 2007). A possible explanation
for this result is that GMCs are strongly bound and hence largely decoupled from
conditions in the local ISM. B08 have cautioned, however, that the apparent universality of GMC properties as measured from CO observations may simply reflect the
4.4. Discussion
227
physical conditions required for CO emission to be excited, and that the properties
and extent of the H2 material surrounding a GMC’s high density CO-emitting peaks
might indeed be sensitive to local environmental factors, a conclusion that is supported
by far-infrared studies of molecular clouds in nearby dwarf galaxies (e.g. Israel, 1997;
Leroy et al., 2007a, 2009a). Our analysis tends to support the view that CO-derived
properties of GMCs are mostly insensitive to environmental conditions, but there are
several exceptions that we discuss below.
GMC properties and Σ∗
In Section 4.3.3, we showed that hTpk i and I(CO) increase for GMCs located in regions
of high Σ∗ , without a corresponding variation in R or σv . A key variable to explain
this result may be the role of the old stars in dust production, as a recent analysis of
Spitzer mid- and far-infrared data for the LMC indicates that very small grains (VSGs)
and polycyclic aromatic hydrocarbon molecules (PAHs) are overabundant in the LMC’s
stellar bar (Paradis et al., 2009). More specifically, if the abundance of VSGs and/or
PAHs were increased by the ejecta from mass-losing old stars, then photoelectric heating
of the molecular gas may be more efficient in regions with high Σ∗ , potentially raising
the CO excitation temperature. Alternatively, a higher overall dust abundance could
reduce the selective photodissociation of CO molecules and lead to a higher abundance
of CO relative to H2 for GMCs in the stellar bar. This could occur since H2 readily
self-shields, while the survival of CO molecules relies more on the attenuation of the
photodissociating radiation by dust (e.g. Maloney & Black, 1988). Although the CO
emission from Milky Way molecular clouds is approximately independent of variations
in the CO abundance – firstly due to the high optical depth of the
12 CO(J
= 1 → 0)
line, and secondly because the angular filling factor of the CO-emitting clumps at any
particular radial velocity within the cloud is ∼ 1 (e.g. Wolfire et al., 1993) – this may
not be true of LMC molecular clouds (e.g. Maloney & Black, 1988). The low Tpk values
of the 12 CO(J = 1 → 0) emission in LMC clouds suggests that the angular filling factor
of the CO-emitting clumps is indeed relatively small, in which case higher CO-to-H2
ratios might produce higher values of hTpk i and I(CO).
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
228
Trends
Contrary to what might be expected if higher interstellar pressures promote the formation of molecular gas, there is no evidence that R or σv for the LMC molecular clouds
increases in regions with high Σ∗ . The absence of these correlations is perhaps not
very significant, however, since our estimate for Ph is dominated by Σg for regions with
Σ∗ ≤ 60 M⊙ pc−2 ; if the H I emission along sightlines towards GMCs has significant
optical depth, Σg will dominate Ph to even higher Σ∗ thresholds (Σ∗ ∼ 100 M⊙ pc−2
for τ = 1). A correlation between G0 and Σ∗ might be expected if regions with strong
stellar gravity promoted the formation of overdensities within GMCs and enhanced
the local star formation rate (e.g. Leroy et al., 2008) or, alternatively, if old stars
made a significant contribution to the dust heating. Stronger external heating in
the stellar bar region has previously been invoked as an explanation for the higher
12 CO(J
= 2 → 1)/(J = 1 → 0) transitional ratios in inner LMC molecular clouds (So-
rai et al., 2001). While the correlation tests in Section 4.3 provided no clear evidence
for a relationship between G0 and Σ∗ , we do not observe clouds with low G0 values
located in regions with Σ∗ ≥ 100 M⊙ pc−2 (see Figure 3.29[b]), so it is possible that
enhanced star formation due to strong stellar gravity and/or dust heating by old stars
becomes important at higher stellar densities.
GMC properties and N (H I)
In Section 4.3.3, we found a weak but significant correlation between N (H I) and σv
(Figure 4.5[b]). Its interpretation is somewhat uncertain, however, since there is no obvious trend between N (H I) and the GMC radius, which would be expected if larger H I
column densities were associated with more massive GMCs (assuming that the average
density of GMCs also remains constant across the LMC). Some positive association
between N (H I) and R would be expected, moreover, simply as a consequence of the
size-linewidth relation for LMC molecular clouds. Perhaps the simplest explanation
is that the mass and size of GMCs increase with N (H I), but that the GMC radius
derived from CO observations is not a sensitive tracer of the true cloud size. Another
possibility is that the density of molecular clouds genuinely increases with the local H I
column density; this could account for some of the scatter in the R − σv relation but
would imply that ΣH2 and XCO – assuming the average CO brightness temperature is
4.4. Discussion
229
constant (see e.g. Dickman et al., 1986; Heyer et al., 2001) – should also increase with
N (H I). A third possibility is that the degree of virialisation in GMCs varies across
the LMC, i.e. GMCs in regions with high N (H I) are less gravitationally bound than
GMCs in regions with low N (H I), due to the higher external pressure. Provided that
the average CO brightness temperature of GMCs in the LMC remains constant, we
would also expect the observed value of XCO to increase with N (H I) in this case.
Our analysis in Section 4.3 revealed some evidence for trends between ΣH2 , XCO and
N (H I), although the correlations involving the high quality subsample did not satisfy
our criteria for significance. There is sufficient scatter in Figures 4.1 and 4.5 that none
of these explanations can be definitively ruled out.
GMC properties and Ph
Although the MAGMA clouds do not follow the predictions of the E89 molecular cloud
model, we find that σv and ΣH2 increase with the interstellar pressure (panels [b]
and [e] of Figure 4.6). These correlations suggest that the external pressure on a
GMC in the LMC may indeed play a key role in regulating its dynamical properties,
although we caution that we cannot readily distinguish between the role of pressure
and shielding in our analysis due to the dominant contribution of Σg to our estimate
for Ph . The low absolute values of ΣH2 and I(CO) for the MAGMA clouds imply
that their average internal pressure is also low. From the virial theorem, a GMC with
ΣH2 ∼ 50 M⊙ pc−2 will have internal pressure Ph /kB ∼ 5×104 K cm−3 (e.g. Krumholz
& McKee, 2005); this is not much greater than the average external kinetic pressure
for the MAGMA GMCs, hPh /kB i ∼ 3.9 × 104 K cm−3 , estimated from Equation 2.6.
Plausible optical depth corrections for the H I emission along sightlines towards GMCs
(i.e. for τ values between 0.5 and 1.5) would effectively balance these estimates for
the average pressure internal and external to the cloud, although the dense clumpy
structure within the GMC would be likely to remain significantly overpressured. A
gentle pressure gradient across the molecular cloud boundary may explain why we have
found that some properties of the MAGMA clouds are correlated with environmental
conditions. It would be interesting to test whether GMCs in nearby spiral galaxies
– which have hΣH2 i ∼ 130 M⊙ pc−2 (B08) and presumably higher internal pressures
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
230
Trends
relative to the surrounding ISM (see also Krumholz et al., 2009b) – exhibit any of the
correlations that we have identified for the MAGMA GMCs.
4.4.3
The Kennicutt-Schmidt Law at Cloud Scales in the LMC
Galaxies have star formation rate surface densities that span more than six orders of
magnitude (Kennicutt, 1998). On global scales (i.e. averaged over entire star-forming
disks), empirical studies find ΣSF R = AΣngas , where Σgas is the mass surface density of
neutral gas. For a composite sample of ∼ 100 normal and starburst galaxies, Kenni1.4±0.15 . Σ
cutt (1998) derived a best-fitting relation of ΣSF R = (2.5 ± 0.7) × 10−4 Σgas
gas
is usually estimated from observations of H I and
12 CO(J
= 1 → 0) emission, which
are presumed to trace the atomic and molecular gas phases. A combination of H α or
far-ultraviolet (FUV) and 24 µm emission have lately become the preferred estimator
for the star formation rate (e.g Leroy et al., 2008; Bigiel et al., 2008; Kennicutt et al.,
2007), on the basis that both obscured and unobscured star formation activity are represented by emission at these wavelengths.
A key project of recent nearby galaxy surveys (e.g. THINGS, BIMA-SONG, HERACLES, STING, Walter et al., 2008; Helfer et al., 2003; Leroy et al., 2009b; Rahman
et al., 2010) is to study the relationship between star formation and gas density within
galaxies, using azimuthal averages (radial profiles) or measurements of ΣSF R and Σgas
within apertures corresponding to a resolution element (typically ∼ 500 pc or larger).
These studies have found a strong correlation between ΣSF R and the surface density of molecular gas, ΣCO,H2 (e.g. Wong & Blitz, 2002), but there is considerable
variation in the power-law indices and coefficients that have been determined for the
local molecular and total gas star formation laws (e.g. Boissier et al., 2003; Heyer
et al., 2004; Schuster et al., 2007). Bigiel et al. (2008) demonstrate that these discrepancies can mostly be attributed to methodological differences and assumptions
regarding the stellar initial mass function and the CO-to-H2 conversion factor. They
is good description for spiral galaxies with
find ΣSF R = (1.0 ± 0.5 × 10−3 )Σ0.96±0.07
H2
H2 -dominated central regions, noting that their range of observed ΣH2 values may correspond to differences in the covering factor of GMCs rather than intrinsic variations
4.4. Discussion
231
in the H2 surface density.
While the correct parameterisation of the Kennicutt-Schmidt Law has been extensively investigated, its physical origin remains an open question. An important contribution to this debate would be to determine whether the correlation holds on the
scale of an individual GMC, or if it is only evident when averaging over several GMCs
that exhibit a range of evolutionary states. In Figure 4.8, we plot the star formation
rate surface density against i) ΣHI , ii) ΣH2 and iii) ΣHI+H2 for the MAGMA clouds.
completeness, we also plot ΣSF R against the mass surface density of gas and stars,
ΣHI+H2 +∗ . For consistency with extragalactic investigations where individual GMCs
cannot be resolved, we estimate ΣH2 from the CO luminosity. The range of spatial
scales represented in Figure 4.8 is approximately 15 to 200 pc, corresponding to the
sizes of clouds in the MAGMA catalogue. To facilitate comparison with the detailed
examination of the resolved Kennicutt-Schmidt Law by Bigiel et al. (2008), we adopt
−1
XCO = 3.0×1020 cm−2 (K km s−1 )
and do not apply a correction for the contribution
of helium to the gas surface density measurements.
Figure 4.8 shows that there is no obvious relationship between ΣSF R and the mass
surface density of neutral gas at the scale of individual GMCs in the LMC. This does
not mean that the GMCs are unrelated to star formation in the LMC, since the regions
targeted by the MAGMA survey are strongly biased towards high far-infrared surface
brightness. Within the CO-emitting boundaries of the MAGMA GMCs, however, there
is no correlation between ΣH2 and our estimate for cloud’s level of star formation activity. As noted by Onodera et al. (2010), a range of ΣSF R values would be expected
if we are observing a sample of GMCs at different stages of their evolution. In this
scenario, the CO emission from GMCs becomes observable before (or simultaneous
with) the onset of high-mass star formation (low ΣSF R ). The nascent stars ionize their
immediate surroundings and heat the interstellar dust, but also dissociate and/or mechanically disrupt the molecular gas (high ΣSF R ). Ultimately, the new stars and the
radiation from star formation activity will disperse, exceeding the boundaries of the
progenitor molecular cloud (low ΣSF R ). In an evolutionary model, the “breakdown”
1
log(SFR/[Msol yr−1 kpc−2])
log(SFR/[Msol yr−1 kpc−2])
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
232
Trends
[a]
0
−1
−2
−3
−4
0.5
1.0
1.5
2.0
1
[c]
−1
−2
−3
1.0
1.5
0
−1
−2
−3
1.0
pc−2])
0
−4
0.5
[b]
−4
0.5
2.5
2.0
2.5
log(ΣHI+H2/[Msol pc−2])
1.5
2.0
log(ΣH2/[Msol
log(SFR/[Msol yr−1 kpc−2])
log(SFR/[Msol yr−1 kpc−2])
log(ΣHI/[Msol
1
1
2.5
pc−2])
[d]
0
−1
−2
−3
−4
0.5
1.0
1.5
2.0
log(ΣHI+H2+*/[Msol
2.5
−2
pc ])
Figure 4.8 The star formation rate surface density, ΣSF R plotted as a function of (a) the
atomic gas surface density ΣHI , (b) the molecular gas surface density ΣH2 (c) the atomic +
molecular surface density ΣHI+H2 , and (d) the surface density of neutral gas and stars ΣHI+H2 +∗
for MAGMA GMCs. The plot symbols are the same as in Figure 4.1. The dashed line and
grey shading in panel (b) represents the relation derived by Bigiel et al. (2008) and its 1σ
0.96±0.07
uncertainties, ΣSF R = (1.0 ± 0.5 × 10−3 )ΣH
. The vertical dot-dashed line in panel (a)
2
−2
indicates ΣHI = 9 M⊙ pc , which Bigiel et al. (2008) identify as a saturation threshold (at
750 pc resolution) for spiral and dwarf galaxies in their sample.
4.4. Discussion
233
of the Kennicutt-Schmidt Law is intimately connected to the minimum scale on which
extragalactic methods for estimating the star formation rate remain valid (e.g. Calzetti
& Kennicutt, 2009).
Figure 4.8 shows that the ΣHI values span a relatively narrow range (∼ 0.6 dex), and
that the median hΣHI i = 22 M⊙ pc−2 is approximately twice the saturation threshold
identified at 750 pc resolution in the Bigiel et al. (2008) dataset. On one hand, this is
not unexpected: we would expect to find large H I column densities in dwarf galaxies,
where ISM conditions are less favorable for H2 formation. Bigiel et al. (2008) found
that ΣHI saturated at 9 M⊙ pc−2 for all the galaxies in their sample, however, including
dwarf galaxies with lower metallicity and mass than the LMC. The difference in hΣHI i
between the LMC and the THINGS galaxies might therefore be non-physical. Resolution and the shape of the N (H I) probability distribution function (PDF) will also play
a role in determining the H I “saturation” value. If high values of N (H I) are rare –
which is likely if the PDF is approximately log-normal – then they will make a negligible contribution to ΣHI when averaged over large scales (see Figures 4.9 and 4.10),
and the apparent ΣHI threshold corresponds to the average value of ΣHI throughout
the galactic disk. A common cut-off for ΣHI among galaxies could arise because the
shape of the N (H I) PDF and the average spatial separation between regions of high
ΣHI are similar in those galaxies. The higher ΣHI values for the MAGMA GMCs reflect
the smaller spatial scales that we can observe in the LMC, combined with the fact that
GMCs are preferentially located at N (H I) peaks.
To assess whether a correlation between the star formation rate and gas surface density
is recovered on larger scales in the LMC, we measure ΣSF R , ΣHI , ΣH2 and ΣHI+H2
over apertures with radii between 50 and 500 pc, centred on the positions of MAGMA
GMCs. We only use GMCs that are located within 2.5 kpc of the LMC’s kinematic centre for this analysis, to ensure that the circumference of each aperture remains within
the edge of the LMC’s H I disk. The resulting correlations are presented in Figure 4.11.
We emphasise two caveats that are important for the interpretation of the plots in
Figure 4.11. First, the MAGMA survey covers ∼ 10% of the LMC’s H I disk and only
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
234
Trends
Figure 4.9 A map of the H I column density in the north-west of the LMC at (a) 1.′ 0 (b) 5.′ 0
(c) 16.′ 6 and (d) 50.′ 0 resolution.
4.4. Discussion
235
Fraction of Pixels
0.07
15pc
75pc
240pc
730pc
0.06
0.05
0.04
0.03
0.02
0.01
10
20
ΣHI [Msol
30
pc−2]
Figure 4.10 The frequency distribution of the H I column density (expressed in mass surface
density units) for the maps in Figure 4.9. The saturation threshold for each distribution, defined
as the 95th percentile of the ΣHI values, is indicated along the top axis.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
236
Trends
contains ∼ 70% of the total CO luminosity obtained by the NANTEN survey, so the
ΣH2 and ΣHI+H2 measurements should properly be regarded as lower limits. If the
remaining CO emission were distributed uniformly across the LMC, the slope of the
correlations would not change, but the MAGMA measurements would move towards
higher ΣH2 and ΣHI+H2 values by ∼ 0.2 dex. Second, GMCs in the LMC are spatially
clustered. This means that our larger apertures overlap, and hence there are fewer
independent data points as the resolution degrades. This is particularly evident in
Figure 4.11[h], where the two clusters of points with high ΣSF R correspond to GMCs
associated the northern part of the molecular ridge and the N44 star forming complex.
We are hesitant to ascribe physical significance to the detailed aspects of Figure 4.11
– e.g. the offset between the MAGMA data and the relation between ΣSF R and ΣH2
derived by Bigiel et al. (2008) – because of these limitations to our analysis. Nevertheless, it is clear from Figure 4.11 that moderately strong correlations between ΣSF R ,
ΣH2 and ΣHI+H2 are present on larger scales in the LMC, and that these correlations
have similar slopes to those determined by Bigiel et al. (2008). In the LMC, these correlations are local in the sense that they arise once the SFR and gas surface densities are
averaged over a spatial scale that encompasses several star-forming regions (∼ 0.5 kpc),
regardless of galactic location. Radial gradients in the values of ΣH2 and ΣSF R for
individual GMCs are not observed (refer panels [d] and [h] of Figure 4.2), although
the azimuthally-averaged value of ΣH2 falls by factor of . 2 between dKC = 0.5 and
3 kpc (Figure 4.12, see also panel [a] of Figure 3.12). Our results would therefore seem
consistent with the suggestion by Bigiel et al. (2008) that variations in ΣH2 seen on
sub-kiloparsec scales are due to changes in the covering fraction of GMCs, rather than
systematic variations in their intrinsic H2 surface density.
The MAGMA data demonstrate that a linear relation between ΣSF R and ΣH2 is reproduced on large scales even if the ΣH2 measurements for individual GMCs vary by
more than an order of magnitude. For clarity, we refer to the average molecular mass
surface density of a GMC ensemble as Σe and the molecular mass surface density of
an individual GMC as Σc for the rest of this section. Qualitatively, this can be un-
4.4. Discussion
237
log(ΣSFR/[Msol yr−1 kpc−2])
R=80pc
0
R=150pc
[a]
HI
R=250pc
[b]
[c]
R=500pc
[d]
r=0.55
0
−2
−2
−4
−4
0
H2
[e]
[f]
[g]
[h]
r=0.49
0
−2
−2
−4
−4
0
HI+H2
[i]
[j]
[k]
[l]
r=0.54
−2
−4
0
−2
−1 0
1
2
−1 0
1
2
−1 0
1
2
−1 0
1
2
−4
log(Σgas/[Msol pc−2])
Figure 4.11 The star formation rate surface density ΣSF R plotted as a function of the atomic
gas surface density ΣHI (top row), the molecular gas surface density ΣH2 (middle row), and the
atomic+molecular surface density ΣHI+H2 (bottom row). The columns correspond to the size
of the aperture over which the SFR and gas surface densities are measured, increasing from left
to right. The dotted lines represent the average relations derived by Bigiel et al. (2008) for a
subsample of THINGS galaxies at 750 pc resolution. The red points in the final panel of each
row represent a subset of apertures with centres that are separated by more than 700 pc. The
Spearman correlation coefficient for the relations at 500 pc is indicated in the rightmost panels.
We verified that the correlations were significant at the 99% confidence level (p < 0.01).
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
238
Trends
derstood as follows. It can be shown algebraically that Σe is insensitive to whether
Σc = Σe for all the members of the ensemble, or if the Σc values are distributed symmetrically about Σe . We propose that the intrinsic width of the ΣSF R vs ΣH2 relation
on sub-kiloparsec scales reflects a combination of evolutionary effects and variations
in the Σc distributions for resolution elements that have a similar covering fraction of
GMCs. The intrinsic width should be relatively narrow in galactic disks, firstly because
evolutionary differences between regions will be minimized by averaging over multiple
GMCs, and secondly because plausible changes in physical conditions that would produce gross variations in the Σc distributions would also be likely to alter the GMC
covering fraction and hence Σe . Analogously, it is not necessary for the intrinsic star
formation efficiency of GMCs to be constant, only that the values of ΣSF R for individual clouds are distributed symmetrically about the ensemble average.
Finally, we note that there is some evidence for a correlation between ΣSF R and ΣHI
on the largest scales (Figure 4.11[d]), despite the limited dynamic range of ΣHI values.
We attribute this correlation to an increase in the the GMC covering fraction in regions
where the average ΣHI is high, and not because i) H I participates directly in the star
formation process or ii) the ΣH2 increases with ΣHI on the scale of individual GMCs
(cf. Figure 4.5[d]).
4.5 Conclusions
In this chapter, we examined the empirical scaling relations between the basic physical
properties of the GMCs in our MAGMA LMC cloud list, and dependencies between
the cloud properties and the local interstellar environment. We report the following
results and conclusions:
1. The MAGMA clouds exhibit scaling relations that are similar to those previously
determined for Galactic and extragalactic GMC samples (e.g. Solomon et al., 1987;
Bolatto et al., 2008). However the MAGMA LMC clouds are offset towards narrower
4.5. Conclusions
239
Galactocentric Radius [kpc]
0
2
3
Hα
3
2
2
HI
1
1
0
0
CO (NANTEN)
log(ΣHα/dR]
3
log(Σgas/Msol pc−2]
1
−1
−1
−2
0
50
100
150
200
250
Galactocentric Radius [arcmin]
Figure 4.12 Azimuthally-averaged radial profiles of H α surface brightness (solid grey line), H I
surface density (dashed grey line) and H2 surface density (black line) for the LMC. The adopted
centre is RA 05h19m30s, Dec -68d53m (J2000), and the adopted inclination and major axis
position angle are 35◦ and 340◦ respectively (Wong et al., 2009). We use the NANTEN survey
to estimate ΣH2 for this plot, since its coverage is more complete than MAGMA. We assume
XCO = 3 × 1020 cm−2 (K km s−1 )−1 for the CO-to-H2 conversion factor. Prior to calculating
the azimuthal averages, the maps were smoothed to 6.′ 6 (∼ 100 pc) resolution.
Chapter 4. Properties of MAGMA GMCs: II. Scaling Relations and Environmental
240
Trends
linewidths and lower CO luminosities relative to GMCs of a similar size in these samples.
2. We find a significant positive correlation between the peak CO brightness and CO
surface brightness of the MAGMA clouds and the stellar mass surface density. We
propose that these correlations are due to an increase in the CO brightness temperature and/or an increase in the abundance of CO relative to H2 in the stellar bar region.
3. The velocity dispersion σv of the MAGMA GMCs increases in regions with high
H I column density N (H I). Higher volume densities and/or higher virial parameters for
GMCs in regions with high N (H I) could produce the observed correlation, although the
MAGMA data does not provide unambiguous evidence for either of these alternatives.
4. We find no correlation between the molecular mass surface density of non-starforming GMCs and the radiation field. A correlation between these properties would
have been expected if photoionization in GMC envelopes regulated cloud collapse, as
proposed by McKee (1989).
5. There is some evidence that the H2 mass surface density of the MAGMA LMC
clouds increases with the interstellar pressure, Ph . Although the molecular cloud model
proposed by Elmegreen (1989) predicts a relation between Pext and the mass surface
density of an atomic+molecular cloud complex, the MAGMA clouds do not fulfil the
predictions of this model for plausible values of the metallicity, radiation field and GMC
envelope mass.
6. We find no correlation between the star formation rate and neutral gas surface
densities on the scale of individual GMCs in the LMC, but correlations between these
properties become apparent on larger scales (∼ 300 to 500 pc). These results can be
qualitatively understood if the molecular mass surface density on sub-kiloparsec scales
reflects the covering fraction of GMCs, as proposed by Bigiel et al. (2008), and if the
GMCs are in diverse evolutionary states. We argue that a constant mass surface density
for individual GMCs is not required for a linear relation between the star formation
4.5. Conclusions
and molecular gas surface densities on large scales.
241
5
An ATCA 20cm Radio Continuum Study of the
Large Magellanic Cloud
In this chapter, we present a mosaic image of the 1.4 GHz radio continuum emission from
the Large Magellanic Cloud (LMC) observed with the Australia Telescope Compact
Array (ATCA) and the Parkes Telescope. The mosaic covers 10.8◦ × 12.3◦ with an
angular resolution of 40′′ , corresponding to a spatial scale of ∼ 10 pc in the LMC. The
final image is suitable for studying emission on all scales between 40′′ and the surveyed
area. Two non-standard reduction techniques that we have used may be of interest
for future wide-field radio continuum surveys. We measure a 1.4 GHz flux density of
426 Jy for a 7.5◦ × 7.5◦ field centred on the LMC’s gas disk, of which ∼ 15% is due
to background sources. We construct a model of the thermal free-free emission in
the LMC from an extinction-corrected map of the H α emission, obtaining a thermal
fraction at 1.4 GHz of ∼ 30%. The star formation rate implied by the LMC’s total
1.4 GHz emission is 0.15 M⊙ yr−1 , in good agreement with SFR calibrations derived at
other wavelengths. The LMC’s non-thermal flux density is underluminous by a factor
of two relative to normal star-forming galaxies with a similar level of star formation.
In combination with the LMC’s flat non-thermal spectrum, a comparison between the
characteristic timescales of cosmic ray transport and cooling mechanisms suggests that
cosmic rays readily escape the LMC without experiencing significant synchrotron losses,
consistent with its low non-thermal 1.4 GHz luminosity.
243
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
5.1 Introduction
Observations of continuum emission at centimetre wavelengths are a useful tool for
studying star formation processes in galaxies. A particular attraction of radio observations for such studies is that radio continuum emission is unaffected by extinction,
unlike optical and UV tracers. In combination with the high angular resolution that can
be achieved with ground-based facilities, the elimination of uncertain dust-attenuation
corrections makes the radio continuum a potentially powerful probe of star formation
across diverse galactic environments in the local (e.g. Johnson et al., 2009; Murphy
et al., 2008) and distant Universe (e.g. Schinnerer et al., 2007; Murphy, 2009). The two
main components of the radio emission are thermal free-free radiation from ionized gas
in H II regions and synchrotron radiation emitted by relativistic electrons accelerated
in magnetic fields (for a review, see Condon, 1992). Both processes are related to the
evolution of massive stars, but they are associated with different phases of the interstellar medium (ISM) and provide information about different periods in a galaxy’s star
formation history.
Thermal radio emission arises directly from the ionized gas surrounding young highmass stars. The intensity of the emission is proportional to the total number of Lyman
continuum photons, and in the optically thin regime the thermal radio spectrum is
nearly flat (αth = −0.1; we adopt the convention Sν ∝ ν α throughout this chapter). For an isolated star-forming region, the thermal radio emission should persist
over timescales similar to the average lifetime of an H II region (∼10 Myr), suggesting that the thermal component of a galaxy’s radio continuum emission should be a
good tracer of the current star formation rate (e.g. Schmitt et al., 2006). However, the
thermal emission typically comprises a small fraction of a galaxy’s radio luminosity at
frequencies below ∼ 10 GHz: approximately ∼ 90% of the 1.4 GHz emission in a normal
star-forming galaxy is of non-thermal origin (see e.g. figure 1 in Condon, 1992). In
spite of the close physical connection between massive stars and H II regions, the tight
relationship between a galaxy’s total radio luminosity and its star formation rate is
therefore not related to the thermal component of the radio emission.
5.1. Introduction
245
The non-thermal radio emission in galaxies is synchrotron radiation produced by cosmic
ray electrons gyrating in a magnetic field. The intensity of the synchrotron emission
depends on the product of the number density of relativistic electrons and the strength
of the magnetic field. In normal galaxies, equipartition between the cosmic ray and
magnetic field energy densities is likely to apply on large scales (Duric, 1990; Vallee,
1995), in which case the synchrotron emission increases steeply with the magnetic field
strength, SRC ∝ B (3−αnth ) . More generally, the synchrotron emission at frequency ν
follows SRC ∝ N0 B (γ+1)/2 ν (1−γ)/2 for a cosmic ray ensemble with a steady-state energy
spectrum N (E) = N0 E −γ (e.g. Pacholczyk, 1970). The non-thermal spectral index
is directly related to the cosmic ray injection energy spectrum N (E) = N0 E −p via
αnth = (1 − γ)/2 = −p/2, where p ≈ 2 to 2.5 (e.g. Bogdan & Volk, 1983).
The non-thermal radio emission in galaxies is also linked to star formation, since Type II
and Type Ib supernova remnants (SNRs) from short-lived high mass stars (M ≥ 8 M⊙ ,
τlif e ≤ 3 × 107 yr) are considered the primary sites for cosmic ray acceleration (e.g.
Biermann, 1995). If SNRs were responsible for the entirety of a galaxy’s synchrotron
emission, then the timescale of the non-thermal radio emission would be very short
(< 1 Myr, e.g. Woltjer, 1972) and the emission would again provide a prompt tracer
of the galaxy’s star formation activity. Evolutionary considerations about the timing of thermal and non-thermal radio emission in relation to the stellar lifecycle have
prompted several groups to explore whether variations in the radio spectral index might
be a useful method to chronicle starburst activity, at least in simple systems (e.g Bressan et al., 2002; Cannon & Skillman, 2004; Hirashita & Hunt, 2006). In a galaxy with
a single isolated burst of star formation, for example, the emission from discrete SNRs
would dominate the non-thermal emission at early times, while extremely young starbursts should emit almost no synchrotron radiation if insufficient time has passed for
the nascent massive stars to evolve into SNRs.
In general, however, galaxies experience moderate levels of ongoing and spatially distributed star formation. Observations indicate that ≤10% of a normal galaxy’s radio
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
emission is due to discrete SNRs; the remaining sychrotron emission is from electrons
that escape their parent SNRs and diffuse into the disk and halo, where they are accelerated by the galactic magnetic field (e.g. Lisenfeld & Völk, 2000). Analysis of beryllium
isotopes suggests that the confinement time of cosmic rays in the solar neighbourhood
is τc ∼ 2 × 107 yr (Garcia-Munoz et al., 1977). Over this period, cosmic rays should
p
travel a distance d ∼ D(E)τc , where D(E) = 1029 (E/GeV)1/2 cm2 s−1 is an empirical
energy-dependent diffusion coefficient (Ginzburg et al., 1980). For a 4.6 GeV electron
emitting near its critical frequency of 1.4 GHz in a 5 µG magnetic field, the cosmic ray
diffusion scale is nearly 4 kpc. Provided that the synchroton cooling timescale is longer
than the confinement time (which is true in this example by a factor of a few) and that
other cosmic ray energy loss processes are minor, then a cosmic ray under these conditions should emit synchrotron radiation for the duration of its confinement over this
length scale. Hence, the emission from cosmic rays generated in distinct star-forming
regions will overlap, and maps of the non-thermal 1.4 GHz emission in normal galaxies
should appear relatively smooth.
The non-thermal radio spectral index of galaxies remains an active area of research.
Resolved imaging surveys of the radio continuum emission in nearby galaxies have highlighted the utility of αnth as a probe of cosmic ray transport and loss mechanisms (e.g.
Tabatabaei et al., 2007; Paladino et al., 2009). The emission directly associated with
SNRs has a relatively flat spectrum αnth ∼ −0.6 (e.g. Lisenfeld & Völk, 2000), while a
non-thermal spectral index of αnth ≤ −1.0 is expected for galaxies that efficiently extract synchrotron radiation from their cosmic ray population (i.e. when the synchrotron
timescale is less than the timescale of cosmic ray escape, and synchrotron cooling dominates over energy loss processes). For global measurements of radio luminosity, normal
galaxy samples yield hαnth i = −0.7 to −0.8 (e.g. Niklas et al., 1997; Klein, 1988; Gioia
et al., 1982), suggesting either that cosmic rays manage to escape their host galaxies, or
that non-synchrotron losses are significant. In summary, the connection between star
formation and the properties of the non-thermal radio emission in galaxies is complex,
involving a number of uncertain parameters such as the supernova rate, magnetic field
strength and the relative importance of diffusive and/or convective escape versus other
5.2. Observations
247
cosmic ray energy loss processes. Empirical calibrations for the star formation rate at
radio, infrared and optical wavelengths may be in reasonable agreement, but a definitive theory for why the total radio luminosity of normal galaxies is linked to their star
formation rate has not been established.
In this chapter, we present a high-resolution survey of the 1.4 GHz radio continuum
emission from the Large Magellanic Cloud (LMC). Here we focus on the methods that
we have used to image the survey data, and on the basic properties of the LMC’s
radio continuum emission. We return to the connection between the non-thermal radio
emission, molecular gas and star formation in Chapter 6, where we investigate the local
radio-FIR correlation within the LMC. The current chapter is organized as follows. In
Section 5.2, we outline the observing strategy of the 1.4 GHz survey. The methods that
were used to reduce and combine the interferometer and single-dish data are described
in Section 5.3. In Section 5.4, we present the final 1.4 GHz image of the LMC, and
construct a map of the overall radio spectral index by combining our new 1.4 GHz map
with a Parkes map of the 4.8 GHz emission in the LMC. In Section 5.5, we summarise
the method that we have used to separate the thermal and non-thermal components
of the 1.4 GHz emission. Potential interpretations for spatial variations in the LMC’s
radio spectral index are briefly discussed in Section 5.6, where we also compare different
empirical estimates for the LMC’s recent star formation activity. A summary of our
key results is presented in Section 5.7.
5.2 Observations
The Australia Telescope Compact Array (ATCA) is an east-west interferometer with
a north-south spur located at the Paul Wild Observatory in Narrabri, Australia. The
interferometer consists of five 22 m antennae positioned at stations on a 3 km east-west
track or the 214 m north-south spur, with a sixth antenna located 3 km from the western end of the main track. ATCA observations of the 1.4 GHz emission in the LMC
were conducted between October 1994 and February 1996, simultaneously with the H I
spectral line survey by Kim et al. (1998, 2003a), using four 750 m array configurations.
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Table 5.1 Summary of observing dates and array configurations used for the ATCA 1.4 GHz
LMC survey.
Year
Date
Array Configuration
1994
1995
1995
1995
1996
Oct 26 - Nov 9
Feb 23 - Mar 11
Jun 02 - Jun 07
Oct 15 - Oct 31
Jan 27 - Feb 8
750D
750A
750B
750B
750C
Planning, data acquisition and flux density calibration of the ATCA survey were not
the responsibility of the author, but we summarize these aspects of the observations
here for completeness. The observing log is presented in Table 5.1. Across the four
array configurations, there are a total of 40 independent baselines ranging from 30 to
750 m.
The 1.4 GHz LMC survey mapped a 10.8◦ × 12.3◦ field centred on RA 05h19m, Dec
-68d50m (J2000). The total survey area was divided into 12 regions, each containing
112 pointing centres. The array was cycled around the 112 pointing centres within each
region according to a hexagonal grid pattern determined by Nyquist’s theorem. In this
case, the angular separation of the pointing centres is given by
2 λ
,
θ=√
3 2D
(5.1)
where λ is observing wavelength and D is the diameter of the antenna. For the survey observations, λ = 21 cm and D = 22 m, yielding a pointing centre separation of
θ = 19 arcmin. Each pointing was observed between 95 and 140 times during the entire
survey, which corresponds to between 18 and 26 minutes of total integration time per
pointing. A map of the pointing centres and scanning direction for the ATCA mosaic is
shown in Figure 5.1. The u − v coverage for a single pointing centre within the mosaic
is shown in Figure 5.2.
All observations were recorded in wideband continuum mode with 32 channels across a
5.2. Observations
249
Figure 5.1 The scanning strategy and individual pointing centres of the ATCA LMC mosaic.
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Figure 5.2 The u − v coverage of a single pointing within the ATCA LMC mosaic.
5.3. Data Reduction
251
total bandwidth of 128 MHz, i.e. the channel width is 4 MHz. The centre frequency was
1.384 GHz. The ATCA feeds receive two orthogonal linear polarisations, X and Y, and
the four polarisation products XX, YY, XY, and YX were measured. In this chapter,
we discuss the total intensity data; a preliminary analysis of the polarised emission has
already been presented (Gaensler et al., 2005a). As noted above, the H I emission from
atomic hydrogen in the LMC was recorded in the second frequency chain at the same
time as the continuum observations. The processing of the H I data and the basic properties of the LMC’s H I emission have been described elsewhere (Kim et al., 1998, 2003a).
5.3 Data Reduction
5.3.1
Calibration
The ATCA data were flagged, calibrated and imaged using the MIRIAD software
package (Sault et al., 1995a). The source PKS B1934-638 was used for bandpass and
absolute flux density calibration, assuming a 1.377 GHz flux density of 14.95 Jy for PKS
B1934-638. One of either PKS B0407-658 or PKS B0454-810 was observed every 30
minutes in order to calibrate the time variation in the complex antenna gains.
5.3.2
Deconvolution
The individual pointings of the LMC 1.4 GHz survey were linearly combined and imaged using a standard grid-and-FFT scheme with superuniform weighting. Like uniform
weighting, superuniform weighting minimizes sidelobe levels to improve the dynamic
range and sensitivity to extended structure of the final mosaicked image. Uniform
weighting reduces to natural weighting, however, if the total field-of-view of the mosaic
is much larger than the primary beam. Superuniform weighting overcomes this limitation by decoupling the weighting from the size of the field. It attempts to minimize
sidelobe contributions from strong sources over a region smaller than the total image
and is typically more successful than uniform weighting for large mosaics (Sault et al.,
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
1996).
We developed a two-step Fourier deconvolution strategy for the survey data. After
inverting the mosaic visibilities, we constructed a preliminary CLEAN model using
1.2 million iterations of the Steer-Dewdney-Ito (SDI) CLEAN algorithm on our dirty
map (Steer et al., 1984). The residuals of the CLEAN model, mainly corresponding to
diffuse emission, were then deconvolved using the maximum entropy method (Cornwell,
1988). The CLEAN model and the maximum entropy model were linearly combined
and restored with a 40′′ Gaussian beam in order to construct the ATCA mosaic image.
5.3.3
Peeling
The deconvolved ATCA image exhibits ring-like artefacts at the ∼0.5% level. These
become significant close to bright compact sources such as 30 Doradus, limiting the
sensitivity that can be achieved in these regions. The artefacts are mainly due to errors
in the calibration of off-axis sources. There are number of possible causes for off-axis
calibration errors, including pointing errors, small differences between individual antenna dishes, errors in the primary beam model, and the rotation of the primary beam
diffraction lobes. In order to improve the dynamic range of the ATCA image, we applied a “peeling” technique that was described to us by Tom Oosterloo.1 Contrary
to the usual assumption that one set of antenna gain solutions is adequate across the
field of a single pointing, peeling explicitly solves for the antenna gains at the position
of off-axis sources, so that different calibration solutions can be applied to different
regions within the field of each pointing.
To identify pointings that were badly affected by errors from off-axis sources, we deconvolved and imaged the visibility data for each of the 1344 pointings. Peeling was
attempted if the following criteria were satisfied: i) the flux density of the off-axis source
was greater than 10 mJy beam−1 , ii) the off-axis source was located at an angular dis1
Dr.
Osterloo’s presentation about peeling to the Square Kilometre Array Workshop
on Wide-Field Imaging (Dwingeloo, June 2005) is archived at the following URL:
http://www.skatelescope.org/pages/news/Wrksp20220605.htm.
A summary of the peeling
technique is also presented in Mitchell et al. (2008) and Intema et al. (2009).
5.3. Data Reduction
253
Figure 5.3 Example of peeling for a single pointing of the ATCA mosaic. Only the region of
sky containing the field centre and off-axis source is shown. The field centre is indicated with
a black cross. (a) Original deconvolved image of the pointing. (b) Deconvolved image of the
pointing after the on-axis sources have been subtracted. The appropriate gain solution for the
off-axis source is determined from this data using self-calibration. (c) Deconvolved image of the
pointing after subtracting the off-axis source and its associated errors. (d) Final deconvolved
image of the pointing after self-calibration on the on-axis sources.
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
tance greater than 1.5 times the primary beam FWHM from the pointing centre, and
iii) errors due to the off-axis source were evident within the primary beam. If these
criteria were not satisfied, no corrections to the visibility data were made.
For pointings with significant off-axis errors, we constructed a simple model of the
on-axis sources using 10000 iterations of the SDI CLEAN algorithm, and subtracted
the model of the on-axis sources from the visibility data. The resulting visibility data
(the “model data”) represent the off-axis source and its associated errors. The model
data were imaged, and a model of the off-axis source was constructed using 10000 iterations of the SDI CLEAN algorithm. We then performed an amplitude and phase
self-calibration on the model data in order to obtain a good set of antenna gain solutions for the off-axis source (the “model gains”). The model gains were applied to the
original visibility data for the pointing, and then the model of the off-axis source was
subtracted. Next, the model gains were “un-applied” to the model-subtracted visibility
data, i.e. having multiplied the original visibility data by the antenna gain solutions for
the off-axis source, we multiplied the model-subtracted visibility data by the inverse of
these model gains. At the end of this process, we are left with visibility data that are
identical to the original visibility data for the pointing, except that the off-axis source
and its errors have been removed. Figure 5.3 illustrates the four main stages of the
peeling process for a single pointing in the ATCA mosaic.
For a number of pointings, additional corrections to the basic antenna gain solutions
were required due to calibration errors for sources located within the primary beam.
To improve the antenna gain solutions for these pointings, amplitude and phase selfcalibration was performed. In total, the peeling technique was applied to 269 of the
1344 pointings. Self-calibration of on-axis sources was applied to a further 78 pointings.
The final set of corrected visibility data were combined, deconvolved, imaged according
to the strategy described in Section 5.3.2 above. The final ATCA-only mosaic is shown
in Figure 5.4. To highlight the improvement achieved by applying the peeling process,
a more detailed view of the 30 Doradus region is shown in Figure 5.5.
5.3. Data Reduction
255
Figure 5.4 The deconvolved ATCA 1.4 GHz mosaic of the LMC, after peeling and selfcalibration of individual pointings, but prior to combination with the Parkes single-dish data.
A square-root intensity scale has been used to reveal the low surface brightness emission. The
units are Jy per 40′′ beam.
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Figure 5.5 A detailed view of the 1.4 GHz continuum emission in the 30 Doradus region of
the LMC. The two panels present the final ATCA+Parkes image with (panel [a]) and without
(panel [b]) applying peeling corrections to the visibility data. Note that single-dish data is
included for the images in both panels.
5.3.4
Combination of Inteferometer and Single Dish Data
Mosaicking observations are sensitive to information on angular scales smaller than
θ = λ/(d − D/2), where d is the effective shortest baseline, and D m is the diameter of
a single antenna. For the ATCA, d = 30.6 m and D = 22 m, so our 1.4 GHz survey data
is limited to angular scales smaller than ∼ 36 arcmin. To recover information on larger
scales, the ATCA mosaic data were combined with single-dish data from the Parkes
Telescope. Here we only provide information about the Parkes data that is relevant for
the combination process; a detailed description of the Parkes 1.4 GHz survey observations and data reduction was presented by Haynes et al. (1986).
Single-dish and interferometer data can be combined in the spatial frequency domain
(e.g. Bajaja & van Albada, 1979) or in the image domain (e.g. Schwarz & Wakker,
1991). The combination can take place before (e.g. Stanimirovic et al., 1999), after (e.g. McClure-Griffiths et al., 2001) or during the deconvolution of the dirty image
(Sault et al., 1996). Stanimirovic (2002) presents a comparison between different strategies to combine interferometer and single-dish data, showing that similar results may
be achieved using several common approaches. We chose to combine the data in the
spatial frequency domain after deconvolution of the ATCA data, using the MIRIAD
5.3. Data Reduction
257
task immerge. In this case, the ATCA visibility data are imaged and deconvolved, the
Parkes data are imaged, and the deconvolved ATCA and Parkes images are Fourier
transformed. The data are then linearly combined in the Fourier plane after applying
tapering functions that downweight the low spatial frequencies in the interferometer
data. We used the default tapering functions supplied by immerge, which give unit
weight to the Parkes data across all spatial frequencies, and weight the ATCA data
such that the sum of the single-dish and tapered interferometer datasets produces a
Gaussian beam with FWHM that matches the beam of the untapered ATCA data (see
figure 7 of Stanimirovic, 2002). The final Parkes+ATCA image is obtained by applying
an inverse Fourier transform to the combined datasets.
Ideally, the calibrated Parkes and ATCA 1.4 GHz datasets would have identical flux
density scales. In practice, slight differences between the calibration of the two datasets
require the use of a relative flux correction factor, f , and the Parkes data must be multiplied by f prior to combination. In general, f can be determined by comparing the
intensity of data in an annulus where the spatial frequencies of the single-dish and interferometer observations overlap. Alternatively, f can be obtained directly by comparing
the flux densities of bright unresolved sources in the single-dish and interferometer
maps. For both methods of estimating f , the ratio between the interferometer and
single-dish beamsize represents a significant source of uncertainty in the flux density
scale of the combined image, so good knowledge of the respective telescope beams is
required. As the Parkes and ATCA 1.4 GHz surveys imaged a significant field-of-view
beyond the LMC’s gas disk, we were able to identify ∼ 20 bright, compact sources that
were suitable for estimating the effective size of the Parkes beam, and for calculating f .
The Parkes FWHM beam size was determined by fitting a two-dimensional Gaussian
function to the bright sources using the MIRIAD task imfit. The median of the beam
measurements was 16.′ 6, with a dispersion of ∼ 15%. This is in excellent agreement
with the value obtained by Filipovic et al. (1995), who analysed the effective Parkes
beam size at 1.4 GHz using a similar approach. We then measured the flux densities
of strong, compact sources in the Parkes and ATCA maps using imfit. This direct
comparison in the image domain yielded f = 1.07, consistent with the value that we ob-
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
tained by comparing data in the overlap region of the Fourier plane (f = 1.1). The final
ATCA+Parkes image of the 1.4 GHz emission in the LMC is presented in Figure 5.6.
5.3.5
Sensitivity of the ATCA+Parkes 1.4 GHz Image
The final ATCA+Parkes image of the 1.4 GHz emission in the LMC is sensitive to all
angular scales from the synthesized beam size (40′′ ) up to the final image size. In order
to estimate the map sensitivity, we measured the RMS noise σ in blank regions of sky,
finding σ ∼ 0.3 mJy per 40′′ beam for the ATCA data, 30 mJy per 16.′ 6 beam for the
Parkes data, and 0.3 mJy per 40′′ beam for the combined data. The measured value for
the sensitivity of the ATCA data is in excellent agreement with the theoretical noise
estimate of 0.3 mJy per 40′′ beam for our selected observing strategy and deconvolution
scheme.
5.4 Results
5.4.1
Total 1.4 GHz flux density of the LMC
For our final combined ATCA+Parkes map, we measure a total flux density of 443 Jy
within the entire 10.8◦ × 12.3◦ survey field. The total flux density in the Parkes map
over this same region is 413 Jy. Most of the difference in flux density between the combined ATCA+Parkes map and the Parkes data is due to the relative calibration factor
of 1.07 that we obtained by comparing strong point sources in the Parkes and ATCA
datasets. The flux density of our Parkes 1.4 GHz map is ∼ 20% less than the flux
density quoted for the same map by Klein et al. (529±29 Jy, 1989). This discrepancy
can mostly be attributed to the larger beam size that we have adopted for the Parkes
data. Rather than the nominal FWHM beam size of 15′ , we adopted an effective beam
width of 16.6′ , which reduces the total flux density. We consider that the effective beam
width provides a more reliable estimate of the beam size of the Parkes data, since the
gridding and scanning process used during observations and data reduction is known
to broaden the effective beam (e.g. Filipovic et al., 1995).
5.4. Results
259
Re-calculating the total flux density in the Parkes map using the nominal beam size
of 15.0′ yields 503 Jy. While this is within the uncertainties of the Klein et al. (1989)
estimate, the remaining ∼ 20 Jy difference between the two measurements may result
from the different methods that have been used to obtain the LMC’s integrated flux
density. Here we simply sum all the emission within the rectangular 10.8◦ × 12.3◦
survey field. Klein et al. (1989), by contrast, performed an integration in elliptical
rings, including a correction for non-zero baselines. Towards the map edges, the Parkes
data exhibits a small negative offset. By blanking pixels with negative values in the
Parkes data and recalculating the integrated flux density over the remaining unmasked
area, we find that the pixels at the map edges make an overall negative contribution of
∼ −20 Jy to the measured flux density. Systematic effects, such as the true FWHM of
the Parkes beam and non-zero baselines, would therefore seem to make our estimates
for the LMC’s 1.4 GHz luminosity uncertain by ∼ 20%; compared to these potential
sources of error, the uncertainty due to the finite sensitivity of the data is negligible.
5.4.2
Contribution from Background Sources
The 1.4 GHz image of the LMC contains a large number of point sources, of which
& 90% are background active galactic nuclei (e.g. Marx et al., 1997). For some applications, it is desirable to suppress the emission from these sources. We therefore produced
a median-filtered version of the ATCA+Parkes 1.4 GHz map. The filtering operation,
implemented in the GIPSY routine mfilter, moves a 2.′ 5×2.′ 5 window across the map,
replacing the central pixel value (Scpix ) with the median value of the window (Smed ) if
|Scpix − Smed | > Smed + 1 mJy (van der Hulst et al., 1992). The 1 mJy offset prevents
unnecessary filtering in noisy regions where the median is close to zero. Repeating the
sensitivity measurements using the median-filtered version of the ATCA+Parkes map
– where it was possible to measure the noise over much larger blank regions of sky –
indicated RMS values between 0.25 and 0.35 mJy per 40′′ beam, giving us confidence
in our sensitivity estimate for the unfiltered data. The total flux density of the medianfiltered map is 325 Jy, i.e. the filtering operation removed ∼27% of the total emission
in the original image. The median-filtered version of the ATCA+Parkes 1.4 GHz LMC
260
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
map is presented in Figure 5.7.
While it is very effective at suppressing emission from compact sources, median filtering
makes no distinction between background sources and point sources that are intrinsic
to the LMC. The difference in flux density between the filtered and unfiltered maps
is only an upper limit to the contribution of background radio galaxies to the LMC’s
total 1.4 GHz flux density. We attempted to obtain a more accurate estimate of the
background source contribution using two methods. In our first approach, we used a
smooth-and-mask technique to measure the combined flux density of point sources in
sixteen 1◦ × 1◦ control fields around the edges of our unfiltered 1.4 GHz ATCA+Parkes
map. For this, we smoothed the ATCA+Parkes data to a resolution of 1.′ 0, and blanked
all pixels in the control fields where the flux density of the smoothed map was less than
3 times the RMS noise in the smoothed map (3σ ∼ 10 mJy per 1.′ 0 beam). We then applied the blanking mask to the original unsmoothed data, and measured the combined
flux density of the unmasked pixels in the control fields. From these measurements,
we obtained a direct estimate of the mean point source flux density per square degree.
Multiplying by the angular size of the LMC yields an estimate of the total flux density
due to background sources. Assuming that the LMC subtends 7.5◦ × 7.5◦ on the sky,
we estimate that the 1.4 GHz flux density of sources behind the LMC is 46 ± 10 Jy,
where the quoted uncertainty represents the dispersion of the measurements obtained
from individual control fields.
We obtained a second estimate of the 1.4 GHz flux density from background sources using the differential 1.4 GHz source count distributions of the FIRST and NVSS surveys
determined by Blake & Wall (2002). We fitted a curve to the data presented in their
figure 5, and calculated the total flux density expected for sources in the flux density
range [0.001,1] Jy within an area of 7.5◦ × 7.5◦ . The predicted 1.4 GHz flux density of
background sources is 52 Jy from the FIRST source count distribution, and 55 Jy from
the NVSS data. These values are within the uncertainty of our direct estimate from
the edges of the ATCA+Parkes map. The flux density of the filtered and unfiltered
maps within a 7.5◦ × 7.5◦ field centered on RA 05h20m, Dec -68d40m (J2000) is 367 Jy
5.4. Results
261
Figure 5.6 The combined Parkes + ATCA 1.4 GHz radio continuum map of the LMC. A squareroot intensity scale has been used to emphasise the characteristics of the diffuse emission. The
units are Jy per 40′′ beam.
and 426 Jy respectively. This difference in flux density is only 10 to 30% greater than
our estimates for the contribution by background galaxies, and we conclude that most
of the emission removed by the filtering operation is due to external sources.
5.4.3
Morphology of the LMC’s 1.4 GHz Continuum Emission
The emission associated with the 30 Doradus region appears to dominate the map of the
1.4 GHz radio continuum emission in the LMC. Numerous smaller regions of high surface brightness emission are located throughout the LMC’s disk, and many of the bright
262
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Figure 5.7 The ATCA+Parkes map of 1.4 GHz emission in the LMC, after applying a median
filter to suppress emission from point sources. A square-root intensity scale has been used. The
red contour indicates an H α surface brightness of 50 R. The units are Jy per 40′′ beam.
5.4. Results
263
Table 5.2 The flux density, resolution and sensitivity of the original and median-filtered 1.4 GHz
ATCA+Parkes mosaics, and of the Parkes 4.8 GHz map presented by Haynes et al. (1991). The
second column lists the resolution of each image; note that we adopt the effective beam size
determined by Filipovic et al. (1995) for the Parkes 4.8 GHz data. The third column lists the
flux density within a 7◦ .5 × 7◦ .5 field centred on RA 05h20m, Dec -68d40m (J2000) (Region
1). The fourth column lists the flux density within the 0.9 MJy sr−1 contour of the reprocessed
IRAS 60 µm map (Region 2, Miville-Deschênes & Lagache, 2005). The fifth column lists the flux
density within the 40 mJy per beam brightness threshold of the 4.8 GHz map, which defines the
edges of our spectral index map (Region 3). The boundaries of the three regions are indicated
in Figure 5.9. The sixth column lists the RMS noise in map, measured from blank regions of
sky.
Frequency
Beam
(GHz)
(arcsec)
Region 1
(Jy)
1.4
1.4-mf
4.8
40
40
336
426
367
217
Flux Density
Region 2 Region 3
(Jy)
(Jy)
390
350
214
317
277
185
Sensitivity
0.3 mJy per 40′′ beam
0.3 mJy per 40′′ beam
9.5 mJy per 5.′ 6 beam
1.4 GHz peaks are associated with strong sources of H α emission (see Figure 5.7). Visual inspection therefore seems to suggest that a significant fraction of the total 1.4 GHz
flux density may be thermal emission produced by a few very bright star-forming regions. We used the Southern H α Sky Survey Atlas (SHASSA) map of H α emission in
the LMC to estimate the fraction of the 1.4 GHz emission that is distributed in structures with high H α surface brightness, measuring the total flux density in the 1.4 GHz
map for pixels with H α surface brightness greater than 100 and 500 R. Despite the
visual dominance of 30 Dor and other H II regions in the LMC, the 1.4 GHz flux density
corresponding to these regions is only 140 and 81 Jy. Similar values are obtained if
1.4 GHz flux densities of 5 and 10 mJy beam−1 , rather than H α thresholds, are used
to define the high surface brightness structures. Contrary to our initial impression of
the 1.4 GHz map, the majority of the LMC’s total 1.4 GHz luminosity is contributed
by diffuse emission with low intensity.
Another remarkable feature of the map in Figure 5.6 is that the distribution of the
diffuse emission is asymmetric, showing a steep decline along the eastern edge of the
LMC and a more gradual decrease with increasing distance from 30 Doradus in other
directions. There is minimal diffuse emission along the western edge of the LMC,
even surrounding active star-forming complexes such as N11 and N87 (Henize, 1956).
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
log(SRC/[Jy beam−1])
90
85
80
75
70
0
−1
−2
−3
[a]
1.4GHz, 0.’8 resn
1
[b]
1.4GHz, 5.’6 resn
4.8GHz, 5.’6 resn
0
−1
−72
log(SRC/[Jy beam−1])
264
1.0
−68
−66
[e]
1.4GHz, 0.’8 resn
1
[d]
1.4GHz, 5.’6 resn
4.8GHz, 5.’6 resn
0
−1
−2
[c]
S4.8/S1.4
S4.8/S1.4
−2
−70
0
−1
−2
−3
0.5
90
85
80
75
70
Right Ascension [degrees]
1.0
[f]
0.5
−72
−70
−68
−66
Declination [degrees]
Figure 5.8 Profiles of the 1.4 GHz (black) and 4.8 GHz (grey) emission along E-W (panels [a]
and [b]) and N-S ([d] and [e]) cuts through 30 Doradus. The plots in panels [c] and [f] show the
ratio between the 1.4 and 4.8 GHz profiles presented in the middle panels.
Figure 5.8 presents 1.4 and 4.8 GHz intensity profiles along E-W and N-S cuts through
30 Doradus. For the 4.8 GHz profiles, we used data from the Parkes survey by Haynes
et al. (1991), assuming an effective beam size of 5.′ 6 at 4.8 GHz (Filipovic et al., 1995).
As well as an abrupt eastern edge to the LMC’s radio continuum emission, the profiles
reveal that the intensity of the diffuse emission declines more slowly towards the south of
30 Doradus than to the north or west. The ratio between the 1.4 and 4.8 GHz intensity
profiles mostly fluctuates between 0.5 and 1.0, but shows some evidence for a systematic
decline for declinations south of 30 Doradus. We discuss possible interpretations for the
asymmetric distribution of the diffuse radio emission in the LMC, and for the properties
of the radio emission south of 30 Doradus, in Section 5.6.3.
5.4.4
The Radio Spectral Index
We calculated the global spectral index of the LMC using the 1.4 and 4.8 GHz flux densities measured over i) a 7.5◦ × 7.5◦ field centred on RA 05h20m, Dec -68d40m (J2000),
ii) the region where the 60 µm emission in the reprocessed IRAS map of the LMC
is greater than 0.9 MJy sr−1 (Miville-Deschênes & Lagache, 2005), and iii) a smaller
region where the 4.8 GHz flux density was greater than 40 mJy per 5.′ 6 beam (corresponding to a ∼ 4σ sensitivity threshold). The flux density of the LMC at 1.4 and
5.4. Results
265
4.8 GHz within each of these three regions is listed in Table 5.2, and the boundaries of
each region are indicated on the map of the LMC in Figure 5.9. Our three estimates
for the LMC’s global radio spectral index vary by ∼ 0.1, ranging from α = −0.55 for
the measurement across the 7.5◦ × 7.5◦ field, to α = −0.44 for the more restricted region where S4.8 ≥ 40 mJy beam−1 . Using the median-filtered 1.4 GHz map flattens the
spectral index by ∆α ∼ 0.1 in all cases. Our estimates for the LMC’s radio spectral
index are therefore significantly flatter than the mean spectral index of normal spiral
galaxy samples at these frequencies (α ∼ −0.74 ± 0.12, Gioia et al., 1982), suggesting
that the thermal fraction of the LMC’s radio continuum emission at 1.4 GHz may be
relatively large. Previous surveys of late-type galaxies have shown that dwarf galaxies
have higher thermal fractions and flatter spectral indices than normal spirals (e.g. Klein
et al., 1991), which is usually interpreted as a sign that cosmic rays escape more readily
from low-mass galaxies.
To investigate spatial variations of the radio spectral index, we constructed a spectral
index map. The map was produced by smoothing the ATCA+Parkes 1.4 GHz image
to the resolution of the Parkes data, blanking pixels where S4.8 < 40 mJy beam−1 , and
calculating the spectral index for the unblanked pixels. It was not necessary to perform
additional masking based on the sensitivity of the 1.4 GHz map since the 1.4 GHz data
are more sensitive than the Parkes 4.8 GHz data. The resulting spectral index map
is shown in Figure 5.9. The median value of α for unblanked pixels is −0.47, consistent with the global estimates derived above. Our masking technique is biased against
faint emission with a steep spectral index, however, since pixels with low signal-tonoise 4.8 GHz emission are excluded, even if 1.4 GHz emission at that position is welldetected. Dilating the blanking mask to include all pixels within the IRAS 0.9 MJy sr−1
contour increases the number of unblanked pixels by a factor of ∼ 2 and steepens the
median spectral index to −0.59. This variation in the average spectral index with integration area suggests that the spectral index of the diffuse emission located far from
30 Doradus is significantly steeper than −0.47, and that the global estimates for the
spectral index in Regions 2 and 3 should properly be regarded as upper limits. Deeper
4.8 GHz continuum observations are required to determine whether the LMC’s global
266
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
spectral index approaches the mean value observed for spiral galaxy samples.
The dominant feature of the spectral index map in Figure 5.9 is the emission associated with 30 Doradus. Though we are limited by the sensitivity of the 4.8 GHz data,
α appears to become more negative with increasing distance from 30 Doradus. Similar to the decline in 1.4 GHz total intensity, the decrease in α is asymmetric: to the
south-east of 30 Doradus, the spectral index falls away much more abruptly than in
the north-west direction. Several of the LMC’s well-known star-forming regions can
be identified in the spectral index map (e.g. N11 and N87, Henize, 1956), and these
exhibit a variegated pattern with a mean spectral index of ∼ −0.4. The spectral across
the LMC is relatively flat, and few regions have spectral indices more negative than
α ∼ −1.0. The most negative spectral indices in the map are associated with the supernova remnant N132D (Davies et al., 1976), while the interface of the LMC4 and LMC5
superbubbles (near RA 05h25m, Dec -66d15m (J2000), Meaburn, 1980) also exhibits
a steep spectral index. The H I, radio continuum and 8.3µm emission from this region
have been studied in detail by Cohen et al. (2003), who identified the region as a site
of triggered secondary star formation, containing a mixture of young massive stars and
recently exploded supernova remnants.
The map in Figure 5.9 reveals a ring of positive α values around 30 Doradus, with a
width of ∼ 0.5 kpc. We would expect a significant fraction of the radio continuum emission associated with 30 Doradus to be thermal, but it is not clear why the spectral index
should increase and then decline over these spatial scales. Positive spectral indices can
indicate signicant free-free absorption, which has been identified for extremely young
(≤ 1 Myr), heavily embedded star clusters (e.g. Johnson & Kobulnicky, 2003). However
these “ultradense” H II regions are extremely compact (R ∼ 2 to 4 pc) and should be
associated with dense molecular gas (Elmegreen, 2002): neither condition appears to
be satisfied here. Based on a spectral analysis of OB stars in 30 Doradus, Walborn
& Blades (1997) suggested that the most recent star formation activity in 30 Doradus
is occurring to the north-west of the central R136 cluster, and clumps of high-density
molecular gas with embedded infrared sources have recently been identified in this re-
5.5. Thermal and Non-Thermal Components of the 1.4 GHz Emission
267
gion (Rubio et al., 2009). Although the most extended region of positive α values also
lies to the north-west of 30 Doradus, it is significantly displaced (and much larger) than
the region discussed by these studies. As we have no good physical explanation for the
ring of positive α values, we conclude that it may be an artefact of the radio continuum
data. The feature is present when a spectral index map is constructed from Parkes
data alone, which would seem to rule out the ATCA 1.4 GHz mosaic as the origin of
the artefact.
5.5 Thermal and Non-Thermal Components of the 1.4 GHz
Emission
Isolating the synchrotron emission in galaxies is of considerable interest, as properties
of the synchrotron emission can provide empirical constraints on both the magnetic
field and the origin, transport and energy loss mechanisms of cosmic rays (e.g. Crocker
et al., 2010). The non-thermal spectral index of galaxies is probably not constant
at GHz frequencies (Condon, 1992), but in practice many techniques to separate the
thermal and non-thermal radio emission assume a constant value for αnth due to the
limited frequency coverage of the available radio continuum data (e.g. Klein et al., 1984,
1989). Unfortunately, this assumption negates the possibility of using the derived nonthermal map to investigate how cosmic rays lose energy as they diffuse through their
host galaxies. To distinguish the thermal and non-thermal components of the 1.4 GHz
radio emission in the LMC, we use the method recently presented by Tabatabaei et al.
(2007). In essence, this method constructs a model of the thermal radio emission from
an extinction-corrected image of a galaxy’s H α emission. The extinction correction
is derived by estimating the dust optical depth from the 160µm flux density and the
dust temperature. The method is described in detail in sections 3 to 6 of Tabatabaei
et al. (2007). Here we summarise the key equations, and discuss the values of specific
parameters that we have adopted for the decomposition of the 1.4 GHz LMC mosaic.
To estimate the dust temperature, we use the map constructed by Bernard et al. (2008)
268
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Figure 5.9 The radio spectral index in the LMC, calculated from a smoothed version of the
1.4 GHz ATCA+Parkes map and the 4.8 GHz Parkes map of Haynes et al. (1991). The white
contour indicates the 40 mJy beam−1 brightness threshold of the 4.8 GHz map. The grey line
reproduces the 0.9 MJy sr−1 contour of the 60 µm emission in the reprocessed IRAS map presented by Miville-Deschênes & Lagache (2005). The circle of negative spectral indices near
RA 05h25m, Dec -69d38m (J2000) is due to emission associated with the supernova remnant
N132D (Henize, 1956).
log(S160/[MJy sr−1])
5.5. Thermal and Non-Thermal Components of the 1.4 GHz Emission
269
2.5
2.0
1.5
1.0
0.5
15
20
25
Dust temperature [K]
Figure 5.10 The mean optical depth at 160 µm, τ160 , plotted as a function of the dust temperature and 160 µm surface brightness. The colour scale runs from τ160 = 3.5 × 10−5 (light grey) to
τ160 = 2 × 10−3 (black). This plot illustrates the behaviour described by Equation 5.2, showing
that the τ160 varies inversely with the dust temperature for pixels with constant 160 µm surface
brightness.
and described in Section 2.5. From this map, we obtain a map of the dust optical depth
at 160 µm (τ160 ) according to:
I160 = B160 (T ) [1 − exp(τ160 )] ,
(5.2)
where I160 is the flux density at 160 µm, and B160 (T ) is the value of the Planck function
at 160 µm for dust temperature T . The dust optical depth at 160 µm is typically small,
reaching a maximum value of τ160 ∼ 2.5×10−3 for several locations along the molecular
ridge (refer Figure 2.2). For a fixed 160 µm flux density, τ160 increases with decreasing
dust temperature (see Figure 5.10).
Tabatabaei et al. (2007) use the extinction curve of the standard model for dust in the
diffuse ISM to convert between τ160 and the dust optical depth at the wavelength of H α
emission τHα , adopting τHα ∼ 2200τ160 . As the large grain population in the LMC and
Milky Way are likely to have similar optical properties (compare, for example, figures
7 and 8 of Pei, 1992), we use the same conversion factor here. If the sources of H α
270
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
emission were located behind the galaxy, then the observed H α emission IHα would be
related to the intrinsic (i.e. extinction-free) emission IHα,0 via
IHα = IHα,0 exp(−τHα ) .
(5.3)
We use the SHASSA map described in Section 2.5 to estimate IHα at each map pixel.
In general, H α sources lie within the galaxy, so τHα only provides an upper limit to
the attenuation. The effective optical depth is τeff = fd × τHα , where fd ∈ [0, 1] is
the dust-screening factor that represents the relative geometry of the H α emission and
the dust that contributes to the extinction. If the dust, H α sources and diffuse ionized gas are well-mixed, fd = 0.5. For the Milky Way, Dickinson et al. (2003) find
fd = 0.33 ± 0.15, indicating that H α emission has a smaller vertical scale height than
the dust. The porous appearance of the H I emission in the LMC suggests that the ISM
transparency in the LMC may be even greater than in the Milky Way. We therefore
tested three values for the dust screening factor that were equal to or smaller than the
Dickinson et al. (2003) fit: fd = 0.1, 0.15 and 0.3. These values of fd correspond to
mean extinctions of AHα = 0.2, 0.31 and 0.66 mag; for comparison, estimates for the
mean internal extinction at the wavelength of H α range between 0.3 and 0.62 mag (e.g.
Kennicutt et al., 1995; Bell et al., 2002; Israel et al., 2010). To generate our final maps
of the thermal and non-thermal radio continuum emission, we adopted fd = 0.1. We
discuss the reasons for this choice at the end of this Section.
Having obtained an estimate for the intrinsic H α flux density, IHα = IHα,0 exp(−τeff ),
we use equation 9 of Valls-Gabaud (1998) to estimate the emission measure EM:
− 0.029
T
−1.017
IHα,0 = 9.41 × 10−8 Te4
10
e4
EM.
(5.4)
In this equation, Te4 is the electron temperature Te in units of 104 K, and the expression is determined assuming Case B recombination (i.e. each Lyman line photon is
resonantly scattered many times). For twelve H II regions in the LMC, Vermeij & van
der Hulst (2002) derived a mean electron temperature of 10000 K. Individual measure-
5.5. Thermal and Non-Thermal Components of the 1.4 GHz Emission
271
ments varied between 8000 and 16000 K, depending on the location of the H II region
and emission line that they used in their analysis. The electron temperature of the
diffuse ionized gas (DIG) in the LMC is not well-determined; typical estimates in the
Milky Way range between 8000 and 10000 K (e.g. Reynolds, 1985; Alves et al., 2010),
but there is evidence that the electron temperature is ∼ 2000 K higher in the DIG
than in H II regions (summarized in Haffner et al., 2009). For the LMC data, we tested
constant values for Te of 8000, 10000 and 12000 K, ultimately adopting Te = 8000 K.
We discuss our adopted value of Te below.
The optical depth of the radio continuum emission τc at frequency ν is related to the
emission measure derived from Equation 5.4 by
−2.1
(1 + 0.08)EM,
τc = 8.235 × 10−2 aTe νGHz
(5.5)
where νGHz is the observed frequency expressed in GHz, and a is a correction factor
that is approximately equal to unity at 1.4 GHz (see table 3 of Dickinson et al., 2003).
The predicted brightness temperature of the free-free radio continuum emission Tb is
then simply
Tb = Te (1 − exp(τc )) .
(5.6)
To obtain a map of the non-thermal radio continuum emission at 1.4 GHz, we subtract
this model of the thermal radio emission from the median-filtered 1.4 GHz continuum
map. The resulting maps of the LMC’s thermal and non-thermal 1.4 GHz radio continuum emission are presented in Figure 5.11. The integrated thermal and non-thermal
flux densities are 99 and 265 Jy respectively, corresponding to a global thermal fraction
of 27%.
The non-thermal map in Figure 5.11[b] exhibits a mixture of diffuse emission and high
brightness features. On one hand, this could indicate that our thermal/non-thermal
decomposition is failing for H II regions, i.e. that we are underestimating the H α extinction and incorrectly identifying some of the bright thermal 1.4 GHz emission as being
of non-thermal origin. On the other hand, some spatial coupling between the brightest
272
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Figure 5.11 Maps of the thermal (panel [a]) and non-thermal (panel [b]) 1.4 GHz continuum
emission in the LMC. The greyscale, which is the same for both panels, represents the flux
density in Jy per 4.′ 3 beam. The grey contour in panel [b] indicates a non-thermal 1.4 GHz flux
density of 0.08 Jy per beam. The red crosses indicate the location of confirmed LMC supernova
remnants collated by Badenes et al. (2010).
5.5. Thermal and Non-Thermal Components of the 1.4 GHz Emission
273
sources of thermal and non-thermal 1.4 GHz emission would be expected, since the massive stars that ionize the hydrogen gas in H II regions should evolve quickly to become
supernova remnants. Overall, the brightest sources of non-thermal radio emission in
Figure 5.11[b] demonstrate a good correspondence to the positions of confirmed LMC
supernova remnants (Badenes et al., 2010), which should be strong synchrotron emitters. There is an extended region of diffuse non-thermal emission near RA 05h20m,
Dec -68d30m (J2000), however, that is devoid of known SNRs.
In M33, Tabatabaei et al. (2007) find that bright non-thermal features agree well with
the distribution of SNRs and that star-forming regions make a significant contribution
to that galaxy’s non-thermal radio luminosity. Assuming that our thermal/non-thermal
decomposition is reliable, we find that . 20% of the LMC’s non-thermal emission arises
from regions where the non-thermal radio flux density is greater than 0.2 mJy beam−1 .
A similar fraction is obtained if we calculate the non-thermal flux density above an H α
surface brightness threshold of 100 R. In Section 5.4.3, we found that diffuse emission
contributes most of the LMC’s total 1.4 GHz luminosity. Our result for the LMC’s
non-thermal radio luminosity is very similar: the majority of the non-thermal radio
emission in the LMC arises from a diffuse, low surface brightness component that is
not directly connected to H II regions.
The method that we have used to separate the thermal and non-thermal components
of the radio continuum emission has a number of limitations. In particular, we assume a fixed value of the dust-screening factor and the electron temperature across the
LMC, even though both quantities should vary with interstellar environment. As noted
above, Te may be systematically lower in the H II regions than in the DIG. There is also
empirical evidence for Te fluctuations within individual H II regions (e.g. Tsamis et al.,
2004). The dust screening factor is probably not uniform either: the dust distribution
may be more clumpy in star-forming regions than in the diffuse ISM for example. For
a constant dust mass, a clumpy distribution is more porous than a uniform layer, so
the effective H α attenuation will be higher in regions where the dust and gas are better
mixed.
274
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Table 5.3 Results matrix showing the derived mean H α extinction hAHα i and the integrated
thermal and non-thermal 1.4 GHz flux densities of the LMC for different combinations of fd
and Te .
hAHα i [mag]
fd = 0.1
fd = 0.15
fd = 0.3
0.20
0.31
0.66
Te = 8000 K
th
nth
99
109
150
265
255
214
Flux Density [Jy]
Te = 10000 K Te = 12000 K
th
nth
th
nth
112
124
171
252
240
192
126
139
191
238
225
172
Since the values of fd and Te are not well-constrained by observations, we tested a grid
of plausible values for these parameters. The thermal and non-thermal 1.4 GHz flux
densities and the mean H α extinction for each combination of fd and Te are listed in
Table 5.3. Maps of the derived non-thermal radio emission for a central 2.◦ 5× 2.◦ 5 region
for four of the (fd ,Te ) combinations are displayed in Figure 5.12. Depending on our
choice of fd and Te , the thermal fraction of the LMC’s integrated radio flux density
varies between 27 and 52%. The values of fd that are most compatible with recent
estimates for the LMC’s mean H α attenuation (∼ 0.65 mag, Israel et al., 2010) tend
to produce maps with extended ‘holes’ of negative non-thermal radio flux densities,
especially in the vicinity of 30 Dor and other bright H II regions (see the bottom row of
Figure 5.12). Negative regions in the non-thermal map indicate that the thermal radio
component is overestimated by the model constructed from the H α emission, which
will occur if our estimates for τeff or Te are too high in these regions. We adopted
fd = 0.1 and Te = 8000 K to avoid negative flux densities in the final radio maps, but
we note that the thermal fraction of the diffuse radio emission outside the H II regions
may be underestimated with this choice of parameters. A more sophisticated model
would allow fd and Te to vary across the LMC, but such a model would be difficult to
justify without further independent constraints on fd and Te .
5.5. Thermal and Non-Thermal Components of the 1.4 GHz Emission
275
Figure 5.12 Maps of the non-thermal emission in the LMC at 1.4 GHz that were derived using
different combinations of fd and Te , which are indicated in the top right corner of each plot.
We use the map in panel [a] with fd = 0.1 and Te = 8000 K for our analysis. This choice was
motivated by the larger regions of negative flux density that occur for higher values of fd and
Te . The map units are Jy per 4.′ 3 beam.
276
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
5.6 Discussion
5.6.1
The Connection between Radio Continuum and CO Emission
in the LMC
Resolved studies of nearby molecule-rich galaxies have identified a strong correlation
between the CO and 1.4 GHz radio continuum on spatial scales down to ∼ 100 pc (Murgia et al., 2005; Paladino et al., 2006). These authors have proposed that the correlation
arises because the molecular gas surface density and the cosmic ray energy density are
both regulated by the midplane hydrostatic pressure, P̄ . Equipartition between the
turbulent and magnetic field energy densities ensures that the magnetic field – the
other key determinant of the synchrotron intensity – also scales with P̄ . Incorporating
a relationship between the FIR emission in galaxies and P̄ (e.g. via a scaling between
P̄ and the stall radius of H II regions, Dopita et al., 2005) makes the proposed model
especially intriguing, since it produces an explanation for the radio-FIR correlation in
star-forming galaxies with no explicit dependence on star formation activity.
In contrast to the galaxies studied by Murgia et al. (2005) and Paladino et al. (2006),
there does not appear to be a strong correlation between the CO and 1.4 GHz emission
in the LMC. This is obvious from visual inspection of the maps in Figures 2.2 and 5.6,
but can be assessed more quantitatively in Figure 5.13, where we plot the CO integrated
intensity I(CO) as function of the thermal and non-thermal components of the 1.4 GHz
emission. The plots in panels [a] to [c] of Figure 5.13 are constructed from the radio
maps presented in Section 5.5 and a smoothed version of the NANTEN I(CO) map
described in Section 2.5, which has more complete spatial coverage than the MAGMA
survey. The data points in these panels correspond to independent resolution elements
with an angular (spatial) scale of 4.′ 3 (60 pc). To extend our comparison to the smaller
scales, the plot in panel [d] is constructed from the MAGMA I(CO) map and the
1.4 GHz map presented in Section, smoothed to a common resolution of 1′ (15 pc).
For pixels with weak CO emission (I(CO) . 2 K km s−1 ), the range of observed 1.4 GHz
1
277
[a]
log(S1.4,th/[Jy beam−1])
log(S1.4/[Jy beam−1])
5.6. Discussion
0
−1
−2
−3
1
[b]
0
−1
−2
−3
0.0
0.5
1.0
0.0
log(I(CO)/[K km s−1])
0.5
1.0
log(I(CO)/[K km s−1])
1
[c]
log(S1.4/[Jy beam−1])
log(S1.4,nth/[Jy beam−1])
1
0
−1
−2
[d]
0
−1
−2
−3
−3
−4
0.0
0.5
1.0
log(I(CO)/[K km s−1])
0.0
0.5
1.0
1.5
2.0
log(I(CO)/[K km s−1])
Figure 5.13 The relationship between the 1.4 GHz flux density and the CO integrated intensity
in the LMC. In panels [a] to [c], we plot the total 1.4 GHz flux density, the thermal and the
non-thermal component of the radio emission respectively. The data points in these panels
correspond to independent resolution elements with a spatial scale of 60 pc. Pixels with I(CO) <
1 K km s−1 in the NANTEN I(CO) map are rejected from the comparison, which produces
a sharp edge at this value of I(CO). In panel [d], we plot the total 1.4 GHz flux density
versus I(CO) as measured by the MAGMA survey, at a linear resolution of 15 pc. Pixels with
I(CO) < 2 K km s−1 in the MAGMA I(CO) map are excluded. The solid line in panels [a]
and [c] represents the best-fitting relation derived using ordinary least squares for pixels with
I(CO) ≥ 2 K km s−1 (vertical dotted line). The dashed line in panel [d] is not a fit, but instead
illustrates the slope of the relation determined for CO and 1.4 GHz continuum emission in
1.3
normal galaxies, S1.4 ∝ I(CO) (Murgia et al., 2005).
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Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
flux densities varies by ∼ 3 orders of magnitude. However, the pixels with the highest
radio intensities (S1.4 & 1 Jy per 4.′ 3 beam) in panels [a] to [c] are all associated with the
30 Doradus complex, where we would expect the CO emission from molecular clouds to
be strongly affected by photodissociation (e.g. Israel et al., 1996; Pineda et al., 2009).
For pixels with I(CO) ≥ 2 K km s−1 , a weak correlation between the total/non-thermal
radio and CO emission is more evident. An ordinary least-squares fit to pixels with
I(CO) ≥ 2 K km s−1 in panels [a] and [c] yields a relationship between the high intensity
radio and CO emission with a slope of ∼ 1.4. This is similar to the slope determined
by Murgia et al. (2005) for the global CO-radio relationship among galaxies, but the
dynamic range of the CO observations included in our fit is too narrow (∼ 1 dex) to
draw strong conclusions. A correlation between the 1.4 GHz and CO emission is not
obvious for the high resolution data in panel [d], although pixels with strong CO emission are rarely associated with low radio flux densities.
We identify several factors that may contribute to the different relationship between CO
and radio emission in the LMC compared to the galaxy sample of Murgia et al. (2005).
First, the thermal fraction of the radio emission is significantly higher in the LMC than
in spiral galaxies, so we would expect the radio-CO correlation to be more similar to
the relationship between CO and dust emission, breaking down near H II regions due to
the photodestruction of molecular clouds. Second, the fraction of neutral gas occurring
in the molecular phase is much smaller in the LMC (fmol ∼ 0.05, Chapter 2) compared
to the central regions of the BIMA-SONG galaxies (where fmol ∼ 0.5, Wong & Blitz,
2002). As CO molecules cannot survive without self-shielding, a smaller molecular fraction leads to a lower volume filling-factor of CO emission, and thus no counterpart to
the extended non-thermal radio emission that is evident in Figure 5.11[b]. Finally, the
combination of strong external pressure due to the LMC’s interaction with the Milky
Way halo and variable internal ISM pressures due to the expansion of bubbles and
supershells suggests that simple hydrostatic equilibrium estimates for the ISM pressure
may not predict the distribution of molecular clouds in the LMC.
5.6. Discussion
5.6.2
279
The Star Formation Rate in the LMC
The star formation rate (SFR) is a fundamental parameter that drives the appearance and evolution of galaxies. Empirical SFR calibrations have been devised at many
wavelengths across the electromagnetic spectrum, including the ultraviolet (UV) where
young high-mass stars emit most of their energy, the infrared (IR) where the radiation
reprocessed by dust is emitted, and the radio continuum, which traces supernova activity. The timescales probed by the different wavebands vary too: the H α emission, for
example, is powered by massive ionizing stars with shorter lifetimes (∼ 10 Myr) than
the massive stars that generate the UV continuum (∼ 100 Myr). As radio emission is
not affected by dust obscuration, a reliable SFR calibration based on radio observations
would be a valuable tool for star formation at high redshift and in dusty environments.
The rich database of IR and UV observations obtained by ISO, Spitzer and GALEX
has recently enabled detailed comparative studies of the validity of SFR tracers across
a wide range of galactic environments, and on sub-galactic scales (e.g. Calzetti et al.,
2007; Pérez-González et al., 2006; Kennicutt et al., 2009; Li et al., 2010). In the Milky
Way and nearby systems, resolved stellar population studies have started to provide an
important complement to SFR recipes that rely on emission at a single wavelength (or
a combination of wavelengths) (e.g. Harris & Zaritsky, 2009; Heiderman et al., 2010).
The LMC remains an interesting test case for comparing SFR calibrations, however,
due to the wide range of angular scales that can be probed, and the excellent multifrequency coverage of existing datasets.
In Table 5.4, we summarize estimates for the global star formation rate in the LMC
obtained using different methods. The functional form of each SFR calibration, and the
datasets that we used to derive the SFR estimates are also tabulated. For consistency,
all our calculations are based on a Kroupa IMF between 0.1 and 100 M⊙ (Kroupa,
2008): where necessary, we have divided SFR indicators that used a Salpeter IMF
across this mass range by 1.5 (Kennicutt et al., 2009; Calzetti et al., 2010). Though we
include them in Table 5.4, we note that the monochromatic L(160 µm) and L(70 µm)
calibrations of Calzetti et al. (2010) should not strictly be applied to the LMC, since
280
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
the LMC’s luminosity is below the lower limit of their applicable luminosity range by
a factor of ∼ 2 in both cases. For the other calibrations, the LMC falls within the
luminosity and metallicity range over which the calibration is supposed to be robust.
Most of the results in Table 5.4 indicate that current star formation in the LMC is
occurring at a rate of ∼ 0.15 M⊙ yr−1 , in good agreement with a recent reconstruction
of the LMC’s star formation rate history using stellar populations (0.2 M⊙ yr−1 for the
past 5 Gyr assuming a Salpeter IMF, Harris & Zaritsky, 2009). The empirical correlations that were used to formulate the SFR calibrations in Table 5.4 exhibit dispersions
between 0.1 and 0.6 dex, so precise agreement between the SFRs obtained at different
wavebands should not be expected. Nevertheless, it is remarkable that the calibrations
derived by Bell (2003) – which were designed to account for the lower dust opacity
and higher 1.4 GHz thermal fraction in low-mass galaxies – agree with each other, and
with the SFRs derived from H α and thermal 1.4 GHz emission, to within a factor of
∼ 2. The SFRs derived from the monochromatic 24 µm and 70 µm are lower by factors
of ∼ 10 and ∼ 5 respectively. Though other interpretations are possible, the LMC
would therefore seem to exemplify the trends that have been noted for low-luminosity
galaxies in nearby samples, i.e. an increased ISM transparency such that unabsorbed
optical/UV emission accounts for a larger fraction of the total star-formation activity, plus cooler effective dust temperatures and/or an increased contribution from old
stellar populations to the dust heating, which increases the fraction of the IR emission
emerging at longer wavelengths.
Table 5.4 shows that the total 1.4 GHz luminosity of the LMC leads us to underestimate
the SFR by a factor of ∼ 3, if we apply the calibrations of Schmitt et al. (2006) or
Yun et al. (2001). These calibrations are constructed from the tight radio-FIR correlation observed for star-forming galaxies, so the low SFR obtained for the LMC suggests
that the LMC’s radio emission is deficient with respect to its FIR luminosity, even
though the FIR itself may be tracing a reduced fraction of the SF activity in the LMC.
The separate SFR calibrations for the thermal and non-thermal components of the
radio emission suggest that it is the synchrotron component that is suppressed. Again
presented in column 3 and the reference for each calibration is noted in column 4. We measure the SFRs using the integrated luminosities
within a 7.5◦ × 7.5◦ field centred on (05h20m,-68d40m)J2000. Where necessary, we have rescaled original calibrations that used a Salpter IMF
between 0.1 and 100 M⊙ to a Kroupa IMF (2008) by dividing the published calibration coefficient by a factor of ∼ 1.5 (Kennicutt et al., 2009).
The total infrared luminosity (TIR) is estimated from the Spitzer SAGE data according to the equation 4 of Dale & Helou (2002).The datasets
that were used as input for the calibrations are listed in column 5. Reference key: (1) Calzetti et al. (2007) (2) Kennicutt (1998) (3) Calzetti
et al. (2010) (4) Bell (2003) (5) Yun et al. (2001) (6) Schmitt et al. (2006) Dataset key: (a) Gaustad et al. (2001) (b) Meixner et al. (2006) (c)
this work.
Band
SFR
M⊙ yr−1
Calibration
M⊙ yr−1
Reference
Data
5.3 × 10−42 L(Hα) [erg s− 1]
5.3 × 10−42 L(Hα) [erg s− 1]
5.3 × 10−42 L(Hα) [erg s− 1]
5.45 × 10−42 [L(Hα)obs + 0.020L(24 µm)]
1.27 × 10−38 (L(24 µm) [erg s−1 ])0.885
5.88 × 10−44 L(70 µm) [erg s−1 ]
1.43 × 10−43 L(160 µm) [erg s−1 ]
3.0 × 10−44 L(TIR)[erg q
s−1 ]
1,2
1,2
1,2
3
1
3
3
2
a
a
a
a,b
b
b
b
b
3
b
L(TIR) expressed in L⊙
3
3
4,5
5
5
c
c
c
c
c
Lc = 6.4 × 1021 W Hz−1
Using the median-filtered 1.4 GHz map
Hα
Hα
Hα
24 µm+ H α
24 µm
70 µm
160 µm
24, 70 + 160 µm (TIR)
0.12
0.15
0.20
0.13
0.009
0.03
0.16
0.12
24, 70 + 160 µm (TIR)
0.16
7.8 × 10−9 L(TIR) 1 +
0.12
0.11
0.05
0.13
0.04
3.68×10
L(1.4 GHz)
0.1+0.9(L(1.4 GHz)/Lc )0.3
1.4 GHz
1.4 GHz
1.4 GHz
Thermal 1.4 GHz
Non-thermal 1.4 GHz
−22
109
L(TIR)
−
[W Hz 1]
As above
4.0 × 10−22 L(1.4 GHz) [W Hz− 1]
4.3 × 10−21 L(1.4 GHz, th) [W Hz− 1]
4.5 × 10−22 L(1.4 GHz, nth) [W Hz− 1]
5.6. Discussion
Table 5.4 The global SFR of the LMC obtained used different empirical SFR calibrations. The functional form of each SFR calibration is
Notes
Assumes no extinction
Extinction correction as per Section 5.5
Assumes AHα = 0.5 mag extinction
L(Hα) and L(24 µm) expressed in erg s−1
281
282
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
this result is not entirely unexpected: an anti-correlation between thermal fraction and
galaxy mass for low-luminosity galaxies has been reported by several studies (e.g. Klein
et al., 1984, 1991; Price & Duric, 1992). This anti-correlation is incorporated into the
1.4 GHz SFR calibration presented by Bell (2003), which yields an SFR for the LMC
that is more consistent with the optical and TIR tracers.
The standard model for the connection between star formation and radio continuum
emission in normal galaxies offers some additional insight into the anomalous nature of the LMC’s radio emission. Empirically, recent supernova surveys have constrained the rate of core-collapse supernovae per unit of stellar mass formed to be
ψ = 0.01 ± 0.002 SNe M⊙ −1 (Maoz et al., 2010), supporting the view that all massive
stars with M ≥ 8 M⊙ produce observable supernovae. For this value of ψ and our
global SFR estimates, we infer a supernova rate of ηSN = SF R × ψ = 0.0015 yr−1
for the LMC. Assuming a non-thermal radio spectral index of αnth = −0.7, the predicted non-thermal 1.4 GHz flux density of the LMC is Snth = 513 Jy, if the LMC were
to follow the relation between Lnth and ηSN that is observed for normal star-forming
galaxies (equation 18 in Condon, 1992). This exceeds the measured total 1.4 GHz flux
density of the LMC by ∼ 100 Jy, and is larger than our estimate for the non-thermal
component at 1.4 GHz by a factor of ∼ 2. We note that the predicted value for Snth is
not especially sensitive to αnth : varying αnth by 0.2 implies a variation of only ∼ 30 Jy
in Snth .
Conversely, we can use equation 17 from Condon (1992) to calculate the supernova
rate implied by the LMC’s non-thermal flux density (265 Jy, Section 5.5). In this case,
we obtain ηSN ∼ 0.0008 yr−1 . Taken at face value, such a low value of ηSN would
suggest that a significant fraction of the LMC’s massive stars collapse “silently”, i.e.
without producing a supernova. Since this would be inconsistent with the supernova
survey results for local galaxies (including the Magellanic Clouds, e.g. Maoz & Badenes,
2010), we conclude that the deficit of non-thermal radio emission is due to the reduced
efficiency of processes that extract synchrotron radiation from the LMC’s cosmic ray
population, rather than an anomalously low supernova rate.
5.6. Discussion
5.6.3
283
Variations of the Radio Spectral Index and Cosmic Ray Losses
in the LMC
In Section 5.4.4, we observed a general decrease of the total radio spectral index with
increasing distance from 30 Doradus. To examine how this effect may be related to
the origin and propagation of cosmic rays in the LMC, we constructed a map of the
non-thermal spectral index αnth . The value of αnth at each pixel was derived according
to equation 1 of Niklas & Beck (1997):
S4.8
= fth
S1.4
ν4.8
ν1.4
αth
+ fnth
ν4.8
ν1.4
αnth
,
(5.7)
using the maps presented in Sections 5.4.1 and 5.5, and the Parkes 4.8 GHz map. In
this equation, fth is the thermal fraction of the radio emission at 1.4 GHz, fnth = 1−fth
is the non-thermal fraction, and S1.4 and S4.8 are the flux densities at 1.4 and 4.8 GHz
respectively. For the thermal spectral index, we adopted a constant value of αth = −0.1
(Condon, 1992). The resulting map is shown in Figure 5.14).
Overall, αnth exhibits similar spatial variations as the total spectral index: the αnth
values are more positive near 30 Doradus, and more negative in the western half of
the LMC. To quantify this, we calculated the median of αnth in semi-circular annuli
centred on RA 05h38m42s, Dec -69d06m03s (J2000), the location of the central star
cluster (RMC136, Høg et al., 2000). We performed separate calculations for pixels
located east and west of 30 Doradus, due to the asymmetry in the 1.4 GHz continuum
emission surrounding the star-forming complex. The radial variation in αnth is plotted
in Figure 5.15[a]; for comparison, we also plot radial profiles for the median total spectral index α (panel [b]) and the median thermal fraction (panel [c]). We refrain from
discussing pixels within 0.5 kpc of 30 Dor, due to the potentially spurious α values in
this region (Section 5.4.4).
Between R ∼ 0.6 and 1.4 kpc, the non-thermal spectral index remains roughly constant,
284
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Figure 5.14 Map of the 1.4-to-4.8 GHz non-thermal spectral index in the LMC, overlaid with
a single contour indicating where the non-thermal 1.4 GHz radio flux density is 0.08 Jy per 4.′ 3
beam.
5.6. Discussion
285
0
1
2
East [a]
West
α
0.0
−0.5
−1.0
αnth
0.0
[b]
−0.5
% Thermal
−1.0
[c]
60
40
20
0
0
1
2
Radial distance to 30 Dor [kpc]
Figure 5.15 The radial variation in (a) total spectral index α, (b) non-thermal spectral index
αnth and (c) thermal fraction of the 1.4 GHz emission. The α and αnth profiles are plotted
with dotted lines for R ≤ 0.6 kpc, as the Parkes radio continuum maps may be contaminated
by an artifact in this region. The horizontal dashed and dot-dashed lines in panels [a] and [b]
represent the mean total spectral index and mean non-thermal spectral index for spiral galaxies
respectively (α = −0.74, αnth = −0.85, Gioia et al., 1982; Niklas et al., 1997). The dashed line
in panel [c] indicates a thermal fraction of 10%.
286
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Table 5.5 Definitions of terms used in Equations 5.8 to 5.12.
Symbol
τsynch
τIC
τbrem
τion
τdiff
B10
νGHz
neff ≡ f hni
f
hni ≡ Σg /2h
Σg
h
Urad,−12
E
Definition
Synchrotron cooling timescale
Inverse Compton cooling timescale
Bremsstrahlung cooling timescale
Ionization cooling timescale
Confinement timescale
Magnetic field strength, normalized by 10 µG
Emission frequency, normalized by 1 GHz
Effective ISM number density experienced by cosmic rays (CRs)
Ratio between ISM density traversed by CRs and mean ISM density
Mean ISM number density within the CR confinement volume
Gas surface density in the LMC disk
CR scale height
Radiation field energy density, normalized by 10−12 erg cm−3
Total energy of cosmic ray
with a value of αnth ∼ −0.5 for the region west of 30 Doradus. αnth then decreases,
falling by ∼ 0.3 between R = 1.4 and R = 2 kpc. Beyond R ∼ 2 kpc, αnth remains
around −0.8, never attaining the characteristic values of a cosmic ray population dominated by synchrotron losses (αnth ≤ 1, Biermann & Strom, 1993; Bogdan & Volk,
1983).2 The radial profile of the total spectral index in panel [a] may be understood as
a combination of the profiles in panels [b] and [c]: α’s shallow decline between R = 0.6
and R = 1.4 kpc reflects the decreasing thermal fraction, but α converges towards αnth
at large R where the thermal fraction is small. Figure 5.15 also confirms the difference
in the spectral index for regions immediately east and west of 30 Doradus. Towards
the eastern edge of the LMC’s disk (R ∈ [0.6, 1] kpc), the non-thermal spectral index
is −0.8, while the median αnth value observed at a similar distance to the west of
30 Doradus is only −0.5. The total spectral index shows a similar east-west offset as
αnth , although the eastern α values decline more steadily in response to the decreasing
thermal fraction over the same range of R.
One possible interpretation of the trends in Figure 5.15 is that 30 Dor is the primary
2
We note that this minimum is obtained from azimuthal averages, which combine data from disparate
ISM environments. Two ∼ 0.3 kpc2 patches with αnth ∼ −1 occur near RA 05h21m43, Dec -71d15m45
and RA 05h17m47, Dec -67d19m35 (J2000).
5.6. Discussion
287
site of cosmic ray production in the LMC, and that the non-thermal spectrum becomes
more negative due to energy losses as the cosmic rays propagate into more distant
parts of the galaxy. Even at its minimum, however, αnth remains greater than the
spectral index of a synchrotron loss-dominated spectrum. This might indicate that
other energy loss processes are significant for cosmic rays in the LMC: Thompson et al.
(2006) demonstrate that cooling by bremsstrahlung and ionization can flatten radio
spectra at GHz frequencies (see their figure 3). Yet bremsstrahlung and ionization
cooling should only be competitive with synchrotron and inverse Compton cooling
under ISM conditions that are typical of starburst galaxies. To assess the relevance of
different loss processes in the LMC, we estimate their characteristic timescales using
the equations presented in Lacki et al. (2010):
−3/2 −1/2
νGHz
τsynch [yr] ≈ 4.5 × 107 B10
(5.8)
f hni −1
;
τbrem [yr] ≈ 3.7 × 10
[cm−3 ]
f hni −1
8 −1/2 1/2
;
[yr] ≈ 2.1 × 10 B10 νGHz
[cm−3 ]
7
τion
;
1/2 −1/2
−1
; and
τIC [yr] ≈ 1.8 × 108 B10 νGHz Urad,−12
7
τdiff [yr] ≈ 2.6 × 10
E
3GeV
−1/2
.
(5.9)
(5.10)
(5.11)
(5.12)
The meaning of the different terms in these equations, and the values that we adopted
in our LMC estimates, are summarised in Tables 5.5 and 5.6.
The diffusion timescale for electrons in the energy range E ∈ [1, 10] GeV is 1.4 to 4.5
×107 Myr. Our estimates in Table 5.6 therefore suggest that diffusive escape will be a
dominant cosmic-ray loss process in the LMC, with inverse Compton cooling becoming
competitive in regions with low density and strong radiation fields. For a magnetic field
strength of B ∼ 6 µG, a gas surface density of Σg ∼ 15 M⊙ pc−2 , and a radiation field
energy density of Urad,−12 ∼ 1.7, the timescales of synchrotron and inverse Compton
cooling are approximately three times longer than τdiff , while the bremsstrahlung and
288
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
Table 5.6 The characteristic timescale for synchrotron (column 5), inverse Compton (column
6), bremsstrahlung (column 7) and ionization (column 8) cooling of cosmic rays at 1.4 GHz.
The estimates in each row are derived using Equations 5.8 to 5.12 and the parameters listed
in columns 1 to 4. In each case, we assume that the scale height of the CR disk is h = 1 kpc
and f = 1 (Lacki et al., 2010). We consider B = 6 µG (Gaensler et al., 2005b; Klein et al.,
1993), Urad,−12 = 1.7 (Bernard et al., 2008), and Σg = 15 M⊙ pc−2 (Section 6.2.1) to exemplify
average ISM conditions in the LMC.
B10
µG
Σg
M⊙ pc−2
neff
cm−3
Urad,−12
τsynch
[107 yr]
τIC
[107 yr]
τbrem
[107 yr]
τion
[107 yr]
1
6
2
10
1
6
2
10
15
15
40
40
15
15
40
40
0.26
0.26
0.71
0.71
0.26
0.26
0.71
0.71
1.7
1.7
1.7
1.7
8.6
8.6
8.6
8.6
120.2
8.1
42.5
3.8
120.2
8.1
42.5
3.8
2.8
6.9
4.0
8.9
0.6
1.4
0.8
1.8
14.2
14.2
5.2
5.2
14.2
14.2
5.2
5.2
284.9
127.4
104.3
46.7
284.9
127.4
104.3
46.7
ionization timescales are longer than τdiff by factors of ∼ 6 and ∼ 60 respectively. The
balance between the competing loss processes could be slightly altered in the south-east
of the LMC’s disk (the SEHO region, Nidever et al., 2008) where gas densities and the
intensity of the radiation field are much higher than elsewhere in the ISM. Increasing
f hni by a factor of three, Urad by a factor of five, and allowing B to scale with the
mean ISM density B ∝ hni0.5 , would decrease the timescales of bremsstrahlung, inverse
Compton, synchrotron cooling to be roughly comparable with τdiff . Ionization losses –
the most effective mechanism for maintaining a flat synchrotron-cooled spectrum (e.g.
Lacki et al., 2010) – would remain insignificant in this scenario, with τion ∼ 20τdiff .
As an alternative interpretation for the trends in Figure 5.15, we therefore propose that
supernova remnants maintain a relatively flat radio spectrum across the main disk of
the LMC (e.g. Lisenfeld & Völk, 2000), and that the cosmic rays readily escape the
LMC without suffering significant synchrotron losses. Our preferred explanation for
the asymmetry of the LMC’s radio continuum morphology and the enhanced surface
brightness of the diffuse 1.4 GHz emission in the SEHO region is that both features
reflect a compression of the magnetic field due to LMC’s interaction with the Milky
Way halo. A stronger magnetic field would be consistent with the unusually low star-
5.7. Summary
289
forming activity of the molecular clouds in this region (Indebetouw et al., 2008), since
higher magnetic pressures should impede cloud collapse.
Finally we note that Murphy et al. (2009) have shown that the radio continuum morphology of Virgo cluster galaxies is strongly affected by their interaction with the intracluster medium (ICM). These authors propose that cosmic rays in the galactic halo of
Virgo galaxies are swept up and displaced by the ICM wind, which also drives shocks
into the interstellar medium (ISM) behind the leading edge of the galaxy-ICM interaction zone. These shocks provide secondary sites for cosmic ray acceleration, and hence
maintain a flat radio spectral index in the ISM interior to the galaxy-ICM interface.
A similar physical scenario may apply in the LMC, although independent estimates
for the magnetic field and cosmic ray energy density across the LMC, combined with
dynamical modelling of the LMC-Milky Way interaction would be required for a proper
test of the Murphy et al. (2009) model. The Virgo cluster galaxies studied by Murphy et al. (2009) exhibit elevated FIR-radio ratios along their leading edge, and global
1.4 GHz luminosities that are enhanced relative to the radio-FIR correlation: as we
demonstrate in the next chapter, neither trend is observed for the LMC.
5.7 Summary
In this chapter, we have presented a sensitive ATCA+Parkes mosaic of the 1.4 GHz
continuum emission in the LMC. The final image is suitable for studying emission on
angular (spatial) scales greater than 40′′ (10 pc). The reduction of the survey data involved a two-step deconvolution procedure that recovers extended and point-like emission features, and a peeling technique that suppresses calibration errors from bright
off-axis sources. Our analysis of the 1.4 GHz data has shown:
1. The total 1.4 GHz flux density within a 7.5◦ × 7.5◦ centred on RA 05h20m, Dec
-68d40m (J2000) is 426 Jy. Systematic errors – in particular concerning the FWHM of
the Parkes beam – lead to an uncertainty of ∼ 20% in this measurement. We estimate
that 10 to 15% of the measured flux density is due to background sources, and that the
290
Chapter 5. An ATCA 20cm Radio Continuum Study of the LMC
intrinsic 1.4 GHz flux density of the LMC is ∼ 370 Jy.
2. Despite the visual dominance of 30 Dor and other H II regions in the LMC, diffuse
emission with low surface brightness contributes the bulk of the LMC’s 1.4 GHz emission. Only ∼ 30% of the LMC’s 1.4 GHz flux density arises in regions where the H α
surface brightness exceeds 100 R.
3. We construct a model for the thermal component of the 1.4 GHz emission in the
LMC from the SHASSA map of H α emission, which is corrected for dust attenuation
using the optical depth at 160 µm. We estimate that 70% of the LMC’s 1.4 GHz emission is of non-thermal origin.
4. For the total spectral index between 1.4 and 4.8 GHz, we obtain α ∼ −0.55, flatter
than the average α measured for spiral galaxy samples by ∼ 0.2. The limited sensitivity of the 4.8 GHz data represents a significant source of uncertainty in this estimate.
5. The diffuse 1.4 GHz emission in the LMC has an asymmetric morphology, exhibiting
a steep decline along the eastern edge of the LMC and a more gradual decrease with
increasing distance from 30 Doradus elsewhere. The diffuse 1.4 GHz emission south of
30 Doradus is relatively bright, and is associated with more negative spectral index values. A plausible explanation for these features is the compression and amplification of
the magnetic field in the SEHO region, resulting from the motion of the LMC through
the Milky Way’s halo.
6. The star formation rate implied by the LMC’s total 1.4 GHz emission is 0.15 M⊙ yr−1 ,
in good agreement with star formation rates derived from its total infrared and H α
luminosities (Bell, 2003; Calzetti et al., 2007). This level of star formation significantly
overpredicts the non-thermal flux density that should be generated by core-collapse supernovae, suggesting that synchrotron radiation is not efficiently extracted from cosmic
rays in the LMC.
5.7. Summary
291
7. The non-thermal spectrum in the LMC is relatively flat, hαnth i = −0.7. For realistic
estimates of the magnetic field strength, gas density and radiation field energy density
in the LMC’s ISM, the timescale of cosmic ray diffusion is less than the synchrotron,
bremsstrahlung and ionization loss timescales by factors between 3 and 60. Inverse
Compton cooling may be competitive with diffusive escape in regions with low density
and strong radiation fields. We conclude that cosmic rays readily escape the LMC
without suffering significant synchrotron losses.
6
A Multi-Resolution Analysis of the Radio-FIR
Correlation in the Large Magellanic Cloud
In this chapter, we investigate the correlation between the 1.4 GHz radio continuum
and far-infrared (FIR) emission in the Large Magellanic Cloud (LMC). Using wavelet
decomposition and pixel-by-pixel techniques, we compare the distribution of neutral
gas, the FIR emission from dust, and the thermal and non-thermal components of the
radio continuum on spatial scales between 0.1 and 3.0 kpc. The dust and gas emission exhibit the tightest pixel-by-pixel correlation, while the wavelet cross-correlation
between the dust and thermal radio emission holds to the smallest scales. There are robust correlations between the non-thermal radio emission and the gas and dust tracers
in smaller fields covering approximately half the projected area of the LMC’s gas disk.
We identify star formation and the neutral gas surface density Σgas as key parameters
that determine the strength of these correlations: in regions where the star-formation
activity is low relative to the availability of dense gas, the non-thermal radio continuum
is more tightly correlated with the gas and dust emission. In these regions, the logarithmic FIR-to-radio ratio q depends weakly on Σgas , whereas elsewhere in the LMC
we find a linear relationship between q and Σgas . The slope of the local radio-FIR
correlation is not constant: in star-forming regions, the correlation is linear whereas a
0.6±0.1
flatter slope, S1.4GHz ∝ S70µm
, applies to the diffuse emission. We demonstrate that
coupling between the magnetic field strength and the gas volume density can account
293
294
Chapter 6. The Radio-FIR Correlation in the LMC
for the exponent of the flatter correlation, using plausible assumptions for the LMC’s
UV opacity, dust-to-gas ratio and cosmic ray distribution. The relative importance of
B − ρ coupling versus calorimetry for the LMC’s location on the global correlation is
not certain, as regions that show evidence for B − ρ coupling account for less than half
the LMC’s total radio and FIR luminosity.
6.1 Introduction
The tight correlation between the far-infrared (FIR) and radio continuum luminosity of
star-forming galaxies is one of the most robust relationships in extragalactic astronomy
(e.g. Yun et al., 2001, see also Figure 6.1). The correlation is essentially linear over
five orders of magnitude with a dispersion of less than 50%. It applies to galaxies out
to at least z = 1.4 (e.g. Appleton et al., 2004; Seymour et al., 2009; Sargent et al.,
2010; Bourne et al., 2010), and encompasses a diverse range of galaxy types, including
normal barred and unbarred spirals, dwarf and irregular galaxies, starbursts, Seyferts
and radio-quiet quasars (for a review, see Condon, 1992).
The conventional explanation for the radio-FIR correlation invokes massive star formation. Young stars radiate ultraviolet (UV) photons that are absorbed by dust grains
and re-radiated at FIR wavelengths. If the UV optical depth in galaxies is high, then
a correlation between the star formation rate and FIR luminosity of galaxies is to be
expected. The radio emission of normal spiral galaxies at centimetre wavelengths is
mostly non-thermal synchrotron radiation (Condon, 1992), which arises from cosmic
rays (CRs) spiralling in a magnetic field. As supernova remnants (SNRs) are thought
to be responsible for accelerating and producing CRs, the rapid evolution of high mass
stars to supernovae provides a connection between the non-thermal radio emission and
star formation activity in galaxies. In the original calorimeter model proposed by Völk
(1989), galaxies efficiently extract all the energy from CRs via synchrotron cooling,
while the UV light from the young stellar population is completely absorbed and reemitted by dust. In this case, the ratio between the FIR and radio emission reflects the
ratio between the UV emission from young massive stars and the total energy supplied
6.1. Introduction
295
log(L1.4GHz/(W Hz−1))
25
24
23
22
21
20
19
7
8
9
10
11
12
13
log(L60µm/Lsol)
Figure 6.1 The 1.4 GHz radio continuum versus 60 µm luminosity for 1809 galaxies in the IRAS
2 Jy Redshift Survey and NRAO VLA Sky Survey, taken from Yun et al. (2001). The dashed line
represents an ordinary least squares fit to the data. The LMC is represented by a black square.
The open square indicates where the LMC would lie if only the non-thermal component of its
1.4 GHz luminosity is included. The measurement of the LMC’s 60 µm luminosity was estimated
by Hughes et al. (2006) using the reprocessed IRAS map (Miville-Deschênes & Lagache, 2005).
to CRs. The radio/FIR ratio will then be constant, provided that the energy supplied
to CRs is a constant fraction of a supernova’s total luminosity.
Although star formation is regarded as the most probable origin of the radio-FIR correlation, it is not clear whether calorimeter models can account for the tightness, linearity and dynamic range of the observed relationship, given the diverse properties of
the interstellar medium (ISM) in star-forming galaxies. Well-known problems with the
calorimeter scenario include the fact that most galaxies are not optically thick to UV
photons (e.g. Popescu et al., 2005), and that the inferred timescale for CR escape is
shorter than the synchrotron cooling timescale for many galaxies (e.g. Lisenfeld et al.,
1996). Depending on their environment, CRs can lose a significant fraction of their
energy via non-synchrotron cooling processes (e.g. ionization, brehmsstrahlung and inverse Compton scattering, Condon, 1992), while several recent studies have pointed out
that the production of secondary electrons should be significant at high gas densities
(e.g. Lacki et al., 2010). Since each of these processes will alter the amount of energy
296
Chapter 6. The Radio-FIR Correlation in the LMC
that is ultimately radiated at FIR and radio wavelengths, the linearity and narrow
dispersion of the global radio-FIR correlation is truly surprising.
The calorimeter model was originally put forward to explain a correlation between the
integrated luminosity of galaxies at radio and FIR wavelengths. As such, it does not
predict a tight correlation between the radio and FIR emission on small spatial scales.
Detailed maps of the gas within several kiloparsecs of the Sun indicate that the radio
emission from star-forming regions is predominantly thermal, and that these regions do
not follow the radio-FIR correlation for integrated galaxy luminosities (e.g. Boulanger
& Perault, 1988; Haslam & Osborne, 1987). On somewhat larger scales, however, FIR
and radio maps of nearby spiral galaxies show a good correspondence (e.g. Hoernes
et al., 1998; Hippelein et al., 2003). With resolved images of twelve disk galaxies,
Murphy et al. (2006b) demonstrated that the radio emission in galaxies resembles a
smoothed version of the FIR emission, and that smearing the FIR images reduces the
dispersion in the FIR and radio correlation within galaxies by a factor of two. Smearing,
rather than parameters such as variations in the gas surface density, was most effective at reducing the dispersion in the local FIR/radio ratio for these galaxies. Murphy
et al. (2006b) also found a better correspondence between the radio and unsmoothed
FIR images of galaxies with high levels of star formation than for images of quiescent
galaxies. They interpreted this result as evidence that CRs have diffused further from
their production sites in galaxies that are no longer actively forming stars.
It is possible, however, that other physical mechanisms are responsible for a local coupling between the radio and FIR emission. In M31, the local correlation between the
radio and FIR emission is constituted by a strong correlation between the thermal radio emission and dust heated directly in H II regions, and a weaker correlation between
the non-thermal radio emission and dust heated by optical radiation from low-mass
stars (Hoernes et al., 1998). While the former correlation is trivial to understand, the
mechanism by which the dust grains couple to synchrotron emission arising through
the interactions of relativistic electrons with the ambient magnetic field remains highly
uncertain. Helou & Bicay (1993) proposed that the magnetic field strength is propor-
6.1. Introduction
297
tional to the gas density, which would ensure a tight radio-FIR correlation in spite of
the sensitive dependence of the sychrotron emission on the magnetic field. Variations
on this idea have been discussed by Hoernes et al. (1998) and Murgia et al. (2005). The
latter authors drew a connection between the radio-FIR correlation and the observed
CO-radio correlation (e.g. Paladino et al., 2006, 2008), and suggested that the CO,
radio continuum and FIR emission in galaxies might be regulated by the hydrostatic
pressure, rejecting an explicit dependence of the radio-FIR correlation on star formation.
An important constraint on all models for the origin of the radio-FIR correlation is the
scale on which the correlation breaks down, since this should shed light on the physical
mechanism of the coupling. Static pressure equilibrium, for example, predicts that the
correlation should not hold on scales smaller than the scale height of a galaxy’s gas
disk (a few hundred parsecs in the solar neighbourhood, e.g. Falgarone & Lequeux,
1973; Cox, 2005), whereas the critical scale for the calorimeter model is the cosmic ray
diffusion scale (∼ 4 kpc for 4.6 GeV cosmic ray in a B ∼ 5 µm G field, e.g. Condon,
1992, see also Chapter 5). In light of this, and the controversial role of dense gas in
maintaining the correlation locally, we propose to study the radio, FIR and neutral
gas emission in the Large Magellanic Cloud (LMC). The proximity of the LMC permits a detailed comparison between the synchrotron emission and tracers of gas and
dust on the scale of individual molecular clouds. In addition to standard pixel-by-pixel
techniques, we use a wavelet cross-correlation method that allows us to quantify the
correlation between different gas and dust tracers on spatial scales between ∼0.1 and
3.0 kpc. To date, wavelets have enjoyed a limited (though rapidly increasing) application within astrophysics (e.g. Frick et al., 2001; Tabatabaei et al., 2007), but their
ability to isolate signal simultaneously in the Fourier and spatial domains makes them
ideal for analysing scale-dependent correlations in astronomical images.
The structure of this chapter is as follows. In Section 6.2, we outline the methods
that we have used to construct maps of derived quantities such as the total neutral gas
surface density, total FIR emission, and the FIR/radio ratio. Section 6.3 describes the
298
Chapter 6. The Radio-FIR Correlation in the LMC
results of a pixel-by-pixel comparison of the dust, gas and radio continuum emission
within the LMC, and our analysis of the LMC maps using wavelet decomposition. We
discuss our results in the context of models for the origin of the radio-FIR correlation
in Section 6.4, and conclude with a summary of our key results in Section 6.5.
6.2 Observational Data
Most of the LMC images that we have used for this study were presented in Chapter 2.
Our map of the LMC’s 1.4 GHz continuum emission, and its decomposition into thermal
and non-thermal components, were described in Chapter 5. In this Section, we outline
the methods that we have used to construct maps of i) the column density of neutral
(i.e. atomic + molecular) gas, ii) the total infrared (TIR, 3 - 1100 µm) flux density and
iii) the FIR/radio ratio in the LMC.
6.2.1
Neutral Gas Column Density Map
To estimate the column density of neutral hydrogen across the LMC, we combined
smoothed versions of the ATCA+Parkes H I and NANTEN CO maps (Kim et al.,
2003a; Fukui et al., 2008). As described in Section 2.5, we estimated the column
density of atomic gas from the H I integrated intensity: N (HI)[ cm−2 ] = 1.823 ×
1018 I(HI) [ K km s−1 ]. Similarly, we estimated the column density of hydrogen atoms
in the molecular phase from the CO integrated intensity as
N (H)mol [ cm−2 ] = 2N (H2 ) = 2 × XCO × I(CO)[ K km s−1 ],
(6.1)
adopting XCO = 2 × 1020 cm−2 (K km s−1 )−1 (e.g. Strong & Mattox, 1996). A map of
the total column density of hydrogen atoms N (H) was obtained by summing these two
maps. Since our main reason for constructing a total gas map is to compare N (H) with
the non-thermal component of the radio emission, the H I and CO maps were smoothed
to the same resolution as the non-thermal 1.4 GHz map (4.′ 3) prior to combination. The
resulting map is shown in Figure 6.2. The mean value of N (H) within the LMC’s disk,
which we define using the 0.9 MJy sr−1 of the reprocessed IRAS 60 µm map (MivilleDeschênes & Lagache, 2005), is hN (H)i = 1.75 × 1021 cm−2 . This value of N (H)
6.2. Observational Data
299
Figure 6.2 Map of the total column density of neutral (atomic + molecular) gas in the LMC,
constructed by linear combination of the H I and CO emission maps. The units are H cm−2 .
The single grey contour indicates a non-thermal 1.4 GHz flux density of 0.08 Jy per 4.′ 3 beam.
corresponds to a atomic + molecular gas surface density Σgas = 19 M⊙ pc−2 , where we
have applied a correction factor of 1.36 to account for the contribution of helium to the
total mass. The average column density in the south-east of the LMC (which we have
referred to elsewhere in this thesis as the SEHO region) is approximately three times
higher than the LMC mean.
6.2.2
Total Infrared Map
We constructed a total infrared (TIR, 3 - 1100 µm) map of the LMC by combining the
SAGE maps of the emission at 24, 70 and 160 µm according to equation 4 of Dale &
300
Chapter 6. The Radio-FIR Correlation in the LMC
Figure 6.3 Map of the total FIR emission in the LMC, constructed from the SAGE maps at
24, 70 and 160 µm according to equation 4 of Dale & Helou (2002). The map is displayed in
units of Jy per 1.′ 0 beam using a square-root intensity scale. The grid indicates the 1.◦ 35 × 1.◦35
fields discussed in the text.
Helou (2002), i.e.
LT IR = ζ24 νLν (24µm) + ζ70 νLν (70µm) + ζ160 νLν (160µm),
(6.2)
where [ζ24 , ζ70 , ζ160 ] = [1.559, 0.7686, 1.347]. We also used the Dale & Helou (2002)
galaxy spectral energy distribution models to estimate that 48% of the TIR emission in
the LMC emerges at FIR wavelengths (42 − 122 µm, see their table 2). The integrated
FIR luminosity of the LMC, as obtained from the 7.◦ 5 × 7.◦ 5 map in Figure 6.3, is
LF IR = 6.43 × 10−9 W m−2 .
6.2. Observational Data
6.2.3
301
FIR/radio Ratio Map
To determine whether variations in the radio-FIR correlation correspond to large-scale
features in the LMC, we created a logarithmic FIR/radio ratio map (“q-map”). Following Helou et al. (1985), we define q according to
q = log
FIR
3.75 × 1012 W m−2
− log
S1.4
W m−2 Hz−1
.
(6.3)
The resulting map is shown in Figure 6.4. Only pixels detected above the 3σ level in
the radio map were included in the calculation. This sensitivity criterion, combined
with the field-of-view of the SAGE data products, produces an irregular blanking mask
in the final map.
The median q across the whole LMC is 2.62±0.24, where the median absolute deviation has been used to quantify the dispersion in the q values. The global value of q,
estimated using the LMC’s total FIR and 1.4 GHz luminosities, is 2.61 (or 2.68, if the
median-filtered 1.4 GHz map is used). For comparison, the median q for the Yun et al.
(2001) galaxy sample is 2.34 ± 0.12. Within the map boundaries where we calculate
q, it thus appears that either the radio emission in the LMC is roughly half the value
that we would expect from the Yun et al. (2001) correlation, or that the FIR emission is overluminous by a factor of two. In contrast to some high-resolution q-maps of
nearby disk galaxies (Murphy et al., 2006a), the most striking structures in the q-map
of the LMC do not correspond to the brightest radio or FIR structures. However, the
variation in the FIR/radio ratio across the LMC is spatially organized: higher q values
tend to be associated with larger gas column densities, although the correspondence
is not exact. The median q for regions with N (HI) > 2 × 1021 cm−2 is 2.71 ± 0.16,
while the median q for regions in the MAGMA survey with I(CO) > 2 K km s−1 is
2.90 ± 0.17. The north-eastern and western edges of the LMC also shows elevated
values of the FIR/radio ratio, even though the H I column density is low. Numerous
patches of low q values are located directly west and north of the SEHO. The supergiant shell LMC4 in the north-east is the largest of these low q regions (Meaburn, 1980).
302
Chapter 6. The Radio-FIR Correlation in the LMC
Figure 6.4 A map of the logarithmic FIR/radio ratio, q, in the LMC. The q map is derived
from a combination of the the SAGE 24, 70 and 160 µm maps and the median filtered 1.4 GHz
map. The black contour indicates where the MAGMA survey measured I(CO) = 2.0 K km s−1 .
6.2. Observational Data
303
Recently, Murphy et al. (2009) have reported high q values along the leading edge
of Virgo cluster galaxies, arguing that the radio deficit in these regions is caused by
ram-pressure stripping of cosmic-ray electrons. It is possible that the rim of high q
values in the north-east is related to the LMC’s proper motion (µalpha = 2.03 mas yr−1 ,
µδ = 0.44 mas yr−1 , Kallivayalil et al., 2006; Piatek et al., 2008), though the radiodeficit regions identified by Murphy et al. (2009) are relatively large (5 − 30% of each
galaxy’s disk area). The Virgo galaxies with local radio deficits also tend have low
global q values, indicating an overall enhancement of their radio luminosity, whereas
the LMC’s radio emission is suppressed relative to the global radio-FIR correlation.
Both 30 Doradus and N11 have a pronounced ring-like morphology in the q-map. The
local peaks in the original radio and FIR maps have q ∼ 2.5, but they are surrounded
by a ring of enhanced q values. An earlier low-resolution study by Klein et al. (1989)
reported that LMC H II regions have an average q = 2.78. Our data suggests that at
higher angular resolution, the q value of an H II region can be separated into two distinct
components: a compact central region where the FIR and radio emission are high but
q is quite close to the mean q across the whole LMC, and a ring of enhanced q values
that arises through the different scale-lengths of the FIR and radio emission associated
with the H II region. This morphology is consistent with the statistical detection of a
“dip-and-ring” structure around LMC H II regions by Xu et al. (1992).
6.2.4
1.◦ 35 × 1.◦ 35 Fields
We are interested in spatial variation of correlations between FIR, radio and gas emission across the LMC, so we divided the LMC into 16 smaller regions, as shown in
Figure 6.3. Each field covers 1.◦ 35 × 1.◦ 35, corresponding to a spatial area of 1.2 × 1.2
kpc2 . The main characteristics of the 16 fields are summarized in Table 6.1. It is
notable that there is a large variation in the 1.4 GHz and FIR flux densities across
the LMC, and that the field which includes 30 Doradus contains roughly a third of the
LMC’s total radio and FIR luminosity. The thermal fraction of the 1.4 GHz emission
varies between 5% in region 4, the field south of 30 Doradus, to 50% in region 13, which
304
Chapter 6. The Radio-FIR Correlation in the LMC
contains the star-forming complex N11 (Henize, 1956).
6.3 Analysis
For this study, we are interested in both the structural correspondence between images
taken at different wavebands and changes in the radio-FIR correlation across the LMC.
These considerations have led us to adopt two techniques for our cross-correlation analysis: a wavelet method, which allows us to probe morphological correlations across the
range of spatial scales present in each image, and a more traditional pixel-by-pixel comparison, which is sensitive to changes in the emission ratio as a function of position.
Prior to conducting our analysis, maps of the whole LMC and the smaller fields were
smoothed to a common resolution. In most cases, the data were smoothed to 1.′ 0 resolution, which is close to the natural resolution of the H I, MAGMA CO and 160 µm
data, but implies degrading the resolution of the 70 µm map by a factor of ∼ 3. For
comparisons with the non-thermal and thermal radio continuum data, all maps were
smoothed to 4.′ 3, i.e. the resolution of the Bernard et al. (2008) dust temperature map.
We refer to the set of maps with 1.′ 0 resolution as the “high resolution dataset”, and
the maps with 4.′ 3 resolution as the “low resolution dataset”.
6.3.1
Pixel-by-pixel Analysis
The simplest measure of the correlation between two images, f1 (x, y) and f2 (x, y), with
the same angular resolution and pixel grid is Pearson’s linear correlation coefficient, rp .
This is a direct calculation of the correlation at each pixel:
rp = p
Σ(f1i − hf1 i)(f2i − hf2 i)
Σ(f1i − hf1 i)2 Σ(f2i − hf2 i)2
.
(6.4)
Identical images should have rp = 1; images that are perfectly anti-correlated should
have rp = −1. We regard 0.5 < |rp | < 0.7 as evidence for a moderate correlation, and
rp ≥ 0.7 to indicate a strong correlation (or anti-correlation if rp is negative). The
formal error on the correlation coefficient depends on the strength of the correlation
6.3. Analysis
Table 6.1 The spatially integrated emission at different wavebands for the sixteen 1.◦ 35 × 1.◦ 35 fields shown in Figure 6.3. The median q
value, star formation rate (SF R), overall radio spectral index (α), and non-thermal radio spectral index (αnth ) are also listed (columns
9 to 12). The CO luminosity was estimated from the NANTEN map (Fukui et al., 2008), which has more complete coverage than
the MAGMA survey. The star formation rate was calculated from the map presented in Section 2.5.8, which was constructed from a
combination of the H α and 24 µm emission according to the prescription of Calzetti et al. (2007). The overall and non-thermal radio
spectral indices were calculated from the data in columns 2 to 5.
Region
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
S1.4
Jy
2.6
7.0
16.8
22.0
9.9
17.4
31.6
111.8
6.2
16.2
28.5
20.9
11.3
7.8
14.1
9.9
Snth
Jy
1.7
5.4
14.2
20.7
6.1
13.8
23.8
70.2
4.3
14.1
21.5
15.2
5.6
6.3
11.3
6.8
Sth
Jy
0.8
1.5
2.5
1.2
3.7
3.5
7.5
40.9
1.7
2.0
6.8
5.5
5.5
1.4
2.8
3.1
S4.8
Jy
1.0
3.1
9.0
10.4
6.8
9.7
20.0
80.5
3.3
8.0
17.2
13.8
7.3
3.3
7.5
6.0
S70µm
103 Jy
0.6
2.0
4.1
4.9
6.0
9.2
12.2
48.1
3.2
5.4
11.3
7.9
5.6
2.5
4.1
3.0
S160µm
104 Jy
0.6
0.7
1.0
1.8
1.5
1.8
2.0
6.0
0.9
1.3
2.2
1.6
1.3
0.7
1.0
0.8
MHI
107 M⊙
1.2
1.3
2.0
5.5
2.1
2.0
2.1
6.6
2.1
2.8
3.5
3.1
2.5
2.2
2.0
1.4
LCO
105 K km s−1 pc2
0.2
1.2
2.4
4.4
1.8
2.9
2.3
6.0
1.4
1.7
3.2
1.3
1.9
0.8
1.0
0.3
hqi
3.09
2.65
2.44
2.57
2.94
2.68
2.56
2.62
2.89
2.59
2.60
2.60
2.74
2.59
2.53
2.58
SF R
10−3 M⊙ yr−1
0.9
1.8
2.8
1.9
4.4
4.5
8.7
44.7
2.2
2.6
7.7
5.9
5.7
1.7
3.1
3.2
α
αnth
-0.7
-0.7
-0.5
-0.6
-0.3
-0.5
-0.4
-0.3
-0.5
-0.6
-0.4
-0.3
-0.4
-0.7
-0.5
-0.4
-1.4
-1.0
-0.6
-0.7
-0.5
-0.6
-0.5
-0.4
-0.8
-0.7
-0.5
-0.4
-0.7
-0.9
-0.7
-0.6
Notes
N132D
30 Dor
N11
PKS 0515-674
305
306
Chapter 6. The Radio-FIR Correlation in the LMC
and the number of independent pixels, n, in an image:
q
1 − rp2
∆rp = √
.
n−2
(6.5)
There are many independent pixels, even in a 1.◦ 35 × 1.◦ 35 field, so the formal error on
rp is always small. The true error is dominated by systematic errors in the data, such
as calibration and zero-level uncertainties, which are not as easily quantified.
For comparisons where we obtain rp ≥ 0.5, we determined a linear fit to the data in the
pixel-by-pixel plot using two estimators: weighted least squares (WLS) and the ordinary least squares bisector (OLSB). The WLS fit is implemented using the Numerical
Recipes fitexy routine (Press et al., 1992). The 1σ uncertainty associated with each
measurement is estimated from the RMS noise in blank regions of sky near the edge of
the whole LMC maps. In logarithmic space, high intensity pixels are thus given greater
weighting due to their smaller relative errors (this assumes the errors are mainly additive rather than multiplicative). The OLSB fit, implemented using the slopes routine
written by Feigelson & Babu (1992), assigns equal weight to each pixel and treats both
variables symmetrically by determining the line which bisects the standard ordinary
least squares solutions of Y on X and X on Y. Measurement uncertainties are assumed
to be unimportant compared to the intrinsic scatter in the data. We therefore expect
that the WLS estimator will provide a better fit to the high-intensity pixels, whereas
the OLSB estimator will provide a better fit to the overall pixel distribution.
i) Comparison between 1.4 GHz and 70 µm emission
A scatter plot showing the 70 µm flux density, S70 , versus the median filtered 1.4 GHz
radio flux density, S1.4 , for independent pixels in the whole LMC is presented in Figure 6.5. Equivalent plots for each of the 1.◦ 35 × 1.◦ 35 fields are shown in Figure 6.6.
All plots are generated using the high resolution dataset. As many map pixels have
similar values, we illustrate the distribution of data points by binning the data into a
two-dimensional histogram and using colour to represent the counts in each cell. The
307
log(S1.4/[Jy arcmin−1])
6.3. Analysis
0
rp = 0.77
m = [1.05,0.71]
−2
−4
−6
−4
−2
0
2
log(S70/[Jy arcmin−1])
Figure 6.5 The pixel-by-pixel correlation between the 70 µm and median filtered 1.4 GHz continuum maps of the LMC. The individual pixel measurements are binned and the value in each
cell is indicated using colour, with red (grey) representing a high (low) density of data points.
The solid line represents the WLS fit to the data, and the dashed line is the OLSB fit. The
Pearson correlation coefficient rp and the slopes of the best-fitting relations (m=[WLS,OLSB])
are indicated in the top left corner of the plot.
Pearson correlation coefficient between log S1.4 and log S70 was calculated for the whole
LMC map and each of the smaller fields, with flux densities expressed in Janskys per
1.′ 0 beam. To ensure statistical independence of the values contributing to rp , the pixels
were sampled at a spatial frequency equal to one resolution element. In general, we
find a moderate to strong local correlation between the 1.4 GHz and the 70 µm emission
over ∼ 4 orders of magnitude in both wavebands. The dispersion in the correlation
across the whole LMC is 0.16 dex. For the whole LMC, rp = 0.77, while the correlation
coefficients for the smaller fields vary between 0.38 and 0.83, with a median value of
0.63. The rp values are indicated in the top left corner of each panel in Figures 6.5 and
6.6, and are also listed in Table 6.2.
The slopes of the best-fitting relations derived using the WLS and OLSB estimators are
indicated in Figures 6.5 and 6.6 for correlations with rp ≥ 0.5. For the whole LMC, the
WLS method determined a slope of 1.05, while the OLSB estimator yielded a flatter
Chapter 6. The Radio-FIR Correlation in the LMC
308
Table 6.2 Summary of the wavelet and pixel-by-pixel correlation results for maps of the whole LMC and 1.◦ 35 × 1.◦ 35 fields. The
spatial scale d at which the wavelet cross-correlation falls below 0.75 and Pearson’s correlation coefficient rp are listed for the
following image pairs: i) 1.4 GHz and 70 µm (columns 3 and 4) ii) non-thermal 1.4 GHz and 70 µm (columns 5 and 6) iii) nonthermal 1.4 GHz and N (H) (columns 7 and 8) and iv) 70 µm and N (H) (columns 9 and 10). Column 2 lists the thermal fraction
fth of the radio emission at 1.4 GHz.
Region
LMC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
fth
0.27
0.32
0.23
0.15
0.06
0.39
0.21
0.24
0.37
0.30
0.13
0.25
0.27
0.50
0.19
0.20
0.32
S70 − S1.4
log(d/[pc])
rp
1.8
0.77
2.7
0.38
2.7
0.51
2.1
0.56
2.2
0.83
2.0
0.59
1.7
0.80
2.2
0.49
1.5
0.83
1.6
0.51
2.2
0.60
1.5
0.79
1.5
0.69
1.5
0.75
2.4
0.65
2.1
0.67
1.7
0.44
S70 − S1.4,nth
log(d/[pc])
rp
2.3
0.74
2.7
0.28
2.6
0.54
2.7
0.56
2.5
0.89
2.7
0.58
2.7
0.79
2.7
0.27
1.8
0.67
2.7
0.58
2.7
0.55
2.2
0.73
2.3
0.65
2.1
0.69
2.7
0.69
2.3
0.73
2.7
0.14
N (H) − S1.4,nth
log(d/[pc])
rp
3.5
0.62
2.7
0.15
2.5
0.61
2.5
0.41
2.2
0.76
2.7
0.39
2.3
0.82
2.4
0.30
2.7
0.38
2.4
0.42
2.2
0.63
2.4
0.76
2.2
0.47
2.6
0.56
2.5
0.69
2.4
0.60
2.7
0.08
N (H) − S70
log(d/[pc])
rp
3.5
0.74
2.7
0.65
2.1
0.79
2.6
0.71
2.5
0.75
2.7
0.89
2.7
0.93
2.2
0.81
2.7
0.39
2.7
0.64
1.8
0.73
2.7
0.76
2.3
0.85
2.5
0.90
2.3
0.89
2.1
0.89
2.4
0.78
6.3. Analysis
log(S1.4/[Jy arcmin−1])
0
309
0.44
0.67
[0.8,0.7]
0.65
[0.5,0.8]
0.75
[1.1,0.7]
0
−2
−2
−4
−4
R16
−6
0
0.69
[0.8,0.8]
R15
0.79
[0.7,0.7]
R14
0.60
[0.8,0.7]
R13
0.51
[0.7,0.8]
−6
0
−2
−2
−4
−4
R12
−6
0
0.83
[1.1,0.8]
R11
0.49
R10
0.80
[0.7,0.6]
R9
0.59
[0.6,0.7]
0
−2
−2
−4
−4
R8
−6
0
−6
0.83
[0.6,0.6]
R7
0.56
[0.7,0.6]
R6
0.51
[0.5,0.6]
R5
0.38
−6
0
−2
−2
−4
−4
R4
−6
−4 −2
0
2
R3
−4 −2
0
2
R2
−4 −2
0
2
R1
−4 −2
0
−6
2
log(S70/[Jy arcmin−1])
Figure 6.6 Pixel-by-pixel correlations between the 70 µm and median filtered 1.4 GHz radio
flux densities in each of the 1.◦ 35 × 1.◦ 35 fields. The fits and plot annotations are the same as in
Figure 6.5. Fitting is only attempted for regions where rp ≥ 0.5.
310
Chapter 6. The Radio-FIR Correlation in the LMC
slope (0.71). Similar values are found for regions 8 and 13, which contain the 30 Dor
and N11 star-forming complexes respectively. We note that region 8 is responsible for
35% (31%) of the LMC’s total 70 µm (1.4 GHz) emission, and that it contributes significantly to the slope of WLS fit that we determine for the LMC overall. The slopes of
the WLS and OLS bisector fits in other regions are flatter, with both methods yielding
slopes between 0.5 and 0.8.
To investigate influences on the S70 − S1.4 correlation within the LMC, we examined
whether the strength and slope of the correlation varied with properties such as the
star formation rate, thermal fraction at 1.4 GHz, and the molecular gas content. A full
list of parameters that we considered is presented in Table 6.3. We detect a clear trend
for the strength of the S70 − S1.4 correlation to increase in fields with larger reservoirs
of neutral gas, Mgas = MHI + MH2 (Figure 6.7[a]). Masses are equivalent to average
surface densities in our analysis, so the trend in Figure 6.7[a] can also be regarded as an
improvement in the S70 − S1.4 correlation with increasing gas surface density (averaged
over a square kiloparsec). Several quantities, such as the total 70 µm and 1.4 GHz flux
densities, are positively correlated with Mgas and hence rp , but the association between
rp and Mgas exhibits the least scatter.
The slope of the correlation at high 70 µm and 1.4 GHz intensities (derived using the
WLS estimator) becomes steeper as the star formation rate increases, although the
star formation rate does not affect the OLSB slope of the S70 − S1.4 correlation. The
star formation rate is well-correlated with the thermal fraction, fth , as well as the total
and non-thermal spectral indices, so a steeper S70 − S1.4 correlation is also associated
with greater fth and more positive values of α and αnth . The OLSB slope is mostly
insensitive to variations of the properties listed in Table 6.3, although there is some
evidence (Figure 6.7[c]) that the slope flattens as the molecular gas depletion time τH2
(i.e. the star formation rate divided by molecular gas mass) increases.
Further insights into the physical origin of the local S70 − S1.4 correlation in the LMC
are provided by Figures 6.8 to 6.10, where we present plots of the relationship between
rp (1.4GHz−70µm)
1.0
311
WLS slope (1.4GHz−70µm)
6.3. Analysis
[a]
6
0.8
13
2
16
4 8
12
10
15
0.6
11
7
1
0.4
0.2
0.0
7.0
7.2
7.4
7.6
7.8
1.2
[b]
1.0
10
0.8
9
OLSB slope (1.4GHz−70µm)
3 6
4
0.6
1211
5
2
0.4
8.0
−3.0
−2.5
−2.0
−1.5
−1.0
log(SFR/[Msol yr−1])
log(Mgas/[Msol])
0.9
8
13
[c]
0.8
8
12
9
14 10
11
0.7
2
0.6
3
4
0.5
7.5
8.0
8.5
9.0
9.5
log(τH2/[yr])
Figure 6.7 Properties that influence the strength and slope of the local S70 − S1.4 correlation.
In panel [a], the Pearson correlation coefficient rp of the S70 − S1.4 relation is plotted against
Mgas , the total mass of neutral gas, in the 1.◦ 35 × 1.◦35 fields. In panel [b], the WLS slope of the
S70 − S1.4 correlation is plotted against the star formation rate for fields with a moderate or
strong correlation (rp > 0.5). In panel [c], the OLSB slope is plotted against the H2 depletion
time for fields where rp > 0.5. The data points are labelled with their corresponding field
numbers; some labels are omitted for clarity.
312
Chapter 6. The Radio-FIR Correlation in the LMC
Table 6.3 Summary of properties that we investigated for their potential influence on the
correlations between dust, gas and radio continuum emission in the LMC. Values were either taken directly from Table 6.1, or derived according to the formulae listed in the second
column. Since the 1.◦ 35 × 1.◦ 35 fields have roughly equal areas (assuming that projection effects are negligible), spatially integrated properties, such as total mass and flux density, are
equivalent to average surface densities (or surface brightnesses) in our analysis. We adopt
XCO = 2.0 × 1020 cm−2 (K km s−1 )−1 for the CO-to-H2 conversion factor. We used Equation 3 of Stanimirovic et al. (2000) to estimate the dust colour temperature, neglecting the
temperature-dependent correction factor (which should be < 1 K in our case) and assuming
β = 2 for the emissivity index. The radio spectral index is estimated using the 1.4 GHz map
described in Chapter 5, and the Parkes 4.8 GHz map of the LMC presented by Haynes et al.
(1991).
Property
Definition
M (HI), Atomic mass
M (H2 ), Molecular mass
M (H2 ) [M⊙ ] = 4.4LCO [ K km s−1 pc2 ]
Mgas , Neutral Gas mass
Mgas = M (HI) + M= (H2 )
M∗ , Stellar mass
SF R, Star Formation Rate
τH2 , Molecular gas depletion time
τH2 = MH2 /SF R
fth , Thermal fraction
α, Overall spectral index
αnth , Non-thermal spectral index
α = log(S4.8 /S1.4 )/ log(4.8/1.4)
−αth
−αnth
S4.8
ν4.8
ν4.8
=
f
+
(1
−
f
)
th
th
S1.4
ν1.4
ν1.4
fmol , Molecular fraction
fmol = M (H2 )/Mgas
fgas , Gas fraction
fgas = Mgas /(Mgas + M∗ )
Td , Dust colour temperature
Td =
q, Logarithmic FIR-to-radio ratio
h(ν70 −ν160 )
k(S160 /S70 ) ln(ν70 /ν160 )3+β
6.3. Analysis
313
log(S1.4/[Jy beam−1])
2
2
[a] rp = 0.75
m = [1.00,0.96]
[b] rp = 0.74
m = [0.91,0.73]
0
0
−2
−2
−4
−4
−6
−6
−2
0
2
4
log(S70/[Jy beam−1])
−2
0
2
4
log(S70/[Jy beam−1])
Figure 6.8 Two-dimensional frequency distributions showing the 70 µm emission versus the
thermal (panel [a]) and non-thermal (panel [b]) components of the 1.4 GHz continuum emission
in the LMC. The fits and annotations are the same as in Figure 6.5.
the 70 µm emission and the thermal and non-thermal components of the radio emission. As there are fewer independent pixels for comparisons involving the low resolution
dataset, we plot the individual pixel measurements directly, rather than constructing
two-dimensional histograms. In general, the correlations between the 70 µm and the
thermal 1.4 GHz emission S1.4,th in Figure 6.9 are strong, and their best-fitting relationships are steeper, than the ones that we obtain from comparisons between the dust and
the non-thermal radio emission S1.4,nth (Figure 6.10). Yet it is notable that a strong
correlation between the S70 and S1.4,nth is still observed for several fields. The correlation in region 4 – a field with high H I column density but only average radio and FIR
surface brightness – is particularly robust (rp = 0.89). The non-thermal fraction of the
1.4 GHz continuum is ≥ 60% across most of the LMC, so the relationship between the
70 µm and the non-thermal 1.4 GHz emission should dominate the S70 − S1.4 correlations. Indeed, fields with a strong S70 − S1.4 correlation also tend to exhibit a strong
S70 − S1.4,nth correlation (Figure 6.11[a]). As before, we find that the S70 − S1.4,nth correlation tends to become stronger for fields with higher values of Mgas (Figure 6.11[b]),
but the trend has more scatter than in Figure 6.7[a].
Close inspection of the LMC maps reveals that there are several low surface brightness
314
Chapter 6. The Radio-FIR Correlation in the LMC
0
0.76
[0.9,0.9]
0.77
[0.8,0.8]
0.69
[0.8,1.7]
0.86
[1.1,1.1]
0
log(S1.4,th/[Jy beam−1])
−2
−2
R16
−4
0
R15
0.76
[1.2,1.2]
R14
0.74
[0.8,1.3]
R13
0.60
[1.3,1.2]
−4
0.66
[1.0,1.1]
0
−2
−2
R12
−4
0
R11
0.86
[1.0,1.5]
R10
0.60
[1.0,1.1]
R9
0.75
[1.1,1.2]
−4
0.73
[0.9,0.9]
0
−2
−2
R8
−4
R7
0.42
R6
0.64
[0.9,1.2]
0
R5
0.44
−4
0.48
0
−2
−2
R4
−4
0
2
R3
4
0
2
R2
4
0
2
R1
4
0
2
−4
4
log(S70/[Jy beam−1])
Figure 6.9 Pixel-by-pixel correlations between the 70 µm and thermal component of the 1.4 GHz
emission in the 1.◦ 35 × 1.◦ 35 fields. The fits and plot annotations are the same as in Figure 6.5.
6.3. Analysis
315
0.14
0.73
[0.9,0.6]
0
0.69
[0.4,0.7]
0.69
[0.8,0.6]
0
log(S1.4,nth/[Jy beam−1])
−2
−2
R16
−4
0
R15
0.65
[0.4,0.7]
R14
0.73
[0.5,0.6]
R13
0.55
[0.4,0.7]
−4
0.58
[0.5,0.7]
0
−2
−2
R12
−4
0
R11
0.67
[1.0,0.7]
R10
0.27
R9
0.79
[0.4,0.5]
−4
0.58
[0.3,0.6]
0
−2
−2
R8
−4
0
R7
0.89
[0.5,0.5]
R6
0.56
[0.4,0.5]
R5
0.54
[0.2,0.7]
−4
0.28
0
−2
−2
R4
−4
0
2
R3
4
0
2
R2
4
0
2
R1
4
0
2
−4
4
log(S70/[Jy beam−1])
Figure 6.10 Pixel-by-pixel correlations between the 70 µm and non-thermal component of the
1.4 GHz emission in the 1.◦ 35 × 1.◦ 35 fields. The fits and plot annotations are the same as in
Figure 6.5.
Chapter 6. The Radio-FIR Correlation in the LMC
1.0
[a]
rp (non−thermal 1.4GHz−70µm)
rp (non−thermal 1.4GHz−70µm)
316
4
6
15 11
8
0.8
9 10
0.6
0.4
1
0.2
7
16
0.0
0.0
0.2
0.4
0.6
0.8
rp (1.4GHz−70µm)
1.0
1.0
[b]
4
6
0.8
1413
0.6
2
5
11
12
8
10
0.4
1
0.2
7
16
0.0
7.0
7.2
7.4
7.6
7.8
8.0
log(Mgas/[Msol])
Figure 6.11 Properties that influence the strength of the S70 − S1.4,nth correlation. In panel
[a], the Pearson correlation coefficient rp of the S70 − S1.4 relation is plotted against rp of the
S70 − S1.4,nth relation for each of the 1.◦ 35 × 1.◦ 35 fields. In panel [b], rp of the S70 − S1.4,nth
correlation is plotted against Mgas , the total mass of neutral gas.
features in the total 1.4 GHz images that have a similar morphology to structures in
the neutral gas column density map. Most of these features lack strong H α emission
and are located in regions where the thermal fraction of the radio continuum emission
is low. Consistent with a low thermal fraction, α tends to become more negative in
these regions, although the correspondence is not perfect. αnth also decreases in these
regions (see Figure 6.12 and Figure 5.14 in the previous chapter), though we caution
that αnth is highly coupled to our estimate for the thermal fraction (Equation 5.7).
One possible interpretation is that we are observing enhancements in the synchrotron
emissivity at 1.4 GHz due to local increases in the gas column density, which would be
expected if the magnetic field were coupled to the local gas density. Regions of high
N (H) without signs of high-mass star formation are often adjacent to regions that are
actively forming stars, however, so another possibility is that the low surface brightness
1.4 GHz emission is simply part of the radio halo generated by CRs as they diffuse away
from their production sites, and that the decreasing total and non-thermal spectral indices reflect the aging of cosmic ray electrons. In this case, the association between the
non-thermal radio emission and N (H) would be a by-product of physically independent
relationships between star formation and high gas column densities, and star formation
regions and their non-thermal radio haloes. Direct measurements of the magnetic field
6.3. Analysis
317
strength along a statistically significant number of LMC sightlines would be required
to distinguish between these two scenarios.
ii) Comparisons with neutral gas surface density
A key outstanding question for models of the radio-FIR correlation is whether the
dense neutral gas plays a significant role in coupling the emission at FIR and radio
wavelengths. To investigate this further, we examine the correlation between the total
neutral gas surface density, the 70 µm and 1.4 GHz flux densities, and the FIR/radio
ratio.
Comparison between 1.4 GHz radio continuum and N (H)
Plots showing the relationship between the neutral gas column density N (H) and the
1.4 GHz radio flux density across the whole LMC and in the 1.◦ 35×1.◦ 35 fields are shown
in Figures 6.13 and 6.14. Overall, there is a moderate correlation (rp = 0.65) between
N (H) and S1.4 , but with a larger dispersion (0.25 dex) than is observed for the S70 −S1.4
relationship (0.16 dex). The range of N (H) values in the LMC is more restricted than
the dust and radio continuum measurements, covering ∼ 2 orders of magnitude. The
relationship between N (H) and the 1.4 GHz across the LMC is quite diverse, ranging
from no relationship in fields 1 and 16, to a strong correlation in fields 4, 6 and 14. For
four of the fields, the N (H) − S1.4 correlation is stronger than the S70 − S1.4 correlation.
In Figures 6.15 to 6.17, we show the correlations between N (H) and the thermal
and non-thermal components of the 1.4 GHz continuum emission separately.
The
N (H) − S1.4,th correlation is generally poor (Figure 6.16), although steep scattered
correlations are arguably detected in a few fields (e.g. fields 5 and 13). As noted previously, the thermal contribution to the total 1.4 GHz flux density is usually minor, so the
correlations in Figure 6.14 are dominated by the relationship between N (H) and the
non-thermal radio emission (except in field 13 where the thermal fraction reaches 50%).
We compared the strength and slope of the N (H) − S1.4 correlations to the properties
318
Chapter 6. The Radio-FIR Correlation in the LMC
log(N(H)/[cm−2])
22.0
[a] α
21.5
21.5
21.0
21.0
20.5
20.5
20.0
20.0
−4
−3
−2
−1
log(S1.4/[Jy
22.0
log(N(H)/[cm−2])
[b] αnth
22.0
0
1
−4
beam−1]
−3
−2
log(S1.4/[Jy
[c] α
−1
0
1
beam−1]
0.1
21.5
−0.1
21.0
−0.3
20.5
−0.6
20.0
−0.8
0.0
0.2
0.4
0.6
0.8
1.0
Thermal Fraction
Figure 6.12 (a) The overall spectral index α plotted as a function of the total 1.4 GHz flux
density and neutral gas column density. (b) The non-thermal spectral index αnth plotted as
a function of the total 1.4 GHz flux density and neutral gas column density. (c) The overall
spectral index, plotted as a function of the thermal fraction at 1.4 GHz and neutral gas column
density. In all panels, the colour scale runs from −0.8 (dark blue) to 0.1 (dark red). In combination, these plots show that the most negative spectral indices and lowest thermal fractions
in the LMC tend to be associated with the diffuse 1.4 GHz emission, but relatively high gas
surface densities.
319
log(S1.4/[Jy beam−1])
6.3. Analysis
0
rp = 0.65
m = [1.94,1.38]
−2
−4
−6
19
20
21
22
23
log(N(H)/[cm−2])
Figure 6.13 A two-dimensional histogram representing the N (H)−S1.4 correlation in the LMC.
Colour represents the number of pixels in each cell, with red (grey) representing a high (low)
density of points. The fits and annotations are the same as in Figure 6.5.
listed in Table 6.3. We find a clear trend for the N (H) − S1.4 correlation to improve
for fields where the H2 depletion time τH2 is long, i.e. where the molecular gas mass
is high relative to the level of star formation activity (Figure 6.18[a]). There is also a
more scattered trend for the N (H) − S1.4 correlation to become stronger as the thermal
fraction of the 1.4 GHz emission fth decreases, but this probably reflects an underlying
anti-correlation between τH2 and fth (Figure 6.18[b]). We note that the anti-correlation
between fth and τH2 appears to be more robust than the relationship of fth with either
the star formation rate (Figure 6.18[c]) or the total molecular mass (Figure 6.18[d]),
i.e. the quantities that are used to define τH2 .
Comparison between 70 µm and N (H)
In Figures 6.19 and 6.20, we plot the correlation between N (H) and the 70 µm flux
density for the entire LMC and the 1.◦ 35 × 1.◦ 35 fields. The correlation coefficient for
the LMC-wide N (H) − S70 corelation is nearly as strong as the S70 − S1.4 correlation
(rp = 0.74), although the N (H) − S70 correlation exhibits a larger dispersion (0.28 dex).
320
Chapter 6. The Radio-FIR Correlation in the LMC
0.20
0.62
[1.4,0.8]
0
0.76
[1.1,1.4]
0.69
[2.6,1.6]
0
−2
−2
R16
log(S1.4/[Jy beam−1])
−4
0.48
R15
0.66
[1.5,1.1]
0
R14
0.63
[1.1,1.0]
R13
0.41
0
−2
−2
R12
−4
0.27
R11
0.37
R10
0.85
[1.3,0.9]
0
R9
0.58
[1.2,1.0]
−4
0
−2
−2
R8
−4
0
−4
0.76
[1.0,1.6]
R7
0.46
R6
0.59
[0.4,0.8]
R5
−4
0.24
0
−2
−2
R4
−4
20
22
R3
20
22
R2
20
22
R1
20
−4
22
log(N(H)/[cm−2])
Figure 6.14 Pixel-by-pixel correlations between N (H) and 1.4 GHz continuum for the 1.◦ 35 ×
1.◦ 35 fields. The fits and annotations are the same as in Figure 6.5.
6.3. Analysis
321
log(S1.4/[Jy beam−1])
[a] rp = 0.40
0
0
−2
−2
−4
−4
−6
−6
19
20
21
22
log(N(H)/[cm−2])
23
[b] rp = 0.62
m = [1.36,1.73]
19
20
21
22
23
log(N(H)/[cm−2])
Figure 6.15 Two-dimensional frequency distributions showing the neutral gas column density
versus the thermal (panel [a]) and non-thermal (panel [b]) components of the 1.4 GHz continuum
emission in the LMC. The fits and annotations are the same as in Figure 6.5.
Yet the correlation between the gas and dust emission in individual fields is often excellent (e.g. field 6, where rp = 0.93), and the rp values in the 1.◦ 35 × 1.◦ 35 fields are
typically higher than those derived for the S70 − S1.4 correlations. We compared the rp
values with the properties in Table 6.3, but found no strong trends.
Rather than a weak correlation between gas and dust, the dispersion in the N (H) − S70
correlation for the whole LMC therefore appears to arise because the slope and normalisation of a strong local relationship varies across the galaxy. In principle, these variations may reflect changes in the dust temperature, the grain size distribution and/or
the dust-to-gas ratio. We consider intrinsic dust-to-gas variations to be the least likely
explanation, since a multi-wavelength analysis of two LMC molecular clouds indicates
a linear relationship between the mass surface densities of gas and dust throughout the
atomic and molecular gas phases (Roman-Duval et al., 2010). On the other hand, previous studies have reported an increase in both the equilibrium dust temperature and
the abundance of polycyclic aromatic hydrocarbon molecules (PAHs) and very small
dust grains (VSGs) in the LMC’s stellar bar, as well as an excess of 70 µm emission
from stochastically heated VSGs in regions with high N (H) (Bernard et al., 2008; Paradis et al., 2009). Incomplete removal of spatially variable Galactic cirrus emission at
322
Chapter 6. The Radio-FIR Correlation in the LMC
0.29
0.49
0.31
0.61
[3.2,2.1]
0
0
log(S1.4,th/[Jy beam−1])
−2
−2
R16
−4
0.37
R15
0.21
R14
0.17
R13
−4
0.26
0
0
−2
−2
R12
−4
0.04
R11
0.26
R10
0.36
R9
0.53
[1.8,1.3]
0
−4
0
−2
−2
R8
−4
0.05
R7
0.30
R6
0.12
R5
−4
0.07
0
0
−2
−2
R4
−4
20
22
R3
20
22
R2
20
22
R1
20
−4
22
log(N(H)/[cm−2])
Figure 6.16 Pixel-by-pixel correlations between N (H) and the thermal component of the
1.4 GHz continuum for the 1.◦ 35 × 1.◦ 35 fields. The fits and annotations are the same as in
Figure 6.5.
6.3. Analysis
323
0.08
0.60
[1.4,0.8]
0
0.69
[0.7,1.2]
0.56
[2.1,1.2]
0
log(S1.4,nth/[Jy beam−1])
−2
−2
R16
−4
0.47
R15
0.63
[0.8,1.0]
0.76
[1.1,1.0]
0
R14
R13
0.42
0
−2
−2
R12
−4
0.38
R11
0.30
R10
0.82
[0.8,0.8]
0
R9
−4
0.39
0
−2
−2
R8
−4
0
−4
0.76
[0.9,1.6]
R7
0.41
R6
0.61
[0.4,1.0]
R5
−4
0.15
0
−2
−2
R4
−4
20
22
R3
20
22
R2
20
22
R1
20
−4
22
log(N(H)/[cm−2])
Figure 6.17 Pixel-by-pixel correlations between N (H) and the non-thermal component of the
1.4 GHz continuum for the 1.◦ 35 × 1.◦ 35 fields. The fits and annotations are the same as in
Figure 6.5.
Chapter 6. The Radio-FIR Correlation in the LMC
1.0
9.5
[a]
[b]
6
0.8
11
14
10
15
0.6
12
0.4
7
0.2
4
9.0
9 3
5
8
4
log(τH2/[yr])
rp (non−thermal 1.4GHz−N(H))
324
3
8.5
8.0
1
13
16
0.0
7.5
8.0
8.5
9.0
9.5
0.0
0.1
log(τH2/[yr])
−1.0
5
8
16
7.5
0.3
0.4
0.5
0.6
[d]
[c]
8
−1.5
711
−2.0
6
3
−2.5
0.2
Thermal Fraction
log(MH2/[Msol])
log(SFR/[Msol yr−1])
62 9
14 11
15
7
12 1
4
142
16
5
13
9
1
−3.0
6.5
8
4
11
6
3
6.0
7
5
10
2
13
9
14
5.5
−3.5
0.0
0.1
0.2
0.3
0.4
0.5
Thermal Fraction
0.6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Thermal Fraction
Figure 6.18 Properties that influence the strength of the local N (H) − S1.4,nth correlation. In
panel [a], the Pearson correlation coefficient rp of the N (H) − S1.4,nth correlation is plotted
against the H2 depletion time for each of the 1.◦ 35 × 1.◦ 35 fields. In the remaining panels, the
H2 depletion time (panel [b]), the star formation rate (panel [c]) and the molecular mass (panel
[d]) are plotted against the thermal fraction of the 1.4 GHz emission.
6.3. Analysis
325
log(S70/[Jy beam−1])
4
rp = 0.74
m = [2.81,1.90]
2
0
−2
−4
19
20
21
22
23
log(N(H)/[cm−2])
Figure 6.19 A two-dimensional histogram representing the N (H)−S70 correlation for the whole
LMC. Colour represents the number of pixels in each cell, with red (grey) representing a high
(low) density of points. The fits and annotations are the same as in Figure 6.5.
70 µm could also contribute to offsets between the 1.◦ 35 × 1.◦ 35 fields. Consistent with
the notion that the 70 µm excess introduces some scatter into the LMC-wide N (H)−S70
correlation, we find a trend for the slope of the N (H) − S70 correlation at high intensities to increase when the molecular mass increases (Figure 6.21[a]). The OLSB slope of
the N (H) − S70 correlation also tends to increase as the molecular gas mass increases,
although the scatter is minimized when we compare the OLSB slopes to Mgas , rather
than the molecular or atomic components individually (Figure 6.21[b]). A further possibility is that the slopes become progressively steeper as we underestimate the true
gas column density for pixels with large N (H). This could occur if these regions have
greater H I opacity or larger reservoirs of “CO-dark” H2 gas. A comprehensive discussion regarding possible explanations for the 70 µm excess (including stochastic VSG
heating, H I opacity and CO-dark H2 gas) was presented by Bernard et al. (2008).
Comparison between the FIR/radio ratio and N (H)
In Figure 6.22, we plot a two-dimensional histogram showing the distribution of the
326
Chapter 6. The Radio-FIR Correlation in the LMC
4
2
0.78
[2.1,1.2]
0.89
[1.8,1.3]
0.89
[2.2,1.9]
4
0.90
[2.9,2.3]
2
0
0
log(S70/[Jy beam−1])
−2
−4
4
2
−2
R16
0.85
[2.3,1.7]
R15
0.76
[2.5,1.6]
R14
0.73
[2.4,1.6]
R13
0.64
[3.2,2.1]
2
0
0
−2
−4
4
2
−2
R12
0.39
R11
0.81
[2.3,1.7]
R10
0.93
[2.4,1.7]
R9
0.89
[2.7,1.6]
0
−2
2
−2
R8
0.75
[3.1,2.9]
R7
0.71
[2.6,1.7]
R6
0.79
[2.3,1.6]
R5
0.65
[2.2,1.4]
−4
4
2
0
0
−2
−4
−4
4
2
0
−4
4
−4
4
−2
R4
19 20 21 22
R3
19 20 21 22
R2
19 20 21 22
R1
−4
19 20 21 22
log(N(H)/[cm−2])
Figure 6.20 Pixel-by-pixel correlations between N (H) and S70 for the 1.◦ 35 × 1.◦ 35 fields. The
fits and plot annotations are the same as in Figure 6.5.
3.5
327
OLSB slope (70µm−N(H))
WLS slope (70µm−N(H))
6.3. Analysis
[a]
9
3.0
4
13
3 11
10
6
7
2
2.5
1
16
14
2.0
15
1.5
5.0
5.5
6.0
3.5
[b]
3.0
4
2.5
13
9
14
2.0
2
7
12
11
1
1.5
16
15
1.0
6.5
log(MH2/[Msol])
7.0
7.2
7.4
7.6
7.8
8.0
log(Mgas/[Msol])
Figure 6.21 Properties that influence the slope of the N (H) − S70 correlation. In panel [a], the
WLS slope of the N (H) − S70 correlation is plotted against the molecular mass in each of the
1.◦ 35 × 1.◦35 fields. In panel [b], the OLSB slope is plotted against the total mass of neutral gas.
FIR/radio ratio and total hydrogen column density measurements across the LMC.
A systematic trend between q and N (H) is not obvious from this plot, although the
dispersion of the q values decreases markedly for N (H) & 1021 cm−2 . By contrast, Figure 6.23 shows that many of the pixels with the low N (H) and high q values are located
in the south-western corner of the LMC. Elsewhere in the galaxy, there is a robust correlation between q and N (H), such that q increases by ∼ 1 dex between N (H) ∼ 1020.5
and 1021.5 cm−2 . The median q value for each 1.◦ 35 × 1.◦ 35 field is often in excellent
agreement with the LMC’s global q value however. The correlation between q and
N (H) is more evident in regions that are actively forming stars (Figure 6.24[a]), while
the slope of the q − N (H) correlation flattens in regions with a strong N (H) − S1.4,nth
correlation (Figure 6.24[b]). This latter trend suggests that the mechanism responsible for the correlation between N (H) and S1.4 may also play a role in maintaining a
constant q value within galactic disks. The former trend, on the other hand, suggests
that H II regions produce local deviations from a galaxy’s average q value, in the sense
that UV photons from massive stars are promptly delivered into the surrounding dense
cloud of gas and dust, raising the q value locally.
328
Chapter 6. The Radio-FIR Correlation in the LMC
6
q
4
2
0
19
20
21
22
23
log(N(H)/[cm−2])
Figure 6.22 A two-dimensional histogram indicating the frequency of q and N (H) values in the
LMC. Colour represents the number of pixels in each cell, with red (grey) representing a high
(low) density of points. The median q value in the LMC, q = 2.62, is indicated by a dashed
horizontal line.
6.3. Analysis
6
4
329
0.70
moslb = 1.0
0.80
moslb = 0.7
0.50
moslb = 0.9
6
0.68
moslb = 1.1
4
2
2
q [FIR/radio ratio]
R16
6
4
R15
0.65
moslb = 0.7
0.67
moslb = 1.1
R14
0.48
R13
6
0.46
4
2
2
R12
6
4
R11
0.74
moslb = 1.3
0.58
moslb = 1.0
R10
0.67
moslb = 0.7
R9
6
0.29
4
2
2
R8
6
0.42
R7
0.67
moslb = 1.1
4
R6
0.33
R5
6
0.04
4
2
2
R4
20
21
22
R3
20
21
22
R2
20
21
22
R1
20
21
22
log(N(H)/[cm−2])
Figure 6.23 Pixel-by-pixel correlations between the logarithmic FIR/radio ratio q and the
neutral gas column density in the 1.◦ 35 × 1.◦ 35 fields. The Pearson correlation coefficient for the
plotted relationship is indicated at the top left of each panel. For panels where rp > 0.5, the
slope of the OSLB best-fitting relation is also shown, and plotted with a dashed line. In all
panels, the dotted line represents q = 2.62, the median q value across the whole LMC, and the
dot-dot-dashed line represents the median q value within the 1.◦ 35 × 1.◦ 35 field.
330
Chapter 6. The Radio-FIR Correlation in the LMC
[a]
15
7
166 12
0.8
rp (q−N(H))
OLSB slope (q−N(H))
1.0
8
0.6
14 10
0.4
2
5
0.2
1
1.5
[b]
7
9
3 12 13
16
1.0
8
10
14
4
2
15 11
6
0.5
0.0
−3.5
−3.0
−2.5
−2.0
log(SFR/[Msol
−1.5
−1.0
yr−1])
0.0
0.2
0.4
0.6
0.8
1.0
rp (non−thermal 1.4GHz−N(H))
Figure 6.24 Properties that influence the slope and strength of the correlation between q and
N (H). In panel [a], Pearson’s correlation coefficient rp for the q − N (H) correlation is plotted as
a function of the local star formation rate in each 1.◦ 35 × 1.◦ 35 field. In panel [b], the OLSB slope
of the q − N (H) correlation is plotted against the strength of the N (H) − S1.4,nth correlation.
Fields exhibiting a moderate to strong q − N (H) correlation (rp > 0.5) are represented with
filled circles; fields with 0.3 < rp ≤ 0.5 are indicated with open circles.
6.3. Analysis
6.3.2
331
Wavelet Analysis
Wavelet analysis involves the convolution of an image with a family of self-similar
basis functions that depend on scale and location. It can be useful to consider the
wavelet transform as the general case of the Fourier transform, where the oscillatory
functions are localised in both time and frequency. The family of basis functions is
constructed by dilating and translating a generating (or mother) function, which is
called the analysing wavelet. For our analysis, we use a two-dimensional continuous
wavelet transform, which can be written as
W (a, x) = w(a)
Z
∞
−∞
Z
∞
′
f (x )ψ
∗
−∞
x′ − x
a
dx′
(6.6)
Here f (x) is a two-dimensional function, such as an image, ψ ∗ is the complex conjugate
of the dilated and translated analysing wavelet, and w(a) is a normalising function. a
is the scale size of the wavelet. Note that the term “continuous wavelet transform” is
used in the literature to distinguish this transform from a “discrete” transform which
employs an orthogonal set of basis functions; however, there is no fundamental difficulty applying the former to discretely sampled data such as astronomical images.
Our use of wavelet transforms follows closely the work of Frick et al. (2001), who
pioneered their application to galaxy images. Our analysing wavelet is their “Pet Hat”
which can be written in Fourier space as

 C(a) cos2
ψ̂(ka) =

π
2
log2 2|k|a
:
0 :
1
4a
< |k| <
|k| <
1
a
1
4a , |k|
>
1
a
(6.7)
This function picks out an annulus in the Fourier plane centred at k=(2a)−1 , and provides both simplicity and good separation of scales. The normalising factor C(a) is
chosen to provide unit total flux density in the wavelet image (or unit total flux, in the
case of the H I and CO data). C(a) is evaluated numerically to be 1.065a/δ, where a
and δ are the scale size (defined below) and pixel size expressed in radians. We adopt
the convention that an angular scale size a in radians corresponds to a spatial frequency
332
Chapter 6. The Radio-FIR Correlation in the LMC
of (2a)−1 wavelengths. This is based on the observation that a positive, Gaussian-like
structure will tend to couple with half of a sine wave rather than a full period, however
it differs from the usual convention by a factor of two.
Expressing the convolution of Equation 6.6 in terms of Fourier transforms, the wavelet
filtered image is calculated as
W (a, x) =
1 X ˆ
f (k) ψ ∗ (ka) e−2πi(k·x)/N ,
N2
(6.8)
(k1 ,k2 )
where N is the linear dimension of the image in pixels, and the wavelet spectrum as
M (a) =
X
(x1 ,x2 )
|W (a, x)|2 .
(6.9)
This spectrum, which can be thought of as a smoothed version of the Fourier power
spectrum, reveals the dominant energy scales in an image.
Finally, we define the wavelet cross-correlation coefficient as
rw (a) =
PP
W1 (a, x)W2 (a, x)
,
[M1 (a)M2 (a)]1/2
(6.10)
where the subscripts refer to two images of the same size. This is the wavelet analogue of the Fourier cross-power spectrum. Following Frick et al. (2001), we assign an
uncertainty of
p
2
1 − rw
∆rw (a) = √
n−2
(6.11)
to this coefficient, where n = (L/a)2 for an image with linear size L.
6.3.3
Wavelet Spectra
The wavelet spectrum defined by Equation 6.9 is a useful mathematical tool to identify the scale of structures that dominate the emission in an astronomical image. The
wavelet spectra of various continuum and spectral line maps of the LMC are shown in
Figure 6.25. To avoid edge effects, these spectra are constructed from LMC maps that
6.3. Analysis
333
have been enlarged to 4096 × 4096 pixels by surrounding the maps in the high and low
resolution datasets with a wide border of zero-valued pixels. The dimensions of a single
pixel in the padded images remains 20′′ × 20′′ . The smallest scale that we can reliably
examine is set by the angular resolution of the data: 15 pc for maps belonging to the
high resolution dataset, and ∼ 65 pc for the lower resolution dataset. The largest scale
depends on the size of the field. To ensure reasonable spatial sampling, we limit our
study to spatial scales less than half the total width of an image prior to zero-padding.
For the wavelet spectra of the 1.4 GHz continuum and 70 µm maps, we trialled two
methods for suppressing the extremely bright emission associated with 30 Doradus,
which dominates the wavelet spectra on spatial scales up to a few hundred parsecs. In
our initial approach, we simply blanked pixels above a certain intensity threshold. The
highest intensity pixels associated with 30 Dor are located within an extended region
of elevated surface brightness, so this method leaves a ring-like structure. The residual
ring introduces power in the wavelet spectra on scales corresponding to its width, which
is not desirable. As a second approach, we replaced the highest intensity pixels with a
constant value equal to the intensity threshold. This is equivalent to applying a simple
brightness transform:
I=


I

I
thresh
I < Ithresh ,
(6.12)
I ≥ Ithresh .
For the value of Ithresh , we chose 25% of the peak intensity at the location of 30 Dor.
In practice, the brightness transform was applied to roughly the same region in both
the 70 µm and 1.4 GHz maps, and the radius of the region with modified pixels was
approximately one resolution element, i.e. 1 arcminute. We verified that the resulting
wavelet spectra were similar to the spectra obtained using our first approach (except
for the spurious power on small scales due to the residual ring in the blanked maps).
We did not attempt to suppress high surface brightness emission in the thermal and
non-thermal radio maps, as they have a much narrower dynamic range than the high
resolution 70 µm and 1.4 GHz maps.
334
Chapter 6. The Radio-FIR Correlation in the LMC
log(d/[parsec])
1.5
2.0
2.5
3.0
3.5
4.0
6
6
HI
log(M(a))
5
4
5
160µ
3
4
3
2
70µ
RCnth
2
1
RC
RCth
1
0
CO
0
2.0
2.5
3.0
3.5
4.0
4.5
log(a/[arcsec])
Figure 6.25 Wavelet spectra for high resolution maps of the H I, 160 µm, 70 µm, 1.4 GHz and
CO emission in the LMC. Spectra for the thermal and non-thermal components of the 1.4 GHz
radio continuum (RC) emission are also shown; these spectra are truncated at larger spatial
scales due to the lower resolution of the maps. The CO spectrum is constructed using the
I(CO) map obtained by MAGMA.
6.3. Analysis
335
To facilitate a comparison between the wavelet spectra using a single figure, we have
added a constant offset to each spectrum in Figure 6.25. The absolute normalisation of
M (a) is therefore not meaningful, but the gradients of the spectra retain their original
values. Indeed, differences between the gradients of the wavelet spectra indicate genuine
variations in how emission at each waveband is distributed across structures at different spatial scales. In general terms, the spectra in Figure 6.25 confirm the impression
conveyed by visual inspection of the individual maps. The CO emission mostly arises in
compact, high surface brightness regions, which is reflected by a wavelet spectrum that
peaks strongly at small scales and then declines with increasing scale. The H I emission, by contrast, is distributed in a diffuse extended disk, and hence M (a) increases
more or less smoothly towards larger scales. The wavelet spectra of the dust and radio continuum emission indicate distributions that are intermediate between these two
extremes. The 160 µm spectrum is roughly flat, while the 70 µm and 1.4 GHz spectra
show shallow declines towards large angular scales.
It is evident from Figure 6.25 that the 70 µm and 1.4 GHz wavelet spectra are quite
similar. The 70 µm spectrum is flatter, indicating that the dust emission is more evenly
distributed across large and small scales, and it also exhibits a more prominent peak
at log(a) ∼ 3.5 than the 1.4 GHz spectrum. Overall, however, there is a good correspondence between the fluctuations and general shape of both spectra. It is therefore
somewhat surprising that neither the thermal nor the non-thermal 1.4 GHz spectrum
bears a close resemblance to the total 1.4 GHz spectrum. After peaking strongly around
log(a) ∼ 2.9, the non-thermal radio spectrum exhibits a local minimum at log(a) ∼ 3.3
and then increases steadily towards larger scales. The thermal radio spectrum, by
contrast, shows a broad peak between log(a) = 3.0 and 3.5, then decreases rapidly.
In combination, these rather disparate spectral shapes produce the weak bump at
log(a) ∼ 3.5 and the shallow decline towards larger scales that is observed for the total 1.4 GHz spectrum. Although we do not attempt decomposition of the dust maps
here, it would be interesting to determine whether the 70 µm spectrum can also be regarded as a composite of dust emission powered by different heating sources, e.g. dust
heated directly by massive stars, and dust heated by the interstellar radiation field (e.g.
336
Chapter 6. The Radio-FIR Correlation in the LMC
Table 6.4 The wavelet cross-correlation coefficient, rw , at four different spatial scales between
image pairs for the whole LMC. The wavelet scales shown are log(a) = 2.0, 2.5, 3.0 and 3.5,
corresponding to spatial scales d = 25, 80, 245 and 770 pc. The final column lists the relevant
panel of Figure 6.26.
Image Pair
rw,2.0
70 µm – RC
160 µm – RC
70 µm – thermal RC
70 µm – non-thermal RC
70 µm – N (H)
160 µm – N (H)
N (H) – RC
N (H) – thermal RC
N (H) – non-thermal RC
0.52
0.47
···
···
···
···
···
···
···
rw (a)
rw,2.5 rw,3.0
rw,3.5
0.79
0.67
0.88
0.83
0.14
0.51
< 0.01
< 0.01
< 0.01
0.97
0.90
0.96
0.95
0.41
0.65
0.37
0.26
0.47
0.94
0.80
0.96
0.91
0.30
0.61
0.16
0.17
0.15
Panel
a
a
b
b
c
c
d
d
d
Hoernes et al., 1998).
6.3.4
Wavelet Cross-correlations
The wavelet cross-correlation spectrum rw (a) was calculated for each of the image pairs
listed in Table 6.4, and the results for the whole LMC maps are shown in Figure 6.26.
Figures 6.27 and 6.28 show the wavelet cross-correlation spectra for the 1.◦ 35 × 1.◦ 35
fields.
i) Cross-correlations between radio and FIR emission
For the whole LMC, it is clear that the cross-correlation between the 1.4 GHz radio and
the FIR dust emission (panels [a] and [b] of Figure 6.26) is very strong, and significantly
better across all spatial scales than the cross-correlations involving the neutral gas (panels [c] and [d]). Frick et al. (2001) regard values higher than 0.75 to be indicative of
an excellent correlation: by this measure, the cross-correlation between the 1.4 GHz
and 70 µm emission in the LMC remains strong down to spatial scales of ∼50 pc. The
cross-correlation between the 70 µm and the thermal 1.4 GHz maps also remains strong
at this spatial scale, whereas the correlation between the 70 µm and non-thermal maps
degrades steeply for scales below ∼ 200 pc. The wavelet cross-correlation between the
6.3. Analysis
337
2.5
3.0
log(d/[parsec])
3.5
1.0
[a]
1.0
1.5
2.0
2.5
3.0
3.5
[b]
1.0
1.0
0.5
0.5
0.5
0.5
0.0
0.0
0.0
0.0
1.0
70µm+RC
160µm+RC
1.5
2.0
1.0
cross−correlation coefficient
2.0
1.0
1.5
2.5
3.0
3.5
4.0
70µm+RCth
70µm+RCnth
4.5
1.5
2.0
2.5
3.0
log(a/[arcsec])
log(d/[parsec])
log(d/[parsec])
2.0
2.5
3.0
3.5
1.0
[c]
1.0
1.0
0.5
0.5
0.5
0.0
0.0
0.0
1.5
2.0
2.5
2.0
2.5
3.0
3.5
log(a/[arcsec])
4.0
4.5
3.0
4.0
4.5
3.5
[d]
1.0
0.5
0.0
RC+N(H)
RCth+N(H)
RCnth+N(H)
70µm+N(H)
160µm+N(H)
1.5
3.5
log(a/[arcsec])
1.5
2.0
2.5
3.0
3.5
cross−correlation coefficient
cross−correlation coefficient
1.5
4.0
cross−correlation coefficient
log(d/[parsec])
1.0
4.5
log(a/[arcsec])
Figure 6.26 Wavelet cross-correlation spectra for the image pairs listed in Table 6.4. In each
panel, the angular scale is indicated on the bottom axis, and the corresponding spatial scale
(for an assumed LMC distance of 50.1 kpc) is shown along the top axis.
338
Chapter 6. The Radio-FIR Correlation in the LMC
1.4 GHz continuum and the 160 µm maps declines less sharply across the observed range
of scales, but also falls below 0.75 at ∼ 200 pc. Henceforth, we refer to the spatial scale
at which the wavelet cross-correlation between two image pairs falls beneath 0.75 as
the cross-correlation’s “breakdown scale”, and denote this scale by db .
Since the emission of the LMC as a whole is strongly influenced by the 30 Dor region,
we present the wavelet cross-correlations for the 1.4 GHz and the 70 µm emission in the
individual 1.◦ 35 × 1.◦ 35 fields in Figure 6.27. The cross-correlation results are diverse:
in the south-west of the LMC (regions 1 and 2), the 70 µm − 1.4 GHz cross-correlation
is poor across the observed range of scales (50 to 500 pc), while other fields exhibit an
excellent correlation down to the smallest scales that we can measure. In most fields,
the 70 µm − 1.4 GHz cross-correlation spectrum follows the cross-correlation between
the dust and the thermal radio maps, even though thermal emission makes a smaller
contribution to the total 1.4 GHz flux density in nearly all fields. The cross-correlation
between the dust and the non-thermal radio maps is typically much weaker, especially
on small scales. A notable exception is region 4, where the good 70 µm − 1.4 GHz
cross-correlation on large scales (& 300 pc) is dominated by a good correlation between
the 70 µm and non-thermal radio maps.
To investigate why the 70 µm − 1.4 GHz cross-correlation breaks down at different
scales across the LMC, we compared db to the properties listed in Table 6.3. For
the 70 µm − 1.4 GHz cross-correlation, we detect a clear anti-correlation between db
and the star formation rate (see Figure 6.29[a]). The thermal fraction, dust color temperature and radio spectral index are strongly correlated with the star formation rate,
and hence also anti-correlated with db . On small scales, the good correlation between
dust and radio emission in the LMC therefore appears to be driven by an association
between FIR emission from dust heated by young massive stars and the thermal radio
emission from the H II regions associated with those stars.
It is more difficult to draw conclusions regarding the breakdown scale of the non-thermal
1.4 GHz−70 µm cross-correlation, since we only have a lower limit of db ≥ 500 pc for
6.3. Analysis
339
log(d/[parsec])
1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0
R13
cross−correlation coefficient
1.0
1.0
0.5
0.0
0.5
R16
R15
R14
70µm+RCnth
70µm+RCth
70µm+RC
0.0
1.0
1.0
0.5
0.5
0.0
R12
R11
R10
R9
0.0
1.0
0.5
R7
R6
R5
0.0
1.0
1.0
0.5
0.5
0.0
R4
R3
R2
R1
2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5
log(a/[arcsec])
Figure 6.27 Wavelet cross-correlation spectra between the 70 µm and total 1.4 GHz continuum
maps (black line), and between the 70 µm and the thermal (open circles) and non-thermal
(black squares) 1.4 GHz continuum maps for the 1.◦ 35 × 1.◦ 35 fields.
0.0
340
Chapter 6. The Radio-FIR Correlation in the LMC
log(d/[parsec])
cross−correlation coefficient
1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0
1.0
1.0
0.5
0.5
0.0
R16
R15
R14
R13
0.0
1.0
1.0
0.5
0.5
0.0
R12
R11
R10
R9
0.0
1.0
0.5
R7
1.0
R4
R6
R5
R3
1.0
0.5
0.0
0.0
0.5
N(H)+70µm
70µm+RCnth
N(H)+RCnth
70µm+RC
R2
R1
2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5
log(a/[arcsec])
Figure 6.28 Wavelet cross-correlation spectra between the neutral gas column density N (H)
and the 70 µm images (open circles) and between the N (H) and the non-thermal 1.4 GHz images
(black squares) of the 1.◦ 35×1.◦ 35 fields. To facilitate comparison with the panels in Figure 6.27,
the cross-correlations between the non-thermal 1.4 GHz and 70 µm maps (black line) and the
total 1.4 GHz and 70 µm maps (grey line) are also shown.
0.0
db (1.4GHz−70µm)
3.0
341
db (non−thermal 1.4GHz−70µm)
6.3. Analysis
[a]
2.5
14
4 10
15
5
2.0
7
6
9
11
1.5
−3.5
−3.0
−2.5
−2.0
log(SFR/[Msol
8
−1.5
−1.0
yr−1])
3.0
[b]
2
4
2.5
15 12
11
13
2.0
8
1.5
−3.5
−3.0
−2.5
−2.0
log(SFR/[Msol
−1.5
−1.0
yr−1])
Figure 6.29 The breakdown scale of the 70 µm − 1.4 GHz wavelet cross-correlations (db , see
text) plotted against the star formation rate in the 1.◦ 35 × 1.◦ 35 fields. In panel [a], we plot db
for the 70 µm − 1.4 GHz cross-correlation, while db for the non-thermal 1.4 GHz−70 µm crosscorrelation is shown in panel [b]. Lower limits – i.e. fields where the correlation breaks down
on larger greater than ∼ 500 pc – are indicated with arrows.
nearly half of the fields. For regions where the non-thermal 1.4 GHz−70 µm crosscorrelation breaks down on smaller scales, we again find that db is anti-correlated with
the star formation rate. The trend in Figure 6.29[b] suggests that a good correlation on
small scales between the 70 µm and non-thermal 1.4 GHz images is due to emission produced directly in star-forming complexes, rather than the diffuse dust and synchrotron
emission within in the LMC’s disk.
ii) Cross-correlations with N (H)
Wavelet cross-correlations involving the neutral gas column density N (H) are presented
in the bottom row of Figure 6.26, and in Figure 6.28. For the whole LMC image
pairs, the cross-correlations between the dust and radio emission with N (H) are significantly weaker at all scales than the 70 µm − 1.4 GHz cross-correlation, although the
N (H) − 160 µm cross-correlation is comparable to the cross-correlation between the
70 µm and non-thermal maps at small scales. All of the cross-correlations involving
N (H) improve slightly on spatial scales of d ∼ 300 pc. Inspection of the wavelet-filtered
images suggests that that this corresponds to the scale of the LMC’s major star-forming
342
Chapter 6. The Radio-FIR Correlation in the LMC
complexes (besides 30 Dor): N11, N44, N48, N83, N159 and N206 (Henize, 1956). On
scales larger than 300 pc, the SEHO begins to dominate the wavelet-filtered N (H)
images. The cross-correlations therefore tend to degrade since the SEHO is not as
dominant at other wavebands. The cross-correlation between the non-thermal 1.4 GHz
and N (H) maps continues to improve – and is clearly better than the correlation between the 70 µm and thermal radio maps – but the value of rw (a) never reaches 0.75.
While the wavelet cross-correlations involving N (H) for the whole LMC image pairs
are only moderate or poor, Figure 6.28 reveals that the cross-correlation between the
gas and dust emission can be better than the 70 µm − 1.4 GHz cross-correlation locally
(e.g. region 1). Even more commonly, the gas and dust demonstrate a similar or
better cross-correlation than the non-thermal 1.4 GHz and 70 µm maps. However the
real surprise of Figure 6.28 is that the wavelet cross-correlation between the N (H) and
non-thermal 1.4 GHz continuum maps is strong in some parts of the LMC. In region 4,
the non-thermal 1.4 GHz−N (H) cross-correlation is the tightest of all the correlations
that we examine, and for a further five fields, it is stronger than the 70 µm−N (H) crosscorrelation (though weaker than the total 70 µm − 1.4 GHz cross-correlation). We find
that the breakdown scale of the non-thermal 1.4 GHz−N (H) cross-correlation tends to
increase with the thermal fraction of 1.4 GHz emission (Figure 6.30[a]), i.e. the gas
and non-thermal radio continuum images are more closely correlated in regions where
the radio emission is mostly of non-thermal origin. No trend between db and the star
formation rate is detected, but there is a slight tendency for db to decrease as the
molecular depletion time increases (panels [b] and [c] of Figure 6.30). We conclude
that the presence of dense, non-star-forming gas is an important factor in determining
whether a good non-thermal 1.4 GHz−N (H) cross-correlation is maintained on small
spatial scales.
343
db (non−thermal 1.4GHz−N(H))
db (non−thermal 1.4GHz−N(H))
6.3. Analysis
[a]
2.8
13
2.6
3
2
15 11 9
2.4
6
4
2.2
0.0
10
12
0.2
0.4
[b]
2.8
13
2.6
14 3
9 15
2.4
6
4 10
2.2
−3.5
0.6
−3.0
−2.5
12
−2.0
log(SFR/[Msol
Thermal Fraction
db (non−thermal 1.4GHz−N(H))
11
−1.5
−1.0
yr−1])
[c]
2.8
13
2.6
14 2 3
7 1511 9
2.4
6
2.2
7.5
12
10
4
8.0
8.5
9.0
9.5
log(τH2/[yr])
Figure 6.30 Properties that influence the breakdown scale of the non-thermal 1.4 GHz−N (H)
cross-correlations (db ) for the 1.◦ 35 × 1.◦ 35 fields. In panel [a], we plot db against the thermal
fraction of the 1.4 GHz emission. db is plotted against the star formation rate in panel [b], and
against the molecular gas depletion time in panel [c]. As in Figure 6.29, arrows indicate lower
limits.
344
Chapter 6. The Radio-FIR Correlation in the LMC
6.4 Discussion
The primary result of this study is that the local radio-FIR correlation in the LMC is
very good. Yet in many parts of the LMC – especially where the thermal fraction of
the 1.4 GHz emission is low – we also find tight correlations between the dust and radio
emission and the gas surface density. In this section, we discuss possible explanations
for the local correlations that we observe. We then briefly consider our results in the
context of models for the origin of the global radio-FIR correlation.
6.4.1
The Local Radio-FIR Correlation
Common Energy Sources
Our results in Section 6.3.1 show that the 70 µm emission in the LMC correlates strongly
with the thermal 1.4 GHz emission, but that a moderate to strong correlation between
the dust and non-thermal radio emission is also present. The former correlation can be
explained by a common dependence of both emissions on massive ionizing stars (e.g.
Xu et al., 1994); we do not discuss it further, since it plays an insignificant role in
maintaining the global radio-FIR correlation (for a discussion of whether diffuse thermal radio emission from the warm ionized medium is important for the total 1.4 GHz
luminosity of luminous galaxies, see Pierini et al., 2003). The correlation between the
70 µm and non-thermal 1.4 GHz emission is considerably more interesting, as it would
seem to imply that there is a physical mechanism that couples dust and relativistic
electrons in the LMC.
An important initial question is whether the local S70 − S1.4,nth correlation is due to
a single stellar population that powers the emission at both frequencies, or whether
the correlation arises because the synchtrotron emissivity is closely linked to the dust
distribution. The FIR emission in galaxies is composed of a ‘warm’ component due to
dust heated directly in H II regions, and a ‘cool’ component due to dust heated by the
interstellar radiation field (ISRF). Under average ISM conditions, the ISRF that heats
the diffuse dust comprises non-ionizing UV photons from intermediate-mass stars, and
6.4. Discussion
[a]
8
1.5
11
12
15
1.0
16 14
7
4
10 3
Non−thermal fraction
(S1.4,nth / [Jy])
2.0
345
6
5
9
0.5
1
[b]
1.0
14
0.8
12
9
16 1
4
10 3
5
0.6
6
2
7
8
13
0.4
0.0
7.0
7.5
8.0
log(M*/[Msol])
8.5
7.0
7.5
8.0
8.5
log(M*/[Msol])
Figure 6.31 The relationship between the stellar mass and non-thermal 1.4 GHz flux density
in the LMC. In panel [a], we plot the non-thermal 1.4 GHz flux density of each field against its
stellar mass. In panel [b], we plot the fraction of the radio emission that is due to non-thermal
processes as a function of the stellar mass. In both panels, fields with a moderate to strong
correlation between S70 and S1.4,nth are plotted with filled circles; other fields are plotted with
small, open circles.
optical/near-IR photons from low-mass stars (e.g. Popescu & Tuffs, 2002; Jones et al.,
2002).1 A possible explanation for the global non-thermal 1.4 GHz−70 µm correlation is
that intermediate-mass stars, which produce non-ionizing UV photons and also evolve
into supernovae that accelerate cosmic ray electrons, power the bulk of the synchrotron
and diffuse dust emission in galaxies (e.g. Xu et al., 1994). The relative contributions
of intermediate and low-mass stars to diffuse dust heating is likely to vary between
galaxies (e.g. Misiriotis et al., 2001), although the importance of these variations may
be minimized if current star-formation activity is spatially coupled to the old stellar
population (e.g. Ryder & Dopita, 1994; Hunter et al., 1998).
Our comparison of different star-formation calibrations in Section 5.6.2 indicated that
the LMC is relatively transparent to UV photons, and that the fraction of FIR emission
emerging at long wavelengths is higher in the LMC than in normal spiral galaxies (see
also Pradhan et al., 2010). Together, these results suggest that dust heated by the
ISRF contributes significantly to the LMC’s total FIR luminosity, but the question of
1
Note that the terms ‘warm’ and ‘cool’ refer to the source of dust-heating; in some environments,
the kinematic temperature of the cool component can exceed that of the warm component (e.g.
Stanimirovic et al., 2000).
346
Chapter 6. The Radio-FIR Correlation in the LMC
whether intermediate or low-mass stars dominate the diffuse dust heating remains open.
Statistically, Bell (2003) showed that old stars contribute ∼ 30% of the total IR luminosity, LTIR , for galaxies with LTIR . 1011 L⊙ , but the scatter of individual galaxies
around this average trend is large, especially for galaxies with 109 < LTIR < 1010 L⊙ .
Comparing the integrated non-thermal flux density and total stellar mass of the individual 1.◦ 35 × 1.◦ 35 fields yields a strong correlation (Figure 6.31). By itself, this trend
is not especially conclusive, as it may simply reflect a mass-scaling effect. There is a
weak trend between the non-thermal fraction of the 1.4 GHz emission and the stellar
mass, however, which would seem to indicate a genuine increase in the intensity of the
non-thermal radio emission at high stellar surface densities. Spatial coupling between
– or identity of – the stellar populations that power the diffuse dust and synchrotron
emission in the LMC may therefore contribute to the S70 − S1.4,nth correlation on kiloparsec scales in the LMC.
A key result of this chapter is that we observe a strong correlation between the 70 µm
and radio synchrotron emission in some parts of the LMC down to the limiting resolution of our data (∼ 65 pc). A common energy source may be sufficient to explain a good
correspondence between the distribution of FIR and non-thermal 1.4 GHz emission on
scales encompassing multiple star-forming complexes in diverse evolutionary states, but
the local correlations in Figure 6.10 are too tight to originate in the weak trend observed in Figure 6.31[b]. As the fields with a strong S70 − S1.4,nth correlation also tend
to exhibit a strong N (H) − S1.4,nth correlation, models that propose a coupling between
the magnetic field strength and the gas density clearly merit further consideration.
A Magnetic Field - Gas Density Coupling Model
Early models for the global radio-FIR correlation focussed on finding a common energy
source for the FIR and synchrotron luminosity of galaxies. However, several authors
have proposed that a coupling between the magnetic field and the interstellar gas
density is required to account for the correlations between the FIR and radio emission
that have been observed within galactic disks (e.g. Helou & Bicay, 1993; Niklas & Beck,
6.4. Discussion
347
1997; Hoernes et al., 1998). Following Hoernes et al. (1998), the flux density of the
non-thermal radio emission S1.4,nth at 1.4 GHz may be written,
S1.4,nth ∝ nCR lCR B 1−αnth ,
(6.13)
where B is the magnetic field strength and lCR is the pathlength through the synchrotronemitting region along the line-of-sight. nCR is the volume density of cosmic ray electrons with energy between E and E + δE, for an injection cosmic ray energy spectrum
N (E) = N0 E −p , where αnth = −p/2. The expression in Equation 6.13 is fairly general,
as it allows for variations in the scale-height of the synchrotron disk, and does not
assume a relationship between B and nCR . On large scales, equipartition between the
magnetic and cosmic ray energy densities and a constant lCR are often assumed (e.g.
Niklas & Beck, 1997). In this case, nCR ∝ B 2 and S1.4,nth ∝ B 3−αnth (Pacholczyk, 1970).
The magnetic field is coupled to the gas volume density ρ via B ∝ ρβ . The physical
mechanism behind this coupling is truly local in nature, involving a relationship between the magnetic field and charge density within (nearly) neutral gas. Observations
indicate β ∼ 0.5 ± 0.1 globally and within galactic disks, even on the scale of individual
clouds (∼100 pc, e.g. Fiebig & Guesten, 1989; Berkhuijsen et al., 1993; Niklas & Beck,
1997). This range of β values is in good agreement with results from turbulent MHD
simulations (β = 0.4 to 0.6, e.g. Ostriker et al., 2001; Cho & Vishniac, 2000; Groves
et al., 2003) and with equipartition between magnetic and turbulent energy densities
in the ISM (β = 0.5, e.g. Ko & Parker, 1989). Dynamo theory and static pressure
equilibrium between the magnetic field and the interstellar gas also predict β = 0.5
(Beck et al., 1996; Kulkarni & Heiles, 1988). In principle, other scalings are possible,
and may provide evidence for less common ISM processes: β ∼ 1 is expected for shearing/compression of magnetic fields in diffuse gas, for example, while β . 0.4 could
occur for a cosmic ray population dominated by strong synchrotron/inverse Compton
losses (Beck & Krause, 2005). Regardless of β’s exact value, B − ρ coupling yields
S1.4,nth ∝ nCR lCR ρβ(1−αnth )
(6.14)
348
Chapter 6. The Radio-FIR Correlation in the LMC
for the correlation between the non-thermal 1.4 GHz emission and the gas volume density. The gas surface density Σgas is simply the projection of the volume density through
the disk, so for a gas disk with constant scale height lgas we would expect to observe a
power-law scaling with a similar exponent, i.e.
nth )
S1.4,nth ∝ nCR lCR Σβ(1−α
.
gas
(6.15)
Later in this section, we construct a prediction for the 70 µm flux density based on
Σgas . However, comparing Equation 6.15 with the plots in Figure 6.17 already offers
some useful insights. In particular, the slope of the S70 − S1.4,nth correlation in different
regions of the LMC is roughly linear: we mostly obtain (OLSB) exponents between
0.8 and 1.2 for the fields exhibiting a moderate to strong correlation (rp ≥ 0.5). In
Figure 6.32, we plot the observed exponents of the N (H) − S1.4,nth correlation against
the prediction from Equation 6.15, assuming a range of β values and allowing for a
weak dependence between the cosmic ray column density NCR ≡ nCR lCR and Σgas . For
αnth , we use the values tabulated in Table 6.1.
Figure 6.32 shows that the observed exponents of the non-thermal 1.4 GHz−N (H) correlations and the predictions from Equation 6.15 are in good agreement for β ∼ 0.6,
assuming that NCR is independent of Σgas (panel [d]). This solution is by no means
unique, and good agreement can also be obtained for the most probable value β ∼ 0.5,
if NCR increases as Σ∆
gas where ∆ = 0.15 (panel [b]). Some coupling between NCR
and Σgas might be expected on physical grounds, since the star formation rate surface
density – and presumably the supernova rate surface density – is known to increase
with Σgas (e.g. Kennicutt, 1998; Bigiel et al., 2008). More significantly, the plots in
Figure 6.32 suggest that equipartition between the magnetic field and cosmic ray energy
densities is unlikely to hold on the scales that we consider. In the case of equipartition,
nCR ∝ B 2 and S1.4,nth ∝ lCR ρβ(3−αnth ) . For our observed exponents and αnth values,
the equipartition assumption would require β ∼ 0.3 for constant lCR , which is much
less than theoretical predictions. Only if lCR scaled as ΣΓgas , with Γ ∼ −0.9, would the
observed N (H) − S1.4,nth correlations be consistent with β = 0.5. An anti-correlation
6.4. Discussion
349
between the synchrotron disk scale height and the star formation rate in galaxies is not
generally observed, although the synchrotron disks of starburst galaxies do tend to be
thinner than those of normal galaxies (e.g. Krause, 2009).
The SEHO seems to present a special case of the N (H) − S1.4,nth correlation, which exhibits a much steeper slope here (∼ 1.6) than in other parts of the LMC. One plausible
explanation for this discrepancy is that the magnetic field in the SEHO region is significantly affected by shear and/or compression, since β = 1 would bring the observed
and predicted exponents into excellent agreement for constant NCR . Potentially this
explanation could also be reconciled with a strongly polarised radio filament that has
been detected in this region (Klein et al., 1993; Gaensler et al., 2005a), and which has
been interpreted as a giant magnetic loop emerging out of the plane of the LMC. On
the other hand, our assumption of a constant NCR and a constant lgas may be inappropriate in the SEHO. If lCR were to increase faster than lgas (as has been inferred
for some Virgo cluster spirals, Vollmer et al., 2010), then this could produce a steep
correlation between S1.4,nth and N (H), even if the underlying relationship between B
and the gas density remained B ∝ ρ0.5 .
Let us now consider whether the local S70 − S1.4,nth correlations that we observe are
consistent with our previous conclusions concerning the origin of the LMC’s FIR luminosity. For galaxies that are optically thick to UV photons, the dust emission should
increase linearly with the intensity of the dust-heating radiation field, which in turn
should trace the star formation rate S70 ∝ Urad ∝ ΣSF R (e.g. Buat, 1992; Calzetti et al.,
2010). In the LMC, by contrast, a significant fraction of UV photons escape without
absorption, and dust heated in the diffuse ISM makes a significant contribution to the
LMC’s FIR luminosity. In this case, the FIR emission should be proportional to the
intensity of the ISRF, multiplied by the optical depth averaged along the line-of-sight
τ , i.e.
S70 ∝ τ Urad .
(6.16)
The optical depth should scale with the dust column density, Ndust , allowing us to
Chapter 6. The Radio-FIR Correlation in the LMC
OLSB slope (1.4GHz,nth−N(H))
350
2.0
[a] β=0.5, ∆=0
4
1.5
13 14
1.0
11
13 14
10 2
1.0
10 2
11
6
15
6
15
2.0
1.5
2.0
[c] β=0.5, ∆=0.3
1.0
2.0
11
2.0
13 14
10 2
1.0
1.0
10 2
11
6
15
1.5
2.0
[e] β=0.3, Γ=0, equipartition
1.0
Slope Prediction: ∆+β(1−αnth)
2.0
[f] β=0.5, Γ=−0.9, equipartition
4
4
1.5
1.5
1314
1.0
1.5
4
6
15
2.0
2.0
1.5
13 14
1.0
1.5
[d] β=0.6, ∆=0
4
1.5
Slope Prediction: ∆+β(1−αnth)
OLSB slope (1.4GHz,nth−N(H))
[b] β=0.5, ∆=0.15
4
1.5
1.0
OLSB slope (1.4GHz,nth−N(H))
2.0
11
13 14
102
1.0
6
15
1.0
11
10 2
6
15
1.5
2.0
Slope Prediction: Γ+β(3−αnth)
1.0
1.5
2.0
Slope Prediction: Γ+β(3−αnth)
Figure 6.32 The OLSB slope of the observed N (H) − S1.4,nth correlations for fields where
rp > 0.5, plotted against the prediction from Equation 6.15. The horizontal error bars reflect
an absolute uncertainty in the non-thermal spectral index of 0.1, and the vertical error bars
indicate the 1σ uncertainties on the OLSB slopes, estimated using a bootstrap procedure (see
e.g. Akritas & Bershady, 1996). The decomposition of 1.4 GHz image into thermal and nonthermal components represents a significant source of uncertainty for the quantities on both
axes, so the true uncertainty will be larger than the error bars suggest. The individual panels
correspond to different assumptions for the appropriate scaling between the magnetic field
strength, CR column density and/or CR scale height and the gas surface density: B ∝ Σβgas
and NCR ∝ Σ∆
gas , where β and ∆ are annotated on the plots. Panels [e] and [f] instead assume
equipartition between the CR and magnetic field energy densities, but allow lCR to vary as
ΣΓgas . We set β and Γ to obtain rough agreement with the observations.
6.4. Discussion
351
write S70 ∝ Urad Ndust . The observed S70 − S1.4,nth correlation supplies the link between
Equations 6.16 and 6.15, yielding
nth )
nCR lCR Σβ(1−α
∝ (Urad Ndust )k ,
gas
(6.17)
where k is the observed exponent of the S70 − S1.4,nth correlation, and we again assume
that lgas is constant.
A number of results from empirical studies of gas and dust in the LMC suggest that
Equation 6.17 can be simplified somewhat. In particular, Roman-Duval et al. (2010)
have studied the dust-to-gas ratio for two LMC clouds, including Spitzer + Herschel
observations at wavelengths between 24 and 500 µm to constrain the dust abundance
and temperature, and MAGMA CO observations to trace the molecular component of
the gas surface density. They obtained a linear correlation between Ndust and Σgas ,
consistent with reddening results in the Milky Way (e.g. Bohlin et al., 1978). Nonetheless, we can allow for some non-linearity between the gas and dust column densities by
setting Ndust ∝ Σζgas , with the expectation that a plausible physical model will produce
ζ ∼ 1. Furthermore, we saw above that the local N (H) − S1.4,nth correlations were most
consistent with β ∼ 0.5 to 0.6, and either a weak positive relation between NCR and
Σgas or constant NCR . Incorporating these additional constraints reduces Equation 6.15
to
(∆+β(1−αnth ))/ζ
nth )
S1.4,nth ∝ Σ∆+β(1−α
∝ Ndust
gas
,
(6.18)
where the potential variation in NCR is parameterised by NCR ∝ Σ∆
gas . By substituting
S70 ∝ Urad Ndust , we then obtain
S1.4,nth ∝
S70
Urad
κ
,
(6.19)
where κ = (∆ + β(1 − αnth ))/ζ.
In their analysis of the radio-FIR correlation within M31, Hoernes et al. (1998) assumed
that nCR and Urad are roughly constant, and that the CR, gas and dust scale heights
352
Chapter 6. The Radio-FIR Correlation in the LMC
remain linearly proportional to each other. With these assumptions, they show that
the observed exponent of the local radio-FIR correlation agrees well with the prediction
of the B −ρ coupling model when ζ and β assume their most probable values (i.e. ζ = 1
and β = 0.5). We refrain from making similar assumptions regarding nCR and Urad ,
since the dust temperature map of Bernard et al. (2008) demonstrates that the ISRF
in the LMC varies by more than an order of magnitude, and the N (H) − S1.4,nth correlations indicate that β = 0.5 is not quite consistent with constant NCR . Instead, we
directly determine the best-fitting relation corresponding to Equation 6.19 for the fields
that show a moderate to strong S70 −S1.4,nth correlation (rp > 0.5). As in Section 2.5.7,
we estimate the ISRF at each pixel according to Urad = U0 (Td /T0 )6 eV cm−3 , assuming
U0 = 0.539 eV cm−3 and T0 = 17.5 K for the local ISRF and dust temperature (Weingartner & Draine, 2001; Boulanger et al., 1996).
In Figure 6.33[a], we plot the predicted exponent κ = (∆ + β(1 − αnth ))/ζ against the
exponent determined from an OLSB fit to the data, assuming ζ = 1, β = 0.5 and
∆ = 0.15. We tested a range of alternative assumptions for β, ∆, ζ and Urad , and plot
a selection of the better results in the other panels of Figure 6.33. Overall, these plots
show that the S70 − S1.4,nth correlations cannot be self-consistently explained within
the context of the B − ρ coupling model that we have described if we assume the most
probable values of β and ζ. The predicted slopes are too steep by 0.2 dex. Reverting to
the assumption of constant Urad in the LMC does not alter this conclusion, but instead
tends to increase the discrepancy. Only by setting ζ ∼ 1.2 to 1.3 (i.e. a varying dustto-gas ratio) can we retain β ∼ 0.5 and also obtain reasonable agreement between the
observed and predicted slopes. ζ ∼ 1.2 is not physically implausible – significant H I
opacity, the presence of a CO-dark H2 gas and/or dust coagulation in molecular clouds
could produce a supralinear relationship between Ndust and Σgas . Another possibility
is that ζ ∼ 1, but the observed S70 − S1.4,nth slopes are “too flat” due to an additional
contribution to the 70 µm emission from stochastically heated VSGs in regions with
high Σgas . Equation 6.16 should equally apply to the dust emission at 160 µm, so we
can test this last possibility by repeating our analysis using the observed correlations
between the non-thermal 1.4 GHz flux density and S160 /Urad . In this case, reasonable
2
6 15
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0.8
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Slope Prediction: (Γ+β(3−αnth))/ζ
1.2
[f] β=0.5, Γ=−0.8, ζ=1.0
+ equipartition, Urad constant
1.0
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1115
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6
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[h] β=0.6, ∆=0, ζ=1.25
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1.2
[c] β=0.5, Γ=−0.9, ζ=1.0
+ equipartition
1.4
[e] β=0.6, ∆=0, ζ=1.0
Urad constant
0.6
OLSB slope (1.4GHz,nth−70µm/Urad)
OLSB slope (1.4GHz,nth−70µm/Urad)
1.0
1.0
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1.4
[g] β=0.5, ∆=0.15, ζ=1.25
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Slope Prediction: (∆+β(1−αnth))/ζ
OLSB slope (1.4GHz,nth−70µm)
OLSB slope (1.4GHz,nth−70µm)
1.0
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2
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[d] β=0.5, ∆=0.15, ζ=1.0,
Urad constant
10
1115
13
4
[b] β=0.6, ∆=0, ζ=1.0
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OLSB slope (1.4GHz,nth−70µm/Urad)
1.0
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[a] β=0.5, ∆=0.15, ζ=1.0
0.8
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Slope Prediction: (Γ+β(3−αnth))/ζ
OLSB slope (1.4GHz,nth−70µm/Urad)
1.2
353
OLSB slope (1.4GHz,nth−70µm/Urad)
OLSB slope (1.4GHz,nth−70µm/Urad)
6.4. Discussion
1.2
[i] β=0.5, Γ=−0.9, ζ=1.25
+ equipartition
1.0
2
6 15
13
11 4 10
0.8
0.6
0.6
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Slope Prediction: (Γ+β(3−αnth))/ζ
Figure 6.33 The observed OLSB slope of the relationship betwen S1.4,nth and (S70 /Urad)
for fields where rp > 0.5, plotted against the prediction from Equation 6.18. The error bars
represent the same uncertainties as in Figure 6.32, where we have assumed an uncertainty of 50%
on the measurement of S70 /Urad at each pixel. This should be roughly appropriate for regions
where the dust is relatively warm and Urad is high, but will underestimate the true uncertainty
for pixels with low Urad .The individual panels correspond to different combinations of input
parameters described in Figure 6.32 and annotated on the plots. The additional parameter ζ
represents the scaling between the gas and dust column densities, Ndust ∝ Σζgas . Note that
equipartition between the CR and magnetic field energy densities is assumed for panels [c], [f]
and [i].
354
Chapter 6. The Radio-FIR Correlation in the LMC
agreement between the observed exponents and the predictions of the B − ρ coupling
model can be obtained for β ∼ 0.5 and ζ = 1 (Figure 6.34[a] and [b]), although the
dynamic range of the observed exponents (0.5 dex) is considerably larger than for the
model predictions (0.15 dex).
In summary, we have shown that B−ρ coupling provides a possible explanation for local
correlations between the dust, gas and non-thermal radio emission across nearly half
the LMC. However, there are at least three caveats that should be considered prior to
linking this conclusion to the origin of the global radio-FIR correlation. First it must be
acknowledged that our interpretation includes several simplifying assumptions. These
include: i) that the gas scale height is roughly constant, which allows us to infer appropriate values for β and NCR based on observations of Σgas ; ii) that the dust-to-gas ratio
is roughly constant in all the neutral gas phases of the ISM; and iii) that the LMC is
uniformly optically thin to UV photons. We implicitly assume, moreover, that we have
accurately decomposed the LMC’s 1.4 GHz emission into its thermal and non-thermal
components. An incorrect decomposition would affect the correlations in Figures 6.10
and 6.17 directly, but would also bias the non-thermal spectral index that we adopt
for each field. Second, it seems unlikely that the model that we have outlined provides
a unique interpretation of the observed correlations, as the radio and FIR emission in
galaxies both depend on several parameters. Even within the framework of the B − ρ
coupling model, equipartition between the B-field and cosmic ray energy densities cannot be decisively excluded on the basis of our calculations (e.g. Figure 6.34[c]). Finally,
the LMC fields that conform to the B − ρ coupling model that we have outlined contribute at most ∼40% of the LMC’s total 70 µm and non-thermal 1.4 GHz luminosities.
While this contribution is not negligible, it is by no means sufficient to guarantee that
the LMC will conform to the global radio-FIR correlation.
1.4
355
OLSB slope (1.4GHz,nth−160µm/Urad)
OLSB slope (1.4GHz,nth−160µm/Urad)
6.4. Discussion
[a] β=0.5, ∆=0.15, ζ=1.0
2
1.2
64
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15 13
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Slope Prediction: (∆+β(1−αnth))/ζ
1.4
[b] β=0.6, ∆=0, ζ=1.0
0.6
0.8
1.0
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Slope Prediction: (∆+β(1−αnth))/ζ
[c] β=0.5, Γ=−0.9, ζ=1.0
+ equipartition 2
1.2
64
1.0
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Slope Prediction: (Γ+β(3−αnth))/ζ
Figure 6.34 The OLSB slope of the relationship between S160 /Urad and S1.4,nth for fields where
rp > 0.5, plotted against the prediction from Equation 6.18. The plot annotations and error
bars are the same as in Figure 6.33. Equipartition between the CR and magnetic field energy
densities is assumed for panel [c].
356
6.4.2
Chapter 6. The Radio-FIR Correlation in the LMC
The Global Radio-FIR Correlation
Calorimeter models
The basic premise of many models for the global radio-FIR correlation is that both
types of emission are associated with high-mass star formation. A common objection
to this hypothesis is that thermal dust emission is a prompt and relatively local measure of ionising radiation from young stars, whereas the radio continuum is due to CRs
losing energy via synchrotron radiation, a process that occurs over a longer timescale
and a larger area. For a steady-state situation, however, a strong global correlation
between the radio and FIR emission might still be expected. Provided that the escape
of CRs from their host galaxy is minimal, the sensitivity of synchrotron emissivity to
the magnetic field strength may not be critical, since a galaxy’s total radio luminosity will reflect the total energy emitted by CRs during their radiative lifetimes rather
than the instantaneous emitted power. Within galaxies, star formation models predict
that the radio emission should appear as a smeared version of the FIR emission, with
deviations on small scales reflecting temporal fluctuations in star formation activity
that violate the steady-state assumption (e.g. Helou & Bicay, 1993). Support for this
prediction comes from the large radial scale length of the radio continuum emission in
galactic disks (relative to the FIR, e.g. Bicay & Helou, 1990), and parameter searches
for properties that minimise the dispersion in resolved measurements of the FIR/radio
ratio (Murphy et al., 2006b, 2008). The classic example of models in the calorimeter
category is the ‘optically thick’ scenario proposed by Völk (1989), which assumes that
the UV photons from massive stars are completely absorbed and reprocessed by interstellar dust, and that CRs are trapped in the galaxy and lose all their energy through
synchrotron and/or inverse Compton scattering. The energy densities of the magnetic
field and the interstellar radiation field are further assumed to be proportional, maintaining a constant ratio of synchrotron to inverse Compton losses. A more general
version of the calorimeter model incorporates finite escape probabilities for the CRs
and variable optical depth of the ISM to UV photons (Lisenfeld et al., 1996).
With regards to a calorimeter interpretation of the global FIR-radio correlation, two
6.4. Discussion
357
results from the LMC seem especially relevant. First, the high thermal fraction of radio
emission, coupled with a higher FIR/radio ratio compared to spiral galaxies, suggests
that a large fraction of CRs escape the LMC without suffering significant synchrotron
losses. This conclusion is supported by the LMC’s flat non-thermal spectral index
(αnth ∼ −0.7), and a comparison between the characteristic timescales of different CR
energy loss processes, which shows that diffusive escape and inverse Compton scattering should generally dominate over synchrotron cooling in the LMC (Section 5.6.3).
The lower dust-to-gas ratio (Roman-Duval et al., 2010) and porous appearance of the
neutral ISM in the LMC suggest that it also may be more transparent to UV photons
than massive spiral galaxies. This inference is consistent with our comparison between
different empirical calibrations for the LMC’s global star-formation rate, and observations of diffuse UV radiation in the LMC (Pradhan et al., 2010). Second, the existence
of a strong FIR-radio correlation locally is often reinforced by a correlation between
thermal radio and FIR emission, for which a tight correlation is naturally expected.
The ‘dip-and-ring’ structure of the q measurements around N11 and 30 Doradus would
seem to provide direct evidence that the mean free path of UV photons is shorter than
the scale length of the synchrotron emission associated with a star-forming complex,
consistent with the basic phenomenology predicted by the calorimeter model (Bicay
& Helou, 1990). The chain of low q regions between N159W and the eastern edge of
the stellar bar – roughly coincident with fields 3 and 7 – demonstrates that the diffuse
non-thermal 1.4 GHz emission with relatively high surface brightness is not always associated with large gas surface densities, although we note that the enhanced magnetic
field in this region may be due to an interaction with the SMC (Klein et al., 1993;
Gaensler et al., 2005a).
B − ρ coupling models
The suggestion that B − ρ coupling is relevant for the global radio-FIR correlation was
originally put forward by Helou & Bicay (1993), as a condition of their alternative “optically thin” version of the original calorimeter theory. Helou & Bicay (1993) argued
that a tight radio-FIR correlation can be maintained, provided that the UV photons
358
Chapter 6. The Radio-FIR Correlation in the LMC
and cosmic rays escape the galaxy in equal proportion. In this case, galaxies must
follow τUV ∝ tesc /tsync , where τUV is the UV optical depth, tesc is the timescale for CR
escape, and tsync is the synchrotron cooling timescale. In practice, Helou & Bicay (1993)
showed that galaxies will conform to this proportionality if the magnetic field B is coupled to the gas density ρ via B ∝ ρ0.5 , assuming that the typical CR path length (lCR )
0.5 . Additional assumptions
depends only weakly on the disk scale height lgas , lCR ∝ lgas
of the model proposed by Helou & Bicay (1993) include a nearly constant dust-to-gas
ratio, and a proportionality between synchrotron and inverse Compton losses, as in the
calorimeter model.
Other models the invoke B − ρ coupling differ slightly in their prescription for CR
confinement (and hence CR number density, nCR ). Helou & Bicay (1993) assume
−0.5 is constant, Niklas & Beck (1997) assume
a confinement process such that lCR lgas
equipartition between the CR and magnetic field energy densities, nCR ∝ B 2 ∝ ρ,
while Hoernes et al. (1998) and Murgia et al. (2005) assume that nCR is roughly constant. In spite of these differences, which may simply reflect our poor understanding
of how cosmic rays are distributed, the basic condition of B ∝ ρ0.5 is common to all of
these models, and is motivated by the sensitive dependence of synchrotron emission on
the magnetic field strength, bearing in mind the large range of magnetic field strengths
observed in galaxies obeying the correlation (Condon et al., 1991). These models have
the advantage of naturally producing a local radio-FIR correlation, breaking down only
on scales ∼ lCR due to cosmic ray diffusion. A key strength of the B − ρ coupling
mechanism is that it should produce a radio-FIR correlation even for galaxies with FIR
luminosities that are dominated by emission from dust heated by older stellar populations.
As we saw above, the local correlations between the gas, dust and radio emission in the
LMC tend to support to the idea of a coupling between magnetic field and gas density.
It remains unclear whether this coupling can explain the existence and tightness of the
global-radio FIR correlation, however, since the majority of the LMC’s 1.4 GHz and
FIR emission arises in regions where B − ρ coupling is not directly substantiated by the
6.4. Discussion
359
observed correlations (or lack thereof). Moreover, the total 1.4 GHz luminosity of the
LMC is suppressed by a factor of two relative to the relationship derived by Yun et al.
(2001), so we must be cautious about drawing general conclusions about the global
correlation on the basis of results obtained for the LMC. Overall, the regions that conform to the B − ρ coupling model in the LMC tend to have low thermal fractions and
q values that are consistent with the galaxy’s global FIR/radio ratio. Their intrinsic
star formation rates are neither unusually high nor low, but their molecular depletion
times are long (relative to other LMC fields), reaching a maximum of τH2 ∼ 1 Gyr in
the SEHO. Globally and on ∼ kpc scales, τH2 values of ∼ 2 Gyr and thermal fractions
of . 10% are found for nearby spiral galaxies (e.g. Leroy et al., 2005; Bigiel et al., 2008;
van der Kruit & Allen, 1976). Though these differences in τH2 and fth are suggestive
rather than conclusive, we might therefore expect B − ρ coupling to be more influential
in normal star-forming galaxies, where the volume filling-factor of dense gas is presumably larger. As we have seen, different phenomena can be responsible for brightness
as opposed to integrated flux density, so the contribution of outer galactic disks to the
total FIR and non-thermal radio luminosities of galaxies merits further investigation,
now that observations of dust emission beyond 100 µm are available (cf. Mayya & Rengarajan, 1997).
As a final caveat, we note that we have failed to develop a physically-motivated scheme
for CR confinement in the LMC. For our analysis of the local N (H)−S1.4,nth correlation,
we constrained nCR by assuming that NCR depends only weakly on Σgas , but we justified
this assumption on the basis that it approximately reproduces the local N (H) − S1.4,nth
correlations (Figure 6.17), rather than physical arguments. Elsewhere in the LMC, nCR
may be significantly altered by CR production and/or non-synchrotron loss processes,
invalidating this assumption. Star-forming complexes are prime candidates for violating the assumption of constant NCR and lgas , not only because they are the sites of CR
injection but also because supernova explosions and strong stellar winds could promote
convection of CRs out of the disk. It is therefore possible that B − ρ coupling holds
widely throughout the LMC, but that the observed N (H) − S1.4,nth correlations break
down because CRs are not able to fully explore the dense gas distribution. Higher
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Chapter 6. The Radio-FIR Correlation in the LMC
rates of cosmic ray escape might also explain the poorer N (H) − S1.4,nth correlations
for fields containing large H I shells (e.g. region 16). Direct measurements of the local
magnetic field strength throughout the LMC, e.g. through Faraday rotation (Gaensler
et al., 2005b), will be required to rigorously test the B − ρ coupling model.
6.5 Conclusions
We have examined the correlation between the 1.4 GHz radio continuum and 70 µm
emission in the LMC, using pixel-by-pixel and wavelet cross-correlation methods. Comparisons between the emission at these wavebands and the neutral (i.e. atomic +
molecular) gas surface density were also conducted, in order to assess the relevance
of dense gas to the local radio-FIR correlation. The high angular resolution datasets
that are available for the LMC allow us to probe the radio-FIR correlation on spatial
scales above ∼ 65 pc, and to identify variations in the FIR/radio ratio corresponding
to different interstellar environments. The key results of our study are:
1. The global logarithmic FIR/radio ratio (q = 2.61) and the median FIR/radio ratio
across the LMC (hqi = 2.62) are higher than the mean global value obtained from the
Yun et al. (2001) galaxy sample (hqi = 2.34). Independent evidence suggests that the
LMC is quite transparent to UV photons, so this discrepancy suggests that the LMC’s
total radio luminosity is suppressed by a factor of two relative to the global radio-FIR
correlation.
2. The 1.4 GHz radio continuum and 70 µm emission are positively correlated across the
LMC. The correlation coefficient for 1.4 GHz and 70 µm emission in the whole LMC is
∼ 0.77, indicating a strong correlation. The correlation improves in regions with higher
gas surface densities, Σgas . The correlation also improves in regions with higher star
formation rates, though this may reflect an underlying correlation between ΣSFR and
Σgas , i.e. the Kennicutt-Schmidt Law
6.5. Conclusions
361
3. Within the LMC, there are two independent correlations between the 1.4 GHz and
70 µm flux densities. A steeper than linear correlation (slope ∼ 1.1) is found for high
intensity pixels associated with star-forming regions, where the thermal fraction of the
radio emission is high. A flatter correlation (slope ∼ 0.5 − 0.8) applies more generally
to the diffuse emission. The correlation becomes flatter as the ratio between the mass
of molecular gas and the star formation rate (i.e. the molecular gas depletion time τH2 )
increases.
4. Across almost half the LMC’s gas disk, we detect robust, approximately linear correlations between the non-thermal 1.4 GHz emission and Σgas . The correlation improves
for regions where the star formation rate is low relative to the availability of dense gas,
i.e. where the molecular gas depletion time is long. For regions demonstrating the
tightest relationship between the non-thermal 1.4 GHz flux density and Σgas , a good
correlation is evident down to ∼ 200 pc scales.
5. There is a good correspondence between maps of the 1.4 GHz continuum and 70 µm
emission in the LMC, even on scales corresponding to a few tens of parsecs. However,
regions that exhibit a strong correlation on small scales have high star formation rates
and thermal fractions. In regions where the thermal fraction is . 20%, the S70 −S1.4,nth
correlation breaks down on scales between 300 and 500 pc.
6. For plausible assumptions regarding the LMC’s UV opacity, dust-to-gas ratio and
cosmic ray distribution, coupling between the magnetic field strength and the gas volume density can account for the exponents of the observed S70 − S1.4,nth and N (H) −
S1.4,nth correlations. The significance of B − ρ coupling versus calorimetry for the
global correlation is less clear, although regions of the LMC that show evidence for
B − ρ coupling have ISM properties that are more similar to the conditions in normal
star-forming galaxies.
7
Concluding Remarks
This thesis has presented new observations and analysis of the molecular gas in the
Large Magellanic Cloud (LMC). After describing the high-resolution mapping survey
of CO emission that we have undertaken (MAGMA), Chapters 2 to 4 focussed on the
properties of the LMC’s giant molecular clouds (GMCs). Chapters 5 and 6 had broader
scope, exploring the connection between star formation, dust, synchrotron radiation and
the dense interstellar gas through an investigation of the local radio–far-infrared (FIR)
correlation in the LMC. Rather than reviewing the conclusions from previous chapters
in detail, this short chapter outlines how our work provides some preliminary answers to
the questions posed in the Introduction, and highlights potentially productive avenues
for future research.
7.1 CO as a Tracer of H2 in Dwarf Galaxies
As the Universe has aged, the interstellar and intergalactic gas have been progressively
enriched by heavy elements. The presence of these heavy elements alters the chemistry and thermodynamics of the gas, with consequences for the formation of stars
and large-scale structure. In particular, the relationship between the cold gas reservoir
and star formation activity in low-mass, low-metallicity dwarf systems remains poorly
understood, presenting a significant stumbling block to cosmological models that aim
to reproduce the galaxy luminosity function and cosmic star formation history (e.g.
Robertson & Kravtsov, 2008; Schaye et al., 2010). Measurements of the molecular hy363
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Chapter 7. Concluding Remarks
drogen (H2 ) mass in low-metallicity dwarfs and galaxies at high redshift are essential to
clarify this relationship, but estimates of H2 masses using CO emission – the standard
tracer of molecular gas – are plagued with uncertainties in these systems (e.g. Leroy
et al., 2009a; Tacconi et al., 2010).
In Chapter 2, we assessed the CO luminosity of the LMC in relation to other global
galaxy properties, such as the B-band luminosity and star formation rate. If CO emission reliably traces H2 in the LMC, then the molecular gas in the LMC is appreciably
different to the molecular gas in spiral galaxies: the mass of H2 relative to the B-band
luminosity (MH2 /LB ) is smaller in the LMC, and the star formation rate per unit H2
mass (SF R/MH2 ) is larger, by an order of magnitude or more. Anomalous ratios such
as these have previously been noted for nearby dwarf galaxies that are metal-poor, e.g.
the SMC, NGC 6822 and NGC 1569 (Z ∼ 0.2 − 0.3Z⊙ ), and these results have been
intepreted as a sign that their H2 mass is significantly underestimated using a Galactic
CO-to-H2 conversion factor (e.g. Leroy et al., 2007b; Bolatto et al., 2008). Our results
showing that the LMC (Z ∼ 0.4Z⊙ ) exhibits a comparably low MH2 /LB and a high
SF R/MH2 ratio raises the question of whether metallicity-dependent variations in the
CO-to-H2 factor (XCO ) are the best explanation for these results, since empirical estimates for XCO in the LMC only diverge from the standard Galactic value by a factor
of a few (e.g. Israel, 1997; Dobashi et al., 2008)
The question of whether the Galactic CO-to-H2 calibration leads to an underestimate
of the molecular mass in dwarf galaxies, or whether they have a genuinely low molecular
(i.e. H2 ) content that is extremely efficient at forming stars, therefore remains open.
The Atacama Large Millimeter Array (ALMA) will provide one obvious way to make
progress on this issue: a sensitive survey of CO emission for a complete volume-limited
sample of nearby (e.g. ≤ 10 Mpc) galaxies. With a sufficiently large number of galaxies, the significance of parameters such as metallicity, radiation field, magnetic field
and mass to a galaxy’s total CO luminosity should become evident. To understand
the physics that regulates these trends, however, detailed studies of the relationship
between CO and H2 on smaller scales are also required. An important investigation
7.2. GMC Properties and Galactic Environment
365
that can be undertaken using the data described in this thesis is to compare the distribution of CO, H I and dust emission associated with individual GMCs in order to
identify and measure the mass of H2 gas that occurs in a “CO-dark” phase. A pilot
study using MAGMA CO and ATCA+Parkes H I data to trace the gas phase, and Herschel and Spitzer data to trace the dust continuum emission between 100 and 500 µm
has tentatively reported the detection of “CO-dark” H2 envelopes surrounding two
LMC GMCs (Roman-Duval et al., 2010); a full investigation using a larger sample of
MAGMA GMCs should be able to confirm whether the ratio between the “CO-bright”
and “CO-dark” H2 mass of a GMC varies as a function of galactic environment, and
estimate the contribution of these H2 envelopes to the LMC’s total molecular mass.
7.2 GMC Properties and Galactic Environment
Another goal of this thesis was to determine whether the physical properties of GMCs
are sensitive to conditions in the local ISM. Previous work on this topic had concluded
that GMCs have roughly homogeneous properties throughout the Local Group: extragalactic GMCs appear to follow similar scaling relations as clouds in the Milky Way,
such that a 105 M⊙ molecular cloud has a similar size, velocity dispersion and CO luminosity regardless of its location. Except for the GMC population of M31, however, the
samples available to past studies contained ≤ 15 clouds and were often biased towards
the most luminous GMCs belonging to each galaxy. By constructing a catalogue of
more than 100 GMCs in the LMC, we have been able to examine the properties of
GMCs as a function of galactic environment within a single galaxy, and to study clouds
that are unremarkable in terms of their CO luminosity and star-formation activity.
Contrary to previous analyses, our investigation has confirmed that the physical properties of GMCs are influenced by their environment. The physical connections that are
suggested by the observed environmental variations in GMC properties have potentially
important implications for our understanding of GMC formation and evolution, and
for our method of observing molecular gas in other galaxies.
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Chapter 7. Concluding Remarks
In particular, several results from this thesis pose a challenge to the conventional view
that GMCs manage to achieve rough dynamical equilibrium. Our analysis of GMC
velocity gradients in Chapter 3 indicated that GMCs in the LMC may remain kinematically coupled to the local interstellar gas, while in Chapter 4 we found that the
GMC velocity dispersion increases with the local H I column density, and that the
internal GMC pressure is only marginally greater than the external kinetic pressure.
Although none of these observations is conclusive, they each query the assumption
of GMC virialisation, and suggest that the dynamical importance of the atomic gas
surrounding GMCs may not have been fully appreciated to date. One possibility is
that the weight of the H I envelope exerts a significant confining force on the molecular
cloud surface, but that the atomic+molecular cloud complex is in hydrostatic equilibrium with the ISM (e.g. Elmegreen, 1989). Another possibility is that the H I envelope
represents a mass reservoir that has grown slowly via accretion (e.g. Fukui et al., 2008)
or been rapidly accumulated in a collision between large-scale interstellar gas flows (e.g.
Vázquez-Semadeni et al., 2007). Quantifying the mass of atomic gas that is physically
associated with MAGMA GMCs and assessing potential signatures of accretion and/or
collisions in the H I line profiles surrounding the GMCs are logical extensions to the
work presented in this thesis that should help to distinguish between these scenarios.
A second unexpected result from our analysis in Chapter 4 was that the CO brightness
of MAGMA GMCs is sensitive to the local stellar mass surface density, Σ∗ : GMCs
coincident with the LMC’s stellar bar have peak CO brightnesses that are higher by
a factor of two than GMCs in the LMC’s outer disk. Though the precise origin of
this variation in hTpk i was unclear, we tentatively attributed it to small-scale physical processes in the ISM, i.e. a higher CO excitation temperature or an increased
dust abundance that reduces the selective photodissociation of CO molecules. Future
research with submillimetre facilities should be able to differentiate between these explanations by conducting an excitation analysis of the higher-J transitions of CO in
LMC clouds, and examining whether the mass fraction of CO-dark H2 gas in a GMC
depends on Σ∗ .
7.3. Molecular Gas and the Radio-FIR Correlation
367
Of more importance, however, will be assessing how severely variations in CO excitation and/or the abundance of CO relative to H2 limit the utility of CO as a probe
of the underlying H2 distribution, not only at high redshift but also within nearby
galaxies. The standard view, based on observations of Milky Way molecular clouds
(e.g. Solomon et al., 1987), is that the CO emission in different GMCs has a similar
excitation temperature, and that the CO-to-H2 conversion factor is not significantly
affected by [CO]/[H2 ] abundance variations since the
12 CO(J
= 1 → 0) transition is
optically thick. Yet if the CO-emitting regions are highly clumped and do not cover
the projected cloud area – this is likely to be the case for MAGMA GMCs – then an
increased abundance of CO relative to H2 will increase the filling fraction f of CO
emission and hence the observed hTpk i (e.g. Wolfire et al., 1993). Although GMCs in
the disks of spiral galaxies may be more like Galactic clouds (f ∼ 1) than Magellanic
ones (f ≪ 1), observational confirmation that hTpk i – and more especially the CO-toH2 conversion factor XCO – do not increase strongly with Σ∗ in these galaxies would
be valuable. Strong variations in XCO with Σ∗ would complicate the interpretation of
recent observations showing that Rmol , the molecular-to-atomic surface density ratio,
varies with galactocentric radius in nearby disk galaxies (e.g. Wong & Blitz, 2002; Blitz
& Rosolowsky, 2006; Leroy et al., 2008). Since Σ∗ also varies with galactocentric radius,
alternative tracers of H2 might be required to distinguish genuine variations in Rmol
from variations in XCO .
7.3 Molecular Gas and the Radio-FIR Correlation
Having examined the properties of LMC GMCs, the final two chapters of this thesis focussed on the molecular gas phase as an agent within the LMC’s interstellar ‘ecosystem’.
A comparison between the luminosity of the LMC at different wavebands – and the star
formation rates that these measurements imply – indicated that the LMC conforms to
several trends observed for other low-luminosity galaxies: it is relatively transparent to
ultraviolet photons (Bell, 2003), and a significant proportion of its cosmic rays escape
the galaxy before losing all their energy to synchrotron radiation (Klein et al., 1991).
368
Chapter 7. Concluding Remarks
In contrast to recent studies that have emphasised the success of calorimetry in explaining the local radio-FIR correlation within disk galaxies (e.g. Murphy et al., 2006b,
2008), our detailed examination of gas and dust tracers in the LMC showed that the
non-thermal radio emission is coupled to the gas column density for regions covering
roughly of the H I disk, and that the exponent of the local radio-FIR correlation in
these regions is consistent with the expectation from a physical coupling between the
gas density and the magnetic field strength.
In light of the long-standing debate about the origin of the global radio-FIR correlation
(e.g. Lacki et al., 2010, and references therein), our results in the LMC clearly merit
further investigation. The main limitation of our current analysis is that agreement
between the observed correlations and the predictions of the basic B −ρ coupling model
can be obtained using several combinations of plausible assumptions regarding the dustto-gas ratio, the cosmic ray distribution, the exponent of the scaling between B and ρ,
and whether equipartition between the magnetic field and cosmic ray energy densities
is attained. A rigorous test of B −ρ coupling would require tighter empirical constraints
on all these parameters; direct measurements of the magnetic field strength throughout
the LMC disk would be even more valuable. There is also room for improvement in
our estimate for the non-thermal component of the LMC’s 1.4 GHz radio luminosity.
Observations of the dust continuum emission at wavelengths between 250 and 500 µm
by Herschel will reduce the degeneracy between the dust temperature, emissivity and
abundance (Gordon et al., 2010) that affects our estimate for the H α attenuation, while
spatial variations in the electron temperature of the ionized gas could be assessed using
O II and H α data from the Magellanic Cloud Emission Line Survey (MCELS, Smith &
MCELS Team, 1998). In the future, multi-frequency (0.7 to 14 GHz) radio continuum
surveys by telescopes such as Australian Square Kilometre Array Pathfinder (ASKAP)
and MeerKAT (van Loon et al., 2010) will construct maps of the LMC’s radio spectral
index and thermal fraction; these should be used to verify the thermal/non-thermal
decomposition that we have described in Chapter 5. Finally, resolved studies in other
galaxies spanning the full range of ISM properties, such as magnetic field strength,
dust abundance, star formation activity and photon energy density, will be required
7.4. Future Outlook: Cosmic Star Formation and the LMC
369
to determine whether B − ρ coupling is relevant to the origin of the global radio-FIR
correlation.
7.4 Future Outlook: Cosmic Star Formation and the LMC
The LMC is central to many fields within modern astronomy, including calibrating
the cosmic distance scale (Schaefer, 2008, and references therein), empirical searches
for baryonic hot haloes (e.g. Anderson & Bregman, 2010) and dark matter candidates
(e.g. Alcock et al., 1997), and understanding the physics of interstellar turbulence (e.g.
Elmegreen et al., 2001; Block et al., 2010), supernovae (e.g. Badenes et al., 2009) and
galaxy interactions (e.g. Connors et al., 2006). As we noted in the Introduction, it
also offers the best view of the interaction between the ISM and star formation in any
galaxy. Due to its low metallicity and dust abundance, moreover, the LMC is an ideal
laboratory to test whether models of local star formation and molecular gas will continue to hold at higher redshift, when gas in galaxies was less chemically enriched.
In the immediate future, an important milestone in LMC star formation studies will be
the construction of a complete young stellar object (YSO) catalogue that extends to
faint limiting magnitudes. Current infrared facilities can resolve individual stars within
the LMC, but the secure identification of YSOs, especially low-mass YSOs, remains
time-consuming (e.g. Gruendl & Chu, 2009). Estimating the level of star formation
activity within an extragalactic GMC through a census of its YSO population will
provide a key test of monochromatic star formation rate diagnostics and an independent
estimate for molecular cloud lifetimes. Slightly further ahead, the Galactic Australian
Square Kilometre Array Pathfinder survey (GASKAP, Stanimirovič et al., 2010) will
substantially improve our understanding of the atomic and molecular gas in the LMC.
GASKAP will map the H I emission in the Magellanic System with high sensitivity
(Tmb ∼ 0.2 K) and resolution (20′′ , 0.2 km s−1 ), and obtain hundreds of H I absorption
spectra for sightlines through the LMC’s disk. The result will be a detailed picture
of the distribution, temperature, density and column density of the cold and warm
atomic gas phases. GASKAP will also map OH emission in the LMC, yielding an
370
Chapter 7. Concluding Remarks
unprecedented map of the diffuse molecular gas phase, which to date has only been
studied along pencil beams (Tumlinson et al., 2002), or inferred within restricted fields
from CO, H I and dust maps (e.g. Roman-Duval et al., 2010). On the horizon, of
course, lie ALMA and the Square Kilometre Array (SKA). These telescopes will obtain
resolved maps of the molecular and atomic gas in galaxies out to z ∼ 1 and beyond
(Wiklind, 2001; van der Hulst et al., 2004), allowing us to observe directly the cycling
of gas between stars and the ISM during the epoch when cosmic star formation was
at its peak. While ALMA and the SKA are likely to revolutionise our view of neutral
gas in the Universe, the LMC will remain indispensable for interpreting the physical
meaning of their results.
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