Download Investigating the Spectral Energy Distribution TARA JILL PARKIN

Investigating the Spectral Energy Distribution
within the Dwarf Irregular Galaxy IC 10
by
TARA JILL PARKIN
A thesis submitted to the
Department of Physics, Engineering Physics, and Astronomy
in conformity with the requirements for
the degree of Master of Science
Queen’s University
Kingston, Ontario, Canada
September, 2008
c TARA JILL PARKIN, 2008
Copyright Abstract
We present new submillimetre images of the dwarf irregular galaxy IC 10, taken
with the Submillimeter Bolometer Common-User Array, mounted on the James Clerk
Maxwell Telescope. Combining this new data with archival data from the 2MASS
survey, ISO, Spitzer IRAC and MIPS, and the VLA, we plot the observed spectral energy distributions from 1.24 µm to 850 µm for two star forming regions within IC 10,
namely IC 10 SE and IC 10 NW. The spectral energy distributions were subsequently
modelled using a dust model with PAHs, and silicate and graphite dust grain components. This is the first time that well-constrained spectral energy distribution models
of two individual regions within IC 10 have been presented. From our results, we find
that IC 10 SE and IC 10 NW share the same physical characteristics in most cases,
such as the gas-to-dust mass ratio, the mass fraction of PAHs comprising the total
dust mass, and the fraction of PAHs that are ionised. The most significant difference
is seen in the peak wavelengths of the SEDs, which are ∼ 70 µm and ∼ 45 µm for
IC 10 SE and IC 10 NW, respectively. From this we conclude that the primary dust
component within IC 10 NW is warmer than that of IC 10 SE, due to the hot young
stars at the heart of the star forming region within IC 10 NW having a larger heating
effect on the nearby dust than the interstellar radiation field. The similar environments of these two regions lead us to suggest that the star formation taking place
i
within them was triggered by the same starburst, and that both stellar populations
evolved together. We also find that IC 10 has physical conditions that are common
amongst other low-metallicity, dwarf irregular galaxies, implying that IC 10 does not
have an abnormal interstellar medium in these regions.
ii
Acknowledgements
First and foremost, I would like to thank my supervisors Dr. Judith Irwin and Dr.
Suzanne Madden for their guidance and support throughout the course of my research,
and for giving me the opportunity to work in France for part of my project. I would
also like to thank Dr. Sacha Hony and Douglas Rubin for their patience and endless
support, and for sharing their knowledge with me.
I would like to thank Dr. Christine Wilson for providing me with the SCUBA data,
and Dr. George Bendo for helping me with the Spitzer MIPS data and our Spitzer
proposal. I also send a special thank you to Dr. Frédéric Galliano for allowing me to
use his SED model for part of my thesis.
Finally I would like to acknowledge and thank everyone from the Service d’Astrophysique at the CEA Saclay, France, for inviting me to work with them for six months.
Without their efforts I would not have had the experience of a lifetime.
This research was funded in part by the R. S. McLaughlin Fellowship awarded by
Queen’s University.
iii
Table of Contents
Abstract
i
Acknowledgements
iii
Table of Contents
iv
List of Tables
vii
List of Figures
ix
Chapter 1:
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1
Dwarf galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2
The spectral energy distribution (SED) of a galaxy . . . . . . . . . .
7
1.3
The interstellar medium (ISM) . . . . . . . . . . . . . . . . . . . . . .
8
1.4
IC 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
Chapter 2:
Data Reduction and Analysis . . . . . . . . . . . . . . . .
31
2.1
ISO data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
2.2
Spitzer data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
iv
2.3
JCMT data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.4
Supplementary data . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
2.5
Background flux evaluation
. . . . . . . . . . . . . . . . . . . . . . .
45
2.6
Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
2.7
Flux evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
2.8
Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
Chapter 3:
Results
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3.1
Morphology of IC 10 . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3.2
SED modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
3.3
Model fitting results . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
Chapter 4:
Analysis and discussion
. . . . . . . . . . . . . . . . . . .
99
4.1
Spatial analysis of IC 10 . . . . . . . . . . . . . . . . . . . . . . . . .
99
4.2
IC 10 SE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3
IC 10 NW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4
Comparing IC 10 SE and IC 10 NW . . . . . . . . . . . . . . . . . . 110
4.5
A comparison with other galaxies . . . . . . . . . . . . . . . . . . . . 114
Chapter 5:
Summary and Conclusions
Bibliography
. . . . . . . . . . . . . . . . . 122
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
v
Appendix A:
List of Acronyms
. . . . . . . . . . . . . . . . . . . . . . 137
Appendix B:
Box Method IDL Code
. . . . . . . . . . . . . . . . . . 139
B.1 “bkgrd box overplot.pro” . . . . . . . . . . . . . . . . . . . . . . . . . 139
B.2 “bkgrd box method.pro” . . . . . . . . . . . . . . . . . . . . . . . . . 142
Appendix C:
Gaussian Method IDL Code
vi
. . . . . . . . . . . . . . . 144
List of Tables
1.1
Characteristics of the various components of the ISM. . . . . . . . . .
1.2
Various parameters pertaining to IC 10 as published to date, adjusted
11
to our adopted distance. . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.1
Characteristics of the original images. . . . . . . . . . . . . . . . . . .
36
2.2
Zero-point magnitude conversions for 2MASS data. . . . . . . . . . .
43
2.3
Background evaluation comparison. . . . . . . . . . . . . . . . . . . .
49
2.4
Aperture characteristics. . . . . . . . . . . . . . . . . . . . . . . . . .
54
2.5
Multiplicative factors for aperture correction. . . . . . . . . . . . . . .
57
2.6
Radio data points used to extract radio continuum equation. . . . . .
61
2.7
Flux in apertures and associated error contributions for IC 10 SE. . .
63
2.8
Flux in apertures and associated error contributions for IC 10 NW. .
64
3.1
Size ranges and mass densities for each dust component. . . . . . . .
88
3.2
Dilution factors and temperatures of the four-component ISRF. . . .
89
3.3
Model Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
3.4
The values of the eight parameters determined by the best-fitting
model, for both IC 10 SE and IC 10 NW. . . . . . . . . . . . . . . . .
4.1
98
A comparison between derived values for IC 10 SE and IC 10 NW. . . 111
vii
4.2
A comparison of the important physical parameters derived for IC 10 SE
and IC 10 NW with those of several other galaxies. . . . . . . . . . . 118
viii
List of Figures
1.1
Dwarf elliptical galaxy IC 225. . . . . . . . . . . . . . . . . . . . . . .
5
1.2
Dwarf irregular galaxy IC 1613. . . . . . . . . . . . . . . . . . . . . .
6
1.3
An example of a dust SED from Galliano et al. (2003) . . . . . . . . .
8
1.4
A schematic of the classical PDR region. . . . . . . . . . . . . . . . .
9
1.5
A schematic of the various components of the ISM. . . . . . . . . . .
10
1.6
A single benzene molecule. . . . . . . . . . . . . . . . . . . . . . . . .
15
1.7
Examples of small PAHs. . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.8
Examples of large symmetrical PAHs. . . . . . . . . . . . . . . . . . .
16
1.9
The IR spectra for NGC7027 and the Orion Bar (H2S1). . . . . . . .
18
1.10 An optical image of IC 10 from the Digitized Sky Survey. . . . . . . .
21
1.11 H i distribution in IC 10 with holes identified. . . . . . . . . . . . . .
23
1.12 The best-fitting SED of IC 10 SE as determined by Bolatto et al. (2000). 28
2.1
Raster mode schematic diagram. . . . . . . . . . . . . . . . . . . . . .
33
2.2
The 850 µm image of IC 10 with the negative bowl left untreated. . .
38
2.3
The 850 µm image convolved to eliminate source structure. . . . . . .
39
2.4
850 µm image comprising data reduced with SURF. . . . . . . . . . .
41
2.5
Boxes used for background evaluation with the “box method”. . . . .
46
2.6
Background evaluation using Gaussian method. . . . . . . . . . . . .
48
ix
2.7
Point spread functions. . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.8
Apertures centred on IC 10 SE and IC 10 NW.
. . . . . . . . . . . .
53
3.1a J-band (1.24 µm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3.1b H-band (1.66 µm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
3.1c K-band (2.16 µm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.1d 3.6 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
3.1e 4.5 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3.1f 5.8 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.1g 6.75 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
3.1h 8 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.1i 11.4 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
3.1j 15 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
3.1k 24 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
3.1l 70 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
3.1m 160 µm
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
3.1n 450 µm
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
3.1o 850 µm
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.1p 3.55 cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
3.1q 6.2 cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
3.2
The model SED for IC 10 SE. . . . . . . . . . . . . . . . . . . . . . .
96
3.3
The model SED for IC 10 NW. . . . . . . . . . . . . . . . . . . . . .
97
4.1
24 µm contours overlaid onto the 8 µm image. . . . . . . . . . . . . . 101
4.2
24 µm contours overlaid onto the 850 µm image. . . . . . . . . . . . . 102
4.3
8 µm contours overlaid onto the 850 µm image. . . . . . . . . . . . . 103
x
4.4
Our model SED for IC 10 SE in units of L⊙ Hz−1 . . . . . . . . . . . . 115
4.5
Our model SED for IC 10 NW in units of L⊙ Hz−1 . . . . . . . . . . . 116
4.6
The model SEDs for four different regions within the LMC (Bernard
et al., 2008). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.7
The model SED of NGC 1569. . . . . . . . . . . . . . . . . . . . . . . 119
4.8
Model SEDs for the plane and diffuse ISM of the Milky Way. . . . . . 121
xi
Chapter 1
Introduction
Nearby galaxies are of great interest to astronomers from all areas of observational
astrophysical research, primarily because of their proximity to us in the Universe.
The advanced telescopes and instruments that we have at our disposal today make
it possible to study the various characteristics of galaxies with higher resolution than
ever before. With this comes the possibility to study individual regions within a single
galaxy and investigate how the various components making up each galaxy such as
the stellar content and the interstellar medium (ISM) influence each other.
The effects that star formation (SF) and the ISM have on each other are very
important for us to understand. Detailed studies of current star formation within a
galaxy, as well as the contents of the ISM can give us clues about the star formation
history of the galaxy (Galliano et al., 2003). Aspects of the star formation history,
such as the frequency of star forming episodes, the types of stars produced, and the
star formation rate all play important roles in the star formation history of a galaxy
and we can use this information to study the evolution of a galaxy as a whole. This
in turn may lead us to advances in our understanding of how the Universe itself has
1
CHAPTER 1. INTRODUCTION
2
evolved.
In particular, the present-day structure of the ISM of a galaxy is strongly dependent on the evolution of its star formation rate (SFR). Clues as to previous episodes
of star formation rates can be found in the various stellar populations within the
galaxy (Tielens, 1995). Low-mass stars with long lifetimes were formed in earlier
star formation episodes and the ejected material from the outer layers of these stars
(ejecta) contributes more hydrogen (H) gas to the ISM by mass than the more massive
stars. On the other hand, high-mass stars are connected to more recent star forming
rates, as they have relatively short lifetimes. During their lifetime they contribute
to the ISM through stellar winds or supernovae, metals such as carbon (C), oxygen
(O) or iron (Fe), large amounts of mechanical energy and a strong flux of high-energy
photons. All stars enrich the ISM with their ejecta through this feedback effect, and
impact how a galaxy evolves.
Material (i.e. gas and dust) from the outer layers of evolved stars mixes with
the contents of the ISM already present, changing the chemical make-up of the ISM
over time. The abundance of metals1 increases, therefore changing the metallicity,
Z/Z⊙ , of the galaxy, where Z⊙ is the metallicity of the Sun. Note that sometimes
the metallicity of a galaxy is characterised by the abundance of oxygen in the galaxy,
which is given by
AO = log(NO /NH ) + 12.0,
(1.1)
where NO and NH are the number abundances per cm−2 of oxygen and hydrogen,
respectively. For reference, the number abundance of hydrogen in the Sun is 12.00,
and its oxygen abundance, AO,⊙ , is 8.83 (Grevesse & Sauval, 1998). Since virtually
1
In astronomy, all elements aside from hydrogen and helium are called metals.
CHAPTER 1. INTRODUCTION
3
all metals are produced through the evolution of stars, metallicity can also give us
insight into the star formation history of a galaxy. A galaxy with a high metallicity
would imply that several generations of stars are present, meaning it is at a later
stage in its evolution. A galaxy with a low metallicity would be at a younger stage
of evolution, with fewer generations of stars populating the galaxy.
Another method of probing the ISM of a galaxy is to study its dust. Dust plays a
key role in the overall heating and cooling processes throughout the galaxy, a direct
result of dust being very efficient at blocking optical light. Through the absorption
of stellar light and its subsequent re-emission at longer wavelengths, the dust reveals
itself optimally at infrared (IR) wavelengths. In addition, important large molecules
called Polycyclic Aromatic Hydrocarbons (PAHs; see Section 1.3.3) that may trace
regions of star formation (Tielens et al., 2004), are thought to make themselves known
through emission lines at mid-infrared (MIR) wavelengths. However, it is important
to note that there is some uncertainty as to whether or not PAHs are, in fact, the
source of these IR emission lines. By analysing the dust Spectral Energy Distribution
(SED; see Section 1.2) of a galaxy, spanning from near-infrared (NIR) wavelengths to
the submillimetre (submm), we can determine the values of certain parameters that
govern the evolution of the galaxy itself. Examples of these characteristics include its
metallicity, the age of the galaxy, the initial mass function (IMF) and even the types
of stars in the galaxy (Galliano et al., 2003). The IMF of a particular group of stars
measures how many stars of a specific mass are formed as a function of stellar mass.
The definition of the IMF, ξ, is (Hunter, 2001)
ξ(log m) = (ln 10)mf (m),
(1.2)
4
CHAPTER 1. INTRODUCTION
where m is the stellar mass, and f (m) = AmΓ−1 is the stellar mass function (the
number of stars per mass bin as observed) with A a constant. Empirically we determine the slope, Γ, of the IMF by plotting stars in a log-log plot of the number
of stars within a given mass range versus the average stellar mass within that range.
Substituting f (m) into Equation (1.2) we obtain
ξ(log m) = CmΓ ,
(1.3)
where C = A(ln 10). Taking the log of both sides and differentiating with respect to
log m we obtain the equation for Γ:
Γ=
∂(log ξ(log m)) .
∂ log m
m
(1.4)
The results of the model SED will give us constraints on parameters such as the dust
mass, stellar mass or PAH abundance, which we can then use to infer the characteristics of the galaxy’s evolution.
1.1
Dwarf galaxies
Local dwarf galaxies are of particular interest because they come in a wide variety of
morphologies, surface brightnesses and masses. In a very broad sense, dwarf galaxies generally fall into two categories, dwarf ellipticals (dE) and dwarf irregulars (dI).
Dwarf ellipticals, such as IC 225, shown in Figure 1.1, are small, ellipsoidal galaxies
with masses ranging between 107 and 109 solar masses (M⊙ ) and diameters ranging
CHAPTER 1. INTRODUCTION
5
Figure 1.1: A Digitized Sky Survey optical image of dwarf elliptical galaxy IC 225.
Image from “http://archive.stsci.edu/dss/index.html”.
between 1 and 10 kpc 2 . They also differ from their larger counterparts, the normal
elliptical galaxies, as they have lower surface brightnesses for a given absolute magnitude, and also lower metallicities. One other subcategory of dwarf galaxies is the
blue compact dwarf (BCD) galaxy (Carrol & Ostlie, 1996). These galaxies are very
blue and have relatively large amounts of gas (in comparison to other dEs, which are
normally gas depleted), indicative of recent star formation and a young stellar population. They normally have diameters less than 3 kpc and a mass of ∼ 109 M⊙ , but
their large luminosities lead to low mass-to-light ratios. A BCD galaxy is sometimes
classified as a dI galaxy, as their characteristics are very similar.
Dwarf irregular galaxies on the other hand, such as IC 1613 in Figure 1.2, are very
irregular in shape and possess a large abundance of gas and dust, as they are very blue
in colour, especially in their nuclei. The blue colour is indicative of young, hot stars,
meaning star formation is likely still ongoing in these galaxies, unlike the dEs where
2
One parsec (pc) is equal to 3.086 × 1018 cm or 3.26 light years.
CHAPTER 1. INTRODUCTION
6
Figure 1.2: A Digitized Sky Survey optical image of dwarf irregular galaxy IC 1613.
Image from “http://archive.stsci.edu/dss/index.html”.
star formation has, for the most part, ended. An important consequence of this young
stellar population is that many dI galaxies have low-metallicities, as evolved stars
have not enriched the ISM with metals. IC 10, the focus of this project is normally
classified as a dI galaxy; however, some authors (e.g. Richer et al., 2001) classify it
as a BCD galaxy. For this project we will use the more common classification, and
assume IC 10 is a dwarf irregular galaxy.
Dwarf irregular galaxies are ideal environments in which to study star formation
and its impact on the ISM (and vice versa). Dwarf galaxies are too small in mass
to promote the development of spiral arms, such as those we see in a spiral galaxy,
yet in spite of this, dense regions still exist where stellar formation can occur (Hunter
& Gallagher, 1989). Investigating the different processes of star formation between
different types of galaxies can lead to a better understanding of the general properties
of star formation that exist in all environments. Furthermore, dwarf irregular galaxies
may, in fact, represent the primordial galaxies that existed during the early stages
of the Universe (Madden et al., 2006), and became the progenitors of some of the
CHAPTER 1. INTRODUCTION
7
larger galaxies we see today (Hunter & Elmegreen, 2004). Many of them possess
low-metallicities compared to the Solar value. This suggests there has not been much
feedback from evolved stars, thereby insinuating that they could be at similar stages
of chemical evolution as young (distant) galaxies in the early universe (Galliano et al.,
2003).
1.2
The spectral energy distribution (SED) of a
galaxy
As already mentioned, star formation and evolution have a strong impact on the
ISM, and likewise the composition of the ISM can affect the chemical structure and
production of new stars. One way to conduct an in-depth study of the ISM in a
galaxy is to plot its spectral energy distribution (SED). A SED is a plot of luminosity
per unit frequency multiplied by frequency (νLν ) versus wavelength for some ranges
of wavelengths, making it an excellent tool to study the various components of the
ISM. The focus of this thesis is on the dust SED, which spans roughly from the
near-infrared (NIR) to mid-infrared (MIR) and through to submillimetre (submm)
wavelengths (e.g. from the J, H and K NIR bands (see Table 2.1 and Section 2.4.1 for
details) through 450 µm or 850 µm). If there are enough data points such that the
SED is well defined, then it can be modelled. The results of the model dust SED can
tell us the relative abundances of the various components of the ISM such as hot and
warm dust, PAHs and other molecules, and cold dust. An example of a dust SED
is shown in Figure 1.3 (Galliano et al., 2003). This is a model of the dust SED of
NGC 1569 which contains four main components: big grains, very small grains and
CHAPTER 1. INTRODUCTION
8
Figure 1.3: The modelled dust SED of NGC 1569 as presented in Galliano et al.
(2003). The components contributing to the overall SED are big grains (dash-dotted
line) of dust, very small grains (dotted line) of dust, polycyclic aromatic hydrocarbons
(dashed line) and very cold dust grains (dash-dot-dot-dot line). Observed data are
shown as crosses with error bars, where the horizontal error bars represent the filter
bandwidth for a given wavelength, not physical error).
very cold grains of dust, and PAHs.
1.3
The interstellar medium (ISM)
The ISM of a galaxy comprises gas and dust found in wide variety of environments
such as molecular clouds, ionised hydrogen (H ii) regions, and photodissociation regions3 (PDRs). The gas content is far more abundant than the dust component, as
90 % of the ISM (and the gas in the Universe as well) is comprised of hydrogen.
3
These regions are sometimes known as photon-dominated regions.
CHAPTER 1. INTRODUCTION
Figure 1.4: A schematic of the classical PDR region. The centre is an H ii region
(dark grey region), usually in the vicinity of hot O and B stars. The outermost region
is composed of molecular hydrogen, H2 (white region). The region in the middle is the
PDR region (pale grey region), where H2 is dissociated by the FUV photons emitted
by nearby stars.
A PDR is simply defined as any region dominated by high energy far ultraviolet
(FUV) photons, which can dissociate and even ionise molecules (primarily H2 but
other molecules as well, depending on the location of the PDR). Examples of these
environments include the more classical definition of a PDR, the environment between
regions of ionised and molecular hydrogen located in the proximity of luminous stars
(see Figure 1.4), molecular clouds and even regions of neutral hydrogen in the ISM
(Tielens, 2005). In Figure 1.5 we show a schematic from Kwok (2007) of the different
components that make up a typical ISM. Also included in this diagram are some of
the characteristics of each region, such as particle density and temperature.
In Table 1.1 we present a summary of the different environments found in the ISM,
along with their most important characteristics. Below we give a quick summary of
each of the primary components of the ISM. For more details see Kwok (2007) and
Tielens (2005).
9
CHAPTER 1. INTRODUCTION
Figure 1.5: A schematic of the various components of the ISM. Temperature, number density of atomic hydrogen
and typical tracers of each medium are quoted. Image from Kwok (2007).
10
11
CHAPTER 1. INTRODUCTION
Table 1.1: Characteristics of the various components of the ISM. Table information
from Kwok (2007)
ISM
Component
Hot ionised
medium
Warm ionised
medium
Warm neutral
medium
Atomic cold
neutral medium
Molecular cold
neutral medium
Molecular hot
cores
a
Common
Designation
Coronal
gas
Diffuse
ionised gas
Intercloud H ic
Diffuse
clouds
Molecular clouds,
dark clouds
Protostellar
cores
Temperature,
T (K)
106
Hydrogen Number
Density, nH (cm−3 )a
0.003
State of
Hydrogen
H iib
104
> 10
H ii
8 × 103 – 104
0.1
Hi
100
10 –100
H i + H2 d
0 – 50
103 –105
H2
100 – 300
> 106
H2
The number density is of molecular hydrogen, nH2 for molecular clouds and cores.
Ionised hydrogen
c
Neutral hydrogen
d
Molecular hydrogen
b
CHAPTER 1. INTRODUCTION
1.3.1
12
Gas
There are three primary environments in which hydrogen is found: neutral hydrogen
(H i), ionised hydrogen (H ii) and molecular hydrogen (H2 ). The majority of the
volume of the ISM is likely comprised of hot H ii regions. Regions of H ii have high
temperatures due to their proximity to molecular clouds containing young, hot stars
(see Figure 1.5). The density of these regions appears to correlate with size: more
dense regions tend to be smaller and more compact than those of lower densities.
Typical tracers of H ii include emission lines at optical, IR and UV wavelengths due
to ions, and through the Hα recombination line. In addition they can also be traced
with continuum radiation due to free electrons (see Section 2.8.3).
Neutral hydrogen is found in both cold environments such as diffuse H i clouds,
and warmer environments called intercloud regions. The most common tracer of H i
is the 21 cm line; however, if there are bright stars located behind a H i region along
its line of sight, optical and UV absorption lines can also reveal its presence (Tielens,
2005).
Molecular hydrogen is most often found in giant molecular clouds. These regions
are typically dense and very cold and with temperatures of ∼ 10 K and average particle densities of ∼ 200 cm−3 with core densities of up to 104 cm−3 . They have a size of
about 40 pc and a mass of order 105 M⊙ , although these numbers can vary with different clouds (Tielens, 2005). The bulk of the molecular hydrogen found in molecular
clouds cannot be observed directly because it does not possess a net dipole moment,
and therefore cannot radiate. Therefore, the presence of CO molecules is often used to
trace H2 via an empirically derived conversion factor of ∼ 2 ×1020 cm−2 (K km s−1 )−1
for the Galaxy, though this number may not be valid for all environments (see Leroy
CHAPTER 1. INTRODUCTION
13
et al. (2006) for a discussion on this factor).
1.3.2
Dust
Dust manifests itself primarily in the infrared and the submillimetre wavebands. It
is found in a variety of carbon, silicate or composite forms and in numerous types of
environments (Tielens, 1998). It is observed in all three hydrogen dominated regions
(i.e. H i, H ii, and H2 ); however, dust can persevere the longest in molecular clouds
where H2 is the primary form of hydrogen. The high density and cold temperatures
of these regions makes them ideal environments for dust to exist and interact with
the gas. The inner regions of the cloud are protected from far-ultraviolet photons by
the outer layers, and the cold temperatures allow for gaseous material to condense
into a solid state. As a result, molecular clouds are the target of most studies of dust.
Grains of dust form in the remnants of older stars in the giant phase of their
evolution, as well as in novae and supernovae. In short, dust develops in environments
where metals have condensed into a solid form and can potentially coagulate. There
are several types of dust grains, with the majority possessing an amorphous structure,
meaning that they do not have a very organised lattice structure between atoms.
These grains can be either carbon-based or silicon-based, depending on the chemical
composition of the parent star (Tielens et al., 2005).
The temperature range of dust is very broad. Cold, large dust grains in radiative
equilibrium with the interstellar radiation field have temperatures of ∼ 15 K and
re-emit any absorbed stellar light at far-infrared (FIR) and submm wavelengths (i.e.
> 60 µm). Hot dust emits in NIR and MIR bands ∼ 4–60 µm and can have temperatures upwards of ∼ 500 K (Tielens, 2005). The high temperatures are primarily
CHAPTER 1. INTRODUCTION
14
from PAHs (see Section 1.3.3) or very small grains which are heated by single photons
up to extreme temperatures and then quickly radiate at NIR and MIR wavelengths,
leading to large temperature fluctuations within the grains.
In the context of star formation and our ability to observe star formation regions,
dust can be a problem at optical wavelengths, as it can block the optical and UV
light emitted by new stars at the core of a molecular cloud. However, it absorbs
this light and re-emits it at infrared wavelengths, contributing to the processes of
heating and cooling taking place in the ISM (Galliano et al., 2003). Depending on
the size of the grain of dust, the wavelengths of emitted light will vary, allowing
the identification of the different types of dust from a spectrum. Large dust grains
may be able to reach a state of thermodynamic equilibrium with their surroundings
after some time following the absorption of a photon, therefore self-radiating at a
steady temperature (Kwok, 2007). On the other hand, small grains can increase
their temperatures drastically with the absorption of a single photon, then cool off
again upon re-emission via stochastic heating. As most environments where dust is
found have relatively low particle densities, gas and dust temperatures are not often
linked together, and can be significantly different due to a lack of collisional heating
of particles (Kwok, 2007). Furthermore, if the dust grains are in a molecular cloud
with a central source of stars the temperature of individual dust grains will vary with
distance from the source. Therefore, an SED can be an excellent aid in determining
the properties of the dust in the proximity of the source, as well as the radiation field
of the source.
Another important characteristic of a galaxy is its gas-to-dust mass ratio (where
the gas mass here is the total mass of hydrogen). This ratio will give the relative
CHAPTER 1. INTRODUCTION
15
Figure 1.6: A single benzene molecule.
Image taken from http://www.amacad.org/images/benzene.gif
contributions of gas and dust to the total mass of a galaxy, and this can be used
as an indicator for the evolutionary state of the galaxy. A higher gas-to-dust ratio
would suggest a galaxy is at an earlier stage of evolution than one with a lower ratio,
as a more evolved galaxy would be depleted of the gas locked up in stars and their
remnants. Values for the gas-to-dust mass ratio for the Milky Way vary between local
environments but the typical factor on a global scale is about ∼ 110 (Galliano et al.,
2005).
1.3.3
Polycyclic Aromatic Hydrocarbons (PAHs)
Polycyclic aromatic hydrocarbons are molecules which have the simple benzene ring
as their primary building blocks. Benzene is a planar (two-dimensional), hexagonal
molecule comprising six carbon (C) atoms joined together to form a ring, with one
hydrogen (H) atom attached to each carbon atom. Figure 1.6 shows a schematic
of a benzene (C6 H6 ) molecule. Note that sometimes the H atoms are not shown
on a benzene molecule or PAH but it is implied that they are present. PAHs are
groups of benzene rings joined together with the hydrogen atoms attached only to
CHAPTER 1. INTRODUCTION
16
Figure 1.7: Examples of small PAHs. Image taken from “chemical compound.”
Encyclopædia Britannica. 2008. Encyclopædia Britannica Online. 25 June 2008
<http://www.britannica.com/eb/article-79584>.
Figure 1.8: Examples of large symmetrical PAHs (Bauschlicher et al., 2008).
the outermost C atoms. Some examples of PAHs are shown in Figures 1.7 and 1.8.
PAHs play an important role in numerous galactic environments. They are evident
in most regions of the ISM, as well as various objects, such as young stellar objects,
galactic nuclei, nebulae, or H ii regions (Peeters et al., 2004; Tielens et al., 2004).
The PAH molecules are easily ionised by local FUV photons and as a result, gas in
the region is heated by the free electrons via the photo-electric effect (Tielens et al.,
2004). In their ionised form they contribute significantly to the overall balance of
CHAPTER 1. INTRODUCTION
17
charge in a photodissociation region (PDR) or a molecular cloud. In addition, their
abundance can drastically change the degree of ionisation within a region. If there
is a very low abundance of PAHs, then the degree of ionisation is primarily affected
by the abundance of heavy metals within the host cloud. On the other hand, if the
abundance of PAHs is high, the degree of ionisation is low in all circumstances, as free
electrons can easily attach themselves to neutral PAHs creating negatively charged
PAHs. These, in turn, will recombine with positively ionised PAHs or other molecules
present. As a result of these interactions between PAHs and their environment, the
chemical composition of the host region can be altered significantly (Tielens et al.,
2004).
The emission lines in the MIR thought to be from PAHs can be excellent tools
to study the physical conditions in which they are situated. The most prominent
occur at λ 3.3, 6.2, 7.7, 8.6 and 11.2 µm (Tielens et al., 2004), and are due to the
relaxation of various stretching and bending vibrational modes of the molecule. In
Figure 1.9 we show two examples of infrared spectra with the emission lines and their
corresponding modes, from Peeters et al. (2004). These features are known to vary
from source to source due to the local physical conditions (Peeters et al., 2004; Tielens
et al., 2004). For example, the strength of the lines corresponding to compact H ii
regions with significant amounts of dust are much weaker due to the absorption of
the FUV photons by the dust. PAHs also trace conditions of star forming regions
as they are excited or ionised by photons emitted by the hot stars in an H ii region;
they can also be destroyed by the hard radiation near or within the H ii region (Haas
et al., 2002). Therefore, observation and analysis of PAH emission can be very useful
in examining the nature of a particular locale within a galaxy.
CHAPTER 1. INTRODUCTION
18
Figure 1.9: The IR spectra for NGC 7027 and the Orion Bar (H2S1), including
the prominent PAH emission lines. The spectra are shaded to reveal detail. The
vibrational modes corresponding to the PAH emission lines are also shown at the
top, along with emission plateaux which may or may not be related to the PAH
features. Image from Peeters et al. (2004).
CHAPTER 1. INTRODUCTION
1.4
19
IC 10
From the earliest publications pertaining to IC 10 (e.g. Mayall, 1935, and references
therein) in the early 20th century, this galaxy has been a fascination to many astronomers. It is a member of the Local Group of galaxies4 , with a distance of approximately 0.82 Mpc (Wilson et al., 1996), although other recently published values range
between 0.66 Mpc (Sakai et al., 1999) and 0.95 Mpc (Hunter, 2001). Determining an
accurate distance to IC 10 has proven quite difficult, as it lies almost in the Galactic
plane, with a Galactic latitude of −3.◦ 3 (Hunter, 2001). Accurate determinations of
the reddening due to the foreground dust in our galaxy must be made before the
distance can be calculated. Current values of the total reddening, E(B − V )t tend
to fall between 0.5 − 1.6 magnitudes (mag), with a typical value of 0.77 (Massey &
Armandroff, 1995; Hunter, 2001). In Table 1.2 we present a full list of parameters for
IC 10, obtained from various publications.
IC 10 (see Figure 1.10 for optical image from the Digitized Sky Survey5 ) is generally classified as a dwarf irregular galaxy which has undergone a recent episode of star
formation; however, Richer et al. (2001) have classified it as a Blue Compact Dwarf
(BCD) galaxy (see Section 1.1 for the definitions of these galaxy types). Regardless
of how IC 10 is classified, it remains that it has an unusually high star formation
rate of 0.03 M⊙ yr−1 kpc−2 (Hunter, 2001), when compared to other irregular galaxies. Most irregular galaxies have star formation rates that fall in the range less than
4
The Local Group consists of about 35 galaxies dominated by our Milky Way and the Andromeda
Galaxy (also known as M 31). The rest of the members are dwarf galaxies some of which are satellites
of the Milky Way and Andromeda.
5
The Digitized Sky Surveys were produced at the Space Telescope Science Institute under United
States Government grant NAG W-2166. The images of these surveys are based on photographic data
obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope.
The plates were processed into the present compressed digital form with the permission of these
institutions.
20
CHAPTER 1. INTRODUCTION
Table 1.2: Various parameters pertaining to IC 10 as published to date, adjusted to
our adopted distance.
Parameter
Distance, D
Galactic Latitude, b
Inclination, i
Absolute Magnitude, MB
Star Formation Rate
Total reddening, E(B − V )t
H i Mass
Molecular gas mass
Metallicity, log(O/H) + 12; Z/Z⊙
Value
0.82 Mpca
−3.◦ 3b
(35 ± 5)◦c
−16.15 magb
0.03 M⊙ yr−1 kpc−2, b
0.77 magb
(1 − 2) × 108 M⊙ d
2.96 × 106 M⊙ e
8.17; ∼ 1/6f
a
Wilson et al. (1996)
Hunter (2001)
c
Shostak (1974)
d
Wilcots & Miller (1998)
e
Leroy et al. (2006)
f
Lequeux et al. (1979)
b
0.01 M⊙ yr−1 kpc−2 , and a large fraction of those have SFRs of ∼ 10−4 M⊙ yr−1 kpc−2
(Hunter, 1997). According to Massey & Armandroff (1995), there are 15 confirmed
Wolf-Rayet6 (WR) stars present in the galaxy, which implies the presence of a large
number of young O- and B-type stars as well7 . More recently, Massey & Holmes
(2002) conducted a deeper survey of IC 10 in search of more WR candidates. They
conclude that there are approximately 100 WR stars throughout the extent of the
galaxy. This means that IC 10 has a global surface density of WR stars that is much
more dense than other galaxies in the Local Group, and approximately 20 times the
density in the Large Magellanic Cloud (LMC; Massey & Holmes, 2002). The abundance of WR stars is important for the evolution and morphology of IC 10, as their
6
A Wolf-Rayet star is a very hot, massive young star that has very strong stellar winds.
Stars are classified by their temperature using a letter scheme, OBAFGKM. Each letter represents a different spectral type of star. O- and B-type stars are the hottest stars, while M-type stars
are the coolest (Zeilik & Gregory, 1998).
7
CHAPTER 1. INTRODUCTION
21
Figure 1.10: An optical image of IC 10 from the Digitized Sky Survey. The two red X’s
mark the centres of our selected regions IC 10 SE (lower left) and IC 10 NW (upper
right), while the circles show the apertures we use for this project. The radii of these
apertures are 0.0145◦ and 0.009◦ for IC 10 SE and IC 10 NW, respectively. Image
from “http://archive.stsci.edu/cgi-bin/dss form?target=IC10&resolver=SIMBAD”.
strong stellar winds and energy can blow out material surrounding them, significantly
altering the structure of the galaxy.
It is important to understand the properties of the stellar population of IC 10 in
order to make conclusions about the evolution of the galaxy. A later study of IC 10
by Hunter (2001) also probed the stellar population. Using optical images from the
Hubble Space Telescope (HST), they set out to determine the stellar initial mass function (IMF) of what they call the starburst region, which corresponds approximately
to our IC 10 SE (see Figure 1.10). As stated in Equation (1.2), the definition the IMF
is ξ(log m) = (ln 10)mf (m) where m is the stellar mass, f (m) = AmΓ−1 , is the stellar
mass function, and Γ is (∂ log ξ(log m))/(∂ log m). As Hunter (2001) was unsure how
CHAPTER 1. INTRODUCTION
22
recent the starburst occurred, she has calculated the IMF for two extremes: a coeval
stellar population, in which all stars formed within the hydrogen burning lifetime of
the highest mass stars, and a stellar population with a constant star formation rate,
which must account for those stars that are now dead, as well as the age of the region
itself. They also considered two metallicities: Z = 0.004 and Z = 0.008, assuming
the true metallicity falls in between these extremes. For Z = 0.004 they determined
Γ = −1.9 ± 0.4 and Γ = −0.9 ± 0.3 for a coeval stellar population and constant
star formation, respectively. For Z = 0.008, Γ = −2.1 ± 0.4 and Γ = −1.0 ± 0.4
for the coeval case and constant star formation case, respectively. The age of the
starburst is less than 13 Myr for the coeval population and approximately 40 Myr
for constant star formation. From these results they conclude that the IMF of stars
with intermediate masses is not unusual for the starburst region because they expect
the true slope to lie in between these extremes, and the slope of the Salpeter IMF,
Γ = −1.3, lies between them as well. The slope of the Salpeter IMF is the classically,
empirically determined value (Salpeter, 1955; Scalo, 1986). The WR stars discovered
by Massey & Armandroff (1995) are thought to be associated with a small burst of
star formation much more recent than the majority of stars in the starburst region,
and small groups of OB stars appear to drive the star formation in IC 10. This theory
has been supported by a more recent study of IC 10 with the Hubble Space Telescope
(HST). According to Vacca et al. (2007), the older starburst occurred approximately
150 − 500 Myr ago while a more recent starburst period occurred only about 10 Myr
ago, the latter of which is in agreement with Hunter (2001).
Equally important are the H i and H ii regions within IC 10. Studies of the
H i content of IC 10 have been carried out for decades by groups such as Shostak
CHAPTER 1. INTRODUCTION
23
Figure 1.11: H i distribution in IC 10 with holes identified (Wilcots & Miller, 1998).
West is to the right.
(1974) Klein & Graeve (1986) using radio maps. More recently, Wilcots & Miller
(1998) conducted an extensive survey of H i in IC 10. They detect ‘holes’ in the
H i emission throughout the galaxy, which are thought to be due to hot OB stars
blowing off material with their strong stellar winds, or possible supernova explosions.
In Figure 1.11 we show one of their H i maps which identifies seven independent holes.
These holes lead to a strong deficit of H i in the western portion of IC 10 (Wilcots &
Miller, 1998). The authors also note that only one to three of the holes were created
by supernovae, based on the current radii of the holes and typical expansion rates.
CHAPTER 1. INTRODUCTION
24
They take this to imply that the starburst episode that appears to be currently taking
place is in its early stages, and that the majority of holes are created by the stellar
winds of the stars in the centres. In accordance with Hunter (2001) and Vacca et al.
(2007), Wilcots & Miller (1998) agree that a new starburst began only a few million
years ago.
The radio continuum emission of IC 10 has also been studied at length. Radio
observations at 6, 20 and 49 cm were carried out by Yang & Skillman (1993) to study
the continuum, with the conclusion that while most sources were associated with
thermal emission, there were several nonthermal sources including one they call a
superbubble, which was likely formed by approximately 10 supernovae. A later study
by Thurow & Wilcots (2005) agreed that there was enough energy in the region to
suggest numerous supernovae; however, just recently Lozinskaya & Moiseev (2007)
suggested that the nonthermal superbubble is the result of a hypernova8 explosion
rather than several supernovae. The large amounts of energy deposited into the ISM,
as well as the enriched metals formed during the explosion(s) can have a significant
impact on the characteristics of the ISM.
The continuum regions showing thermal emission match well with the H ii structure described in Hodge & Lee (1990), which traces free-free emission from free electrons. These authors report that the H ii content has been resolved into 144 individual
regions using a narrow-band Hα filter, and the variety of morphologies amongst these
regions is quite broad. The overall distribution may say something about the mode of
star formation taking place within the galaxy. Thurow & Wilcots (2005) conducted
a study of the kinetics of the ionised gas, and they found that the velocity field of
8
A hypernova is the explosion of an extremely massive star. Basically it is a very large supernova
explosion.
CHAPTER 1. INTRODUCTION
25
the H ii closely matched that of the H i content, as determined by Wilcots & Miller
(1998). In addition, these regions are all in the central starbursting region of the
galaxy.
IC 10 has also been observed extensively at infrared and submillimetre wavelengths. Early far-infrared (FIR) and submillimetre observations were carried out
by Thronson et al. (1990) using the Kuiper Airborne Observatory (KAO). Images
at 95 µm and 155 µm reveal a spatial correlation with infrared emission in the two
concentrated areas of star formation of IC 10 SE and IC 10 NW. The authors concluded that there is only a small amount of cold dust, with temperatures less than
25 Kelvin (K), as they measured average dust temperatures of 35 K over the 60 µm
to 160 µm waveband and 27 K using just the 155 µm KAO data. With the latter
temperature the authors derived a dust mass of Md ≈ 2.3 × 104 M⊙ , and a gas mass
of Mgas ≈ 2.52 × 107 M⊙ for these regions, assuming a gas to dust mass ratio of 750
(we have scaled their values from a distance of 1.3 Mpc to our adopted distance of
0.82 Mpc; Thronson et al., 1990).
Mid-infrared (MIR) studies of IC 10 were carried out by Dale et al. (1999) and
Dale et al. (2000) using the Infrared Space Observatory’s ISOCAM (see Section 2.1 for
details). Our ISO data are those initially published in these papers. In the 6.75 µm
image PAHs are the main contribution, as the band picks up the λ 6.2, 7.7 and 8.6 µm
emission features, while the 15 µm image reveals faint 12.5 µm PAH emission, as well
as emission from a dust continuum between 13 and 18 µm. (see Section 1.3.3). In
Dale et al. (1999) they conclude that IC 10 has a large abundance of high energy UV
photons and a low abundance of PAHs, based on the trends they find in the total
surface brightness ratios Iν (6.75 µm)/Iν (15 µm), of the galaxies in their survey. A
CHAPTER 1. INTRODUCTION
26
ratio less than 1 indicates regions with strong heating, as the continuum intensity
detected by the 15 µm filter increases while the abundance of PAHs decreases (shown
in the 6.75 µm image), as they are thought to be destroyed by FUV photons. A
continuation of this study was carried out by Dale et al. (2000), and they concluded
that the material emitting strongly at MIR wavelengths in IC 10 has a characteristic
temperature between 100 K to 200 K, implying an interstellar radiation field (ISRF)
of ∼ 104 times that of in the Solar vicinity. They also associate this emission with
H ii regions, found either within these regions or in their outskirts.
Images of IC 10 taken with the Spitzer Space Telescope’s Infrared Array Camera
(IRAC; see Section 2.2) have also been previously published within a survey of 18
irregular galaxies by Hunter et al. (2006). They used the 3.6 µm image to study
the older stellar population of these galaxies and observed that a dust lane, which
blocks optical light, runs through the western portion of IC 10 and is transparent
at 3.6 µm revealing otherwise hidden stellar content. The strongest emission at this
wavelength correlates with the dust lane and to regions strong in Hα (λ 0.06563 µm),
while revealing more finely detailed structure in the south-eastern part of the galaxy.
These strongly emitting NIR regions are thought to reveal luminous clusters of stars
hidden in optical wavelengths.
Hot dust, often associated with H ii regions, was studied with the 4.5 µm images.
The authors determined a small correlation between hot dust and the star formation
rate. As the SFR increases, the amount of hot dust also increases, though slowly.
Using the 5.8 µm and 8.0 µm images, Hunter et al. (2006) studied PAHs and observed
that as the SFR increases with respect to stellar emission, the strength of the PAH
emission also increases. For IC 10 in particular, the authors also studied the spatial
27
CHAPTER 1. INTRODUCTION
morphology of the PAH emission, and conclude that the PAHs are heated by stars
embedded in clusters as the PAHs are found in the edges of shells of matter.
IC 10 SE, the “most massive giant molecular cloud complex” in IC 10, has already been studied at 850 µm with the Submillimeter Common-User Bolometer Array
(SCUBA; see Section 2.3 for details) by Bolatto et al. (2000), concurrently with spectral observations of CO transitions. In addition to 850 µm, the authors also carried
out observations at 1350 µm and 450 µm with SCUBA, though they were unable to
make any significant detections at 450 µm. They produced the SED for the FIR dust
continuum shown in Figure 1.12 and found that it was a shallow continuum reflecting
the general form of a greybody (modified blackbody). If a greybody has an opacity
τ = (λ0 /λ)β where λ0 is the wavelength at which the emission becomes optically thick
and β is the greybody emissivity exponent, then its observed thermal emission flux
density is given by (Bolatto et al., 2000)
β
Fν = ΩBν (T )(1 − e−(λ0 /λ) ),
(1.5)
with Ω being the solid angle over which the source is emitting, and Bν (T ) is the equation for a blackbody (see Equation (3.6)). The authors conclude that the graybody
emissivity for IC 10 is low, as β ∼ 0.3 from their best-fit model and it is expected that
1 < β < 2 for most materials depending on their composition. They suggest that the
low grain emissivity is due to IC 10’s low metallicity and strong UV radiation field,
which can destroy small dust grains.
Following in the footsteps of the above paper, a complete survey of the CO (J =
1 → 0) transition was carried out by Leroy et al. (2006) in search of giant molecular
clouds within IC 10. They detected 16 individual clouds and concluded that despite
CHAPTER 1. INTRODUCTION
28
Figure 1.12: The best-fitting SED of IC 10 SE as determined by Bolatto et al. (2000).
Black dots show the original observational measurements, black circles represent the
model fits to the photometry at these wavelengths and the boxes are 3σ error limits.
The solid black, solid grey and dashed lines represent models with β equal to ∼ 0.5,
and β fixed at 1.0 and 1.5, respectively.
CHAPTER 1. INTRODUCTION
29
the low metallicity of IC 10 in comparison to our Galaxy, the characteristics of these
regions such as mass, luminosity, and CO spectral line widths are comparable to those
of the Galaxy.
It is generally agreed that IC 10 has undergone a recent episode of star formation
within the past 10 Myr or so, and that it has an unusually high star formation rate
and surface density of Wolf-Rayet stars. The mechanical energy from these and other
hot O and B stars is observed to have strongly modified the morphology of IC 10,
especially at H i wavelengths where distinct holes have been identified. It is unclear as
to whether or not any of these holes can be attributed to supernova events, although
several groups believe a small number of supernovae may be the source of certain
holes. It is also generally agreed that IC 10 is bathed in a strong interstellar radiation
field, which may be the cause of a lower observed abundance of PAHs.
The objective of this thesis is to investigate the interstellar radiation field within
two different star forming regions of IC 10. We plan to obtain images of the galaxy
at as many wavelengths that we can between approximately one micron and 1000
microns, in order to create a well-constrained SED that can be modelled. The model
will be used to obtain information about some of the physical characteristics of these
two regions, and then we will examine our results.
In this thesis we present archival data from the Infrared Space Observatory (ISO),
and Spitzer Space Telescope. We also present new 450 µm and 850 µm data from the
SCUBA instrument mounted on the James Clerk Maxwell Telescope (JCMT). These
data, combined with supplementary data from the 2MASS survey and the Very Large
Array (VLA), are used to analyse the dust Spectral Energy Distribution (SED) for
two distinct regions within IC 10 (see Figure 1.10). We chose these regions as they
CHAPTER 1. INTRODUCTION
30
are the two primary star forming regions of IC 10 and they show strong emission
through out the majority of our data set; in fact, we are limited to these regions
as they were the only regions with a signal-to-noise ratio sufficiently high for us to
study in detail, but they are still important regions to study. Star forming regions
are ideal environments to study the characteristics of a galaxy, especially the dust, as
it is illuminated by the hot stars at the centre of these regions.
Theoretical SED models are then fit to our observational SEDs using a new model,
and the results are subsequently analysed to obtain important information regarding
the parameters solved for with the code. From this we want to ascertain the extent and
types of activity taking place within this galaxy, and then make useful comparisons
with previous work on IC 10, as well as comparisons to both our own Milky Way as
well as other local dwarf irregular galaxies.
In Chapter 2 we present the data sets and discuss the treatment applied to them.
In Chapter 3 the model and results are presented, with our analysis and discussion
following in Chapter 4. We conclude in Chapter 5.
Chapter 2
Data Reduction and Analysis
We have obtained images of IC 10 at 17 wavelengths that were reduced from data
collected at several different observatories. The three key sources of our infrared and
submillimetre data are the Infrared Space Observatory1 (ISO; Kessler et al., 1996),
the Spitzer Space Telescope2 (Werner et al., 2004), and the Submillimeter CommonUser Bolometer Array (SCUBA; Holland et al., 1999) installed on the James Clerk
Maxwell Telescope (JCMT)3 . We have also gathered supplementary data from the
archives of the Two Micron All-Sky Survey4 (2MASS; Skrutskie et al., 2006) and
1
ISO is a European Space Agency (ESA) project with instruments funded by ESA Member
States (especially the principle investigator (PI) countries: France, Germany, the Netherlands and
the United Kingdom) and with the participation of Japan’s Institute of Space and Astronautical
Science (ISAS) and the United States of America’s National Aeronautics and Space Administration
(NASA).
2
The Spitzer Space Telescope is operated by the Jet Propulsion Laboratory (JPL), California
Institute of Technology (Caltech) under a contract with NASA.
3
The James Clerk Maxwell Telescope is operated by The Joint Astronomy Centre on behalf of
the Science and Technology Facilities Council of the United Kingdom, the Netherlands Organisation
for Scientific Research, and the National Research Council of Canada.
4
The Two Micron All Sky Survey is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology, funded by the National
Aeronautics and Space Administration and the National Science Foundation.
31
CHAPTER 2. DATA REDUCTION AND ANALYSIS
32
the National Radio Astronomy Observatory’s Very Large Array5 (NRAO; VLA). All
of our data are in the Flexible Image Transport System (FITS) format, which is a
common file format for astronomical images.
In this chapter, details about each data set acquired will be described as well as
the methods used to reduce the data for our analysis purposes. A summary of our
observational data is presented in Table 2.1.
2.1
ISO data
We have three images of IC 10 taken by the ISO Camera (ISOCAM; Cesarsky et al.,
1996), at 6.75 microns (µm), 11.4 µm, and 15 µm that were retrieved from the
NASA Extragalactic Database6 (NED) archives. The observations and treatment
of these images were carried out by Dale et al. (2000). They used ISOCAM’s long
wavelength (LW) array with the broadband filters LW2 and LW3 to observe at 6.75 µm
and 15 µm respectively, during two different observing runs. In addition, they also
observed IC 10 at 11.4 µm with the LW8 filter only during the second observing
run. All of the observations were done in raster mode7 , the mode used for observing
extended objects that do not fit within one instrument field of view (see Figure 2.1
for a schematic diagram of the spatial coverage resulting from using this mode). For
these data, 16 observations were made to create a grid of four images by four images,
slightly overlapping one another to ensure the region is fully sampled. They were
5
The National Radio Astronomy Observatory is a facility of the National Science Foundation
operated under cooperative agreement by Associated Universities, Inc.
6
The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space
Administration.
7
This mode is sometimes called “scan-map mode” for other telescopes or instruments.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
33
Figure 2.1: Schematic diagram of the raster mode coverage. The four different
coloured large squares each represent the field of view of the instrument during one
observation, and the various shades of colour represent the regions covered by multiple observations. The ellipse and stars are shown to represent a galaxy which is larger
than one field of view of the telescope.
later combined to form one mosaic image of IC 10 and the surrounding sky.
Reduction of the data for IC 10 was carried out by Dale et al. (2000), completed
with the CAM Interactive Analysis (CIA) software (see Table 2.1 for the details about
each image). Due to the disconnection of column 24 of the LW array (Blommaert
et al., 2003), there is a strip of dead pixels in each map where the pixel values have
been set to “Not a Number” (NaN). In addition, the pixels covering the first raster
position (located in the southeast corner of each image) were also set to NaN (masked
out) by the authors since “the maps still show low-level residuals due to transients
from the sources” (Dale et al., 2000). Transients are residual flux from photons
already detected by the detector that decay over a time period slower than the time
between photon detections. This leads to a build up of flux in the detector from
previous photons which can lead to an overestimate of the true flux from the source.
Note that all pixels set to NaN are excluded from all of our analyses.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
2.2
34
Spitzer data
We have obtained images of IC 10 created with data from Spitzer’s Infrared Array
Camera (IRAC; Fazio et al., 2004) at 3.6 µm, 4.5 µm, 5.8 µm, and 8.0 µm. In
addition, we have three images from the Multiband Imaging Photometer for Spitzer
(MIPS; Rieke et al., 2004) at 24 µm, 70 µm, and 160 µm. All of the IRAC maps were
downloaded from the Spitzer data archive in the “Post-BCD” format, where BCD
means “basic calibrated data” (Reach et al., 2006). These data sets were reduced
using the standard processing pipeline developed for Spitzer, and initially all of our
MIPS data were obtained from the archive in this format as well. However, upon close
examination of the MIPS data, and after consulting the Spitzer Science Centre’s MIPS
data handbook8 we deemed these MIPS post-BDC data not fit for our analyses, as
the standard MIPS processing pipeline was unable to reduce the data to the quality
we need for this study.
As a result, we contacted Dr. George Bendo from the Imperial College in London,
England, who is an expert at dealing with the reduction of MIPS band data, and he
agreed to help us. To improve the quality of the images, he used the raw data from the
Spitzer archives, and reduced the MIPS data himself using the Spitzer data analysis
software package, MIPS Data Analysis Tools (DAT). This software gives the observer
better control over artifact removal and general data processing (Dr. Bendo; private
communication). The key benefits of using raw data and this software package for our
images are that Dr. Bendo was able to adjust the processing to compensate for the lack
of sky coverage in these data, and more accurately determine the background flux.
He determined the median surface brightnesses in the off-target images (not always
8
From “http://ssc.spitzer.caltech.edu/mips/dh/”.
available in the Post-BCD format) relating to IC 10, and subsequently subtracted
these values from each of the target images before sending the results to us.
The MIPS images from Dr. Bendo are still not excellent maps though, as all three
maps were generated with data collected during observations made using Spitzer’s
photometry mode, which is a pointed mapping mode and does not have a large
enough field of view for the size of IC 10 (Dr. Bendo; private communication). As a
result, the 70 µm and 160 µm images are missing about 50% and 20% of the extent
of IC 10, respectively. Ideally, these observations should have been carried out using
the scan map mode, which is the best mode for observing large extended sources
(see Kennicutt et al., 2003). Thus, in November of 2007 we submitted a proposal
for Spitzer’s fifth and final observation cycle, to collect new and properly generated
MIPS maps for IC 10. However, in February of 2008 our proposal was unfortunately
rejected, so we proceed with the MIPS maps generated by Dr. George Bendo, ensuring
to carefully consider and incorporate all errors associated with them where necessary.
Table 2.1: Characteristics of the original images.
2MASSc
Spitzer, IRACe
ISO, ISOCAMf
Spitzer, IRACe
ISO, ISOCAMf
Spitzer, MIPSg
JCMT, SCUBAi
NRAO, VLAj
a
Wavelength,
λ0
(µm)
1.24
1.66
2.16
3.56
4.52
5.73
6.75
7.91
11.4
15.0
23.7
71
156
450
850
3.55 ×104
6.2 ×104
Bandwidth,
∆λ
(∆µm)
0.29
0.28
0.31
0.75
1.01
1.42
3.5
2.93
1.3
6.0
5
19
35
25
70
0.3 ×104
0.8 ×104
Beam
Sizea
(′′ )
2.671
2.57695
2.57695
1.66
1.72
1.88
6.15
1.98
6.384
6.456
6.0
18.0
40.0
7.8
13.8
7.673
13.037
Platescaleb
(′′ /pix)
1.0
1.0
1.0
1.2
1.2
1.2
3.0
1.2
3.0
3.0
1.5
4.5
9.0
3.0
3.0
2.37
4.091
Field
Size
′
( × ′)
8.53 × 17.07
8.53 × 17.07
8.53 × 17.07
22.92 × 11.24
22.92 × 11.24
22.92 × 11.24
7.25 × 7.25
22.92 × 11.24
7.25 × 7.25
7.25 × 7.25
9.475 × 29.75
6.3 × 28.65
8.25 × 13.2
10.0 × 10.0
10.0 × 10.0
5.33 × 5.33
9.273 × 9.273
Original
Units
DNd
DN
DN
MJy/sr
MJy/sr
MJy/sr
mJy/pix
MJy/sr
mJy/pix
mJy/pix
MJy/sr
MJy/sr
MJy/sr
Jy/beam
Jy/beam
Jy/beam
Jy/beam
Conversion
Factor
to Jy/sr
2.957 × 105
3.219 × 105
2.630 × 105
1 × 106
1 × 106
1 × 106
4.727 × 106
1 × 106
4.727 × 106
4.727 × 106
1 × 106
1 × 106
1 × 106
6.172 × 108
1.972 × 108
6.378 × 108
2.209 × 108
Background
Flux
(MJy/sr)
23.5 ± 0.2
121.1 ± 0.3
164.5 ± 0.4
0.16 ± 0.02
0.13 ± 0.02
1.1 ± 0.1
6.5 ± 0.3
4.5 ± 0.2
22.7 ± 0.5
22.7 ± 0.5
21.2 ± 0.1h
24 ± 2h
75 ± 7h
4 ± 30
1±2
—
—
Pointing
Uncertainty
(′′ )
<7
<7
<7
0.3
0.3
0.3
2
0.3
2
2
1.4
1.7
< 3.9
6
6
0.1
0.1
See Section 2.6 for a description of the beam size. Units are arcseconds.
All platescale values are contained within the headers of the images themselves. Units are arcseconds per pixel.
c
Central wavelengths, bandwidths and positional uncertainty are from Cutri et al. (2003). Beam sizes are from the Interactive
2MASS Image Service (http://irsa.ipac.caltech.edu/applications/2MASS/IM/interactive.html).
d
Data-Number unit
e
Central wavelengths, bandwidths and beam sizes are from Fazio et al. (2004).
Positional uncertainty is from
“http://ssc.spitzer.caltech.edu/documents/som/”
f
Beam sizes are from Okumura (2000). Central wavelengths, bandwidths and positional uncertainty are from Blommaert et al.
(2003).
g
Bandwidths and beam sizes are from Rieke et al. (2004). Central wavelengths and positional uncertainties are from
“http://ssc.spitzer.caltech.edu/documents/som/”.
h
(George Bendo; private communication)
i
Central wavelengths, bandwidths and beam widths are from Holland et al. (1999). See Section 2.3 for details about positional
uncertainty.
j
Central wavelengths, bandwidths and positional uncertainty are from Ulvestad et al. (2007). Beam sizes are from the NRAO Data
Archive System Image Retrieval Tool (https://archive.nrao.edu/archive/archiveimage.html).
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Telescope,
Instrument
b
36
CHAPTER 2. DATA REDUCTION AND ANALYSIS
2.3
37
JCMT data
We have two images of IC 10 derived from the SCUBA instrument on the JCMT,
one at 450 µm and the other at 850 µm. These data were obtained by Dr. Christine
Wilson during two different observing runs in 1999 and 2000, both with excellent
observing conditions. Under normal operating conditions, the secondary mirror on
the JCMT should chop both in the azimuthal and declination directions with up to
three different chop throw values in each direction, for a total of six maps. Each image
shows the flux difference between the source and the off-target sky in the chopping
direction, and these images are combined in Fourier space, then transformed back
into real space to obtain the final image (Johnstone & Bally, 1999). However, during
the observation run in 1999, the secondary mirror on the JCMT was not operating
correctly due to technical difficulties, and therefore only chopped in the azimuthal
direction (Dr. Wilson; private communication). Since chopping only occurred in
the one direction, the chop direction constantly changed with respect to the sky.
As a consequence, the usual method of reconstructing chopping mode data used by
the standard SCUBA data reduction software, the SCUBA User Reduction Facility
(SURF; Holland et al., 1999, and references therein) could not be used. With SURF,
the reconstruction method requires that the chop throws remain fixed on the sky.
Therefore, the SURF package could be used for certain steps, but not for the image
reconstruction. Instead, an alternative method which permits a varied chop throw
pointing was used. For details, see Johnstone et al. (2000a).
The observations in 2000 were carried out with a fully operational secondary
mirror, using all six chop throws. In addition, the filter at 450 µm was replaced by a
more sensitive one between the 1999 and 2000 observations, improving the sensitivity
CHAPTER 2. DATA REDUCTION AND ANALYSIS
38
Figure 2.2: The 850 µm image of IC 10 with the negative bowl left untreated. The
scale is in units of Jy/sr.
of the 450 µm map from 2000. In the end, only the data collected in 2000 were used
to produce the image at 450 µm as they were of higher quality, while the 850 µm
image was produced using a combination of data collected both in 1999 and 2000
(Dr. Wilson; private communication). All of the reduction steps were carried out by
a summer student of Dr. Wilson.
Reduced to the state the images were in when we received them, the maps revealed
some structure in IC 10; however, they were not optimal for any analyses because
of several remaining issues. The biggest problem was an artificial “negative bowl”
around the central emission peaks in both images. In Figure 2.2 we show the original
850 µm data. An effect intrinsic to SCUBA scan maps, these negative bowls occur
because the background cannot be quantified by SCUBA when in chopping mode and
therefore the average flux in the final map is set to zero. As a result, the total negative
CHAPTER 2. DATA REDUCTION AND ANALYSIS
39
Figure 2.3: The 850 µm image convolved to 240 ′′ , in order to eliminate source
structure. Note that coordinates are not on this image as they haven’t been assigned
to it; however the spatial scale is the same as that shown in Figure 2.2. Greyscale
units are Jy/sr.
flux balances out the strong positive source emission and cannot be eliminated by
simply adding a constant flux to each pixel (Johnstone et al., 2000b; Reid & Wilson,
2005). Instead, we followed the method discussed by Johnstone et al. (2000b) and
Reid & Wilson (2005), where a masked version of the original image is convolved (see
Section 2.6) using a Gaussian kernel at least twice as wide as the largest chop throw
to eliminate most, if not all of the source structure in the original image. The largest
chop throw was 65′′ , and we convolved the image to 240′′ . The convolved 850 µm
image is shown in Figure 2.3. In our case, we masked out pixels with an absolute
flux greater than twice the standard deviation of the pixel distribution (2σ) before
convolution, by copying the original image to a new file and setting the values of the
pixels to be masked to NaN. This process helps prevent new negative regions from
CHAPTER 2. DATA REDUCTION AND ANALYSIS
40
forming as a result of the next step, which is to subtract the convolved image from
the original, unmasked image (Reid & Wilson, 2005). This new image is then the
image used to determine the background flux contribution requiring removal. The
background flux removal process is discussed further in Section 2.5.2.
The other main issue with the SCUBA maps was that the headers of the FITS
files that contained the images were missing some crucial information, such as the
coordinates of IC 10 and information pertaining to the reference pixels, which are
required to conduct any astrometry on the images. To correct this problem, we set
out to rewrite the headers ourselves given the information we had. We first chose a
reference pixel in each image and determined their corresponding positions in right
ascension (RA) and declination (DEC). The best method we had to assign an accurate
position to our reference pixels required the use of 450 µm and 850 µm images created
by Dr. Wilson with only the data set taken in 2000, but using SURF to fully reduce the
data. We carefully examined these images and visually determined the approximate
centres of each of the three main peaks of emission visible in the galaxy, then noted
their x and y pixel coordinates, as well as their positions in RA and DEC. Concluding
that the southernmost peak of IC 10 SE (see Figure 2.4) was the most reliable peak
in each map, we assigned the centre position of this peak in RA and DEC from both
alternate images to the pixel in each of our images that marked the approximate centre
of the same peak. In general, the pointing uncertainty (how accurately a telescope
is able to point at a set of given coordinates) for the JCMT is 1.5′′ ; however, as we
set the coordinate grid ourselves this uncertainty will be larger. We conservatively
estimate that the uncertainty in correctly determining the coordinates of the 450 µm
and 850 µm is 6′′ . See Table 2.1 for the pointing uncertainties of all instruments.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
41
Figure 2.4: 850 µm image comprising data reduced with SURF. The circled region
highlights the peak we used to determine the coordinates of our images.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
42
Lastly, we converted the units of the original images from Janskys (Jy) per beam
(see Section 2.6 for the definition of a beam) to Janskys per steradian9 (sr), taking
into account the Gaussian response function of the instrument beam which is a factor
of ln 2
10
. In the end we had two SCUBA maps that were ready for background
subtraction (see Section 2.5).
2.4
2.4.1
Supplementary data
2MASS data
To help constrain our results, we obtained near-infrared images from the 2MASS survey archives in the J (1.25 µm), H (1.65 µm), and K (2.17 µm) bands, as well as
radio maps from the VLA archives at 3.6 cm and 6.2 cm. The 2MASS images are
All-Sky Release Survey Atlas Images and were retrieved using the Interactive 2MASS
Image Service, run by the NASA/IPAC Infrared Science Archive11 . To prepare these
2MASS images for background subtraction and convolution, it was necessary to convert the units from the default 2MASS “Data-Number (DN) units” to units of Jy/sr
(see Table 2.1 for the specific conversion factors).
The headers of these images contain the zero point magnitudes (mz ) for each
band, and with that information we can use the following equation to convert the
9
A steradian is a unit of angular area called a solid angle, with the entire surface of a sphere
covering 4π sr (Zeilik & Gregory, 1998).
10
Beam response functions are often Gaussian in shape, and therefore not uniform.
11
The NASA/IPAC Infrared Science Archive is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
43
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Table 2.2: Flux values for the J, H and K bands for a zero-magnitude zero-point
conversion (Cohen et al., 2003).
Wavelength (µm) Flux at 0-mag, F0 (Jy)
1.25
1594 ± 27.8
1.65
1024 ± 20.0
2.17
666.7 ± 12.6
Zero point magnitude, mz (mag)
20.9014
20.3286
20.0821
flux in each pixel from data-number units to a magnitude (mag; Cutri et al., 2003):
m1 = mz − 2.5 log10 (S),
(2.1)
where m1 is the calibrated magnitude, mz is the zero point magnitude listed in the
2MASS image header under the keyword “MAGZP”, and S is the flux in a given
pixel, in DN units. We also have the standard equation relating flux to magnitude,
m1 − m0 = −2.5 log10
F1
F0
,
(2.2)
where in this case, m0 is set to zero and F0 is the flux of the object when its magnitude
is zero. These fluxes are listed in Table 2.2, as well as the zero point magnitudes.
What we ultimately want to solve for is F1 in terms of S. Combining Equations (2.1) and (2.2) we find
F1 = F0 S10−mz /2.5 ,
(2.3)
where we have set m0 = 0. Since the given DN values apply to any single pixel our
44
CHAPTER 2. DATA REDUCTION AND ANALYSIS
last step is to convert these values to units of Jy/sr. The solid angle of a pixel is
Ωpix =
1◦
π
dpix ×
×
′′
3600
180◦
2
sr
(2.4)
where dpix is the diameter of one pixel, taken to be the image platescale in arcseconds
per pixel. We find for a platescale of 1′′ /pix
Ωpix = 2.350 × 10−11 sr,
(2.5)
and thus obtain
F1 =
F0 S10−mz /2.5
,
2.350 × 10−11
(2.6)
where S is the image array of pixels. The calculated values of the conversion factors
FJ , FH and FK are listed in Table 2.1.
2.4.2
VLA radio data
The VLA is an interferometer comprised of 27 25-metre diameter antennae which
can be positioned in five different arrangements to vary resolution12 . The VLA radio
images we have were obtained from the NRAO’s Data Archive System. Background
continuum information is not detected by the interferometer during observations with
the VLA, as the largest angular scale it can detect is λ/D, where λ is the observing
wavelength and D is the closest distance between any two antennae in the array. In our
case, observations were taken with the interferometer in the “D” configuration, so the
largest angular scale that can be detected is approximately 180′′ for the 3.6 cm image
and 300′′ s for the 6.2 cm image. For details see Ulvestad et al. (2007). Therefore, we
12
“http://www.vla.nrao.edu/astro/guides/greenbook/”
CHAPTER 2. DATA REDUCTION AND ANALYSIS
45
did not have to carry out a background subtraction step on these data. The units
of these images were in Jy/beam, so we converted these units to Jy/sr following the
same method as for the SCUBA images. The beam sizes and calculated conversion
factors are listed in Table 2.1.
2.5
Background flux evaluation
The main reduction step that we had to correctly apply to the majority of the maps
(MIPS and VLA maps excluded) was the subtraction of any background and/or
foreground flux present in the maps we obtained. As we cannot fully discern between
foreground and background emission we will refer to their combined contribution as
the background flux. We emphasise that only the diffuse background emission is
evaluated here, as the low Galactic latitude of IC 10 prevents us from discerning
emission from other objects between us and the galaxy along the line of sight.
To accurately determine the background fluxes, we decided to test two different
methods and then proceed with the better of the two. The first method we deemed
the “Box Method” and the second method we called the “Gaussian Method”. Both
methods are described below.
2.5.1
The “Box Method”
This method was the simpler of the two methods we used to evaluate any background
contribution to the total flux in the maps. We carefully examined each map for regions
that contained only distinct background flux, and visually selected three “boxes” or
regions that we were confident were located beyond the extent of the galaxy itself. In
CHAPTER 2. DATA REDUCTION AND ANALYSIS
46
Figure 2.5: Regions used to calculate the background flux with the “box method”
highlighted in red and superimposed on the Spitzer 8 µm image.
Figure 2.5 we show as an example, our 8 µm image with the three boxes highlighted in
red that we selected to carry out our calculations. For each box, the mean flux value
inside was calculated using two programs written in the Interactive Data Language
(IDL; see Appendix B). The results from each box were then averaged to obtain one
final value for the background flux. We took the standard deviation of the mean to
be the error for each box, then propagated these errors to determine the error for
the final value of the background contribution. The program also overlays the boxes
chosen onto the image so that it is clear where the boxes are located with respect to
the galaxy. The background flux values obtained with this method for the Spitzer
8 µm image are shown alongside those obtained with the Gaussian method (see next
subsection) in Table 2.3.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
2.5.2
47
The “Gaussian Method”
The basic idea behind this method is that if we plot a histogram of all of the pixels
in a map of IC 10 including those containing source emission, and assume that the
resulting background flux distribution should be a Gaussian distribution, then all
of the pixels falling within flux bins located to the left of the central peak contain
background flux (see Figure 2.6). Therefore, the left-hand side of the histogram
should represent the actual shape of the distribution of the background flux, while
the right-hand side of the histogram contains not only background flux, but also all
of the source flux superimposed on top. The flux value corresponding to the central
peak of the distribution then represents the average value of the background flux.
To quantify this idea, we begin by creating a histogram of pixel count vs. flux
for all of the pixels (excluding those pixels with a value of NaN) in an image. We
adjust some of the key parameters of the histogram (i.e. the number of bins, and
the minimum and maximum values of the flux) until a satisfactory histogram which
has a clear underlying Gaussian shape due to the background flux is produced. The
final histogram is then examined to see if it is asymmetrical, with the right tail falling
off much more gradually than the left tail. The reason we look for this asymmetry
is that all of the source flux is going to be especially high in comparison with the
majority of pixels in the image, and will fall off gradually, creating an asymmetry in
the histogram. For all of our images, the histogram was asymmetric, with the tail of
increasing flux decreasing more gradually than the tail to the left of the peak. An
example is shown in Figure 2.6, where we show the original histogram in black.
Our next step is to create a symmetrical histogram using only the left-hand side of
the original histogram including the peak itself. We select this part of the histogram
48
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Figure 2.6: The original histogram (black ), symmetrical histogram (red ), and Gaussian fit to the symmetrical histogram (blue) for the Spitzer 8 µm image.
and create a mirror image of it (excluding the peak which remains untouched) to represent the right-hand side of the background flux distribution. Concatenating both
halves together results in a fully symmetric histogram representing the assumed Gaussian distribution of background flux. In Figure 2.6, the red line shows the symmetric
histogram for our 8 µm image.
Lastly, we fit a Gaussian function to our symmetric histogram using a predefined
program in IDL. We chose to fit only three parameters in the function, which results
in
1
f (x) = A0 exp −
2
x − A1
A2
2
,
(2.7)
where A0 is the height of the Gaussian function, A1 is the centre value of the Gaussian
fit, and A2 is the standard deviation (σ) of the Gaussian. The fit to our histogram
CHAPTER 2. DATA REDUCTION AND ANALYSIS
49
Table 2.3: A comparison between background contributions obtained with the “Box
Method” and those obtained with the “Gaussian Method” for a few select wavelengths.
Wavelength (µm)
6.75
8.0
15.0
Background Flux (MJy/sr)
“Box Method” “Gaussian Method”
6.4 ± 0.4
6.5 ± 0.3
4.4 ± 0.2
4.5 ± 0.2
22.7 ± 0.5
22.7 ± 0.5
for the 8 µm data is shown in blue in Figure 2.6. Once we have a Gaussian fit to
the symmetrical histogram, it is simple to obtain the background flux. We take the
centre flux value (A1 ) of this fit to be the background flux value, and the standard
deviation of the distribution (A2 ) is considered to be the error in the background flux
value. While the background value was actually set as soon as we finished adjusting
the original histogram, making all subsequent steps seem redundant, our motivation
for carrying out these extra steps was to enable us to easily read off the background
flux and determine its associated error. The program written to carry out this task
can be found in Appendix C.
We compared the results of the Box method and the Gaussian method to see how
they performed, and all results agreed within error, as shown in Table 2.3. In the
end we chose to use the Gaussian method because the magnitude of the error was
marginally smaller for one wavelength than that obtained with the Box method, and
because the values we determined with the Box method depended on where we chose
to place our boxes. The Gaussian method makes use of all pixels in each map thereby
eliminating any potential selection biases.
In Table 2.1 we summarise the background contribution subtracted from each image, with its corresponding error. For the Spitzer MIPS images, which were already
CHAPTER 2. DATA REDUCTION AND ANALYSIS
50
background subtracted, we include the background flux values that had already been
subtracted off. The resulting images are presented and analysed in Chapter 3, Figures 3.1a through 3.1q.
In Section 2.6 we will describe the process of convolution as we applied it to these
images. This is a crucial step in our analysis, as it allows us to carry out photometry
on each image at the same resolution.
2.6
Convolution
In order to conduct numerical and spatial analyses on all of the images simultaneously,
and plot a spectral energy distribution (SED), each image should have the same
platescale and must have the same beam size (or resolution). The beam size is
related to the point spread function (PSF) of the telescope on which the observations
were made. The PSF is the pattern that light from a point source (i.e. a star or
distant galaxy) makes on the telescope’s detector. When the light passes through
all of the optics of a telescope it is diffracted (spread out) slightly so that when it
is detected by the charge-coupled device (CCD) or other type of detector, a point
source object appears smeared out. An example of this is shown in Figure 2.7, which
is a comparison between the observed and theoretical PSF’s for the MIPS instrument
on Spitzer.
Theoretically, the PSF is a circular diffraction pattern which is determined by the
diameter of the telescope’s objective (lens or mirror) as well as the wavelength of the
light being observed (Zeilik & Gregory, 1998). For a given wavelength λ, and circular
CHAPTER 2. DATA REDUCTION AND ANALYSIS
51
Figure 2.7: A comparison between the observational and theoretical point spread
functions (PSFs) of the MIPS instrument on Spitzer. Image from Rieke et al. (2004)
aperture diameter D, we have
θ ≈ 1.22(206265
λ
),
D
(2.8)
where λ and D must be in the same units. The value of θ is referred to as the angular
resolution of the telescope in units of arcseconds13 . It is also the angular radius
of the first dark ring of the diffraction pattern, called the “Airy Disk”; it contains
about 85% of the light from the source, with the rest of the light contained within the
surrounding concentric rings (Young & Freedman, 2000). The beam size is considered
to be the full width at half-maximum (FWHM) of the PSF. In Table 2.1 we present
the beam size in arcseconds related to each wavelength, in addition to the platescale
of each image. With this information, we can proceed with convolution.
Convolution is a mathematical procedure that lowers an image’s resolution using
a convolving function. In order to compare all of our images, we need to convolve
13
For an ideal telescope this would be the diffraction limit of the aperture; however, the instrumentation on many telescopes cannot achieve this limit.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
52
each image to the same resolution as the image with the poorest resolution. In our
case, the image of IC 10 at 160 µm (shown in Figure 3.1m) has the poorest resolution
at 40′′ , so we convolved all of our images to this resolution. We carried out the
convolution using a routine written in IDL that makes use of the native IDL function
“convol”. The routine assumes that the initial FWHM of the convolving function is
shaped like a Gaussian function with a FWHM (′′ ) of
q
FWHM = (40′′ )2 − θ02 ,
(2.9)
where θ0 is the initial resolution of the image we are convolving. A PSF with this
condition is then generated and used within the “convol” program to convolve our
initial image and create an image with the new resolution.
The last step of this process is to regrid all of the convolved images so that they
have the same platescale of 9′′ /pix as the MIPS 160 µm image. This is carried out
with the program “hastrom” found in the astronomy library of IDL routines14 . Once
this is done, the images are ready to for us to extract the flux in the regions IC 10 SE
and IC 10 NW and create the observed SEDs.
2.7
Flux evaluation
The main focus of our study are the regions known as IC10 SE and IC 10 NW that
we introduced in Chapter 1, where SE and NW stand for south-east and northwest, respectively (see Figure 2.8 for the locations of these regions). To create their
IR spectral energy distributions (SEDs) we need to extract the flux density within
14
Astrolib is a library of IDL routines specifically written for astronomy purposes. The home of
this library is < http://idlastro.gsfc.nasa.gov/ >.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
53
Figure 2.8: Apertures centred on IC 10 SE (lower left) and IC 10 NW (upper right)
of the convolved MIPS 24 µm image. The red circles show our apertures while the
region between each set of green circles highlights the regions used to by the program
to evaluate the local background. The blue crosses mark the centres of our apertures
which correspond to the centres of the emission peaks.
apertures centred on these two regions. We chose aperture sizes that are large enough
to encompass as much of the region as possible, without including too much local flux
from the galaxy surrounding these regions. We also chose two surrounding annuli that
determine local background, as the program we used to evaluate the flux required us
to do so. This is because the program is set up for point source photometry (i.e.
for stars); however, the rings were ignored during actual calculations as we already
determined the background contribution. Figure 2.8 shows the two regions in which
we calculated the integrated flux density (red ), as well the rings used to calculate
the local background (green). In Table 2.4 we present the specific details about the
apertures we chose, and their respective rings.
54
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Table 2.4: Aperture characteristics.
Region
IC 10 SE
IC 10 NW
a
Centre of
Aperture
(RA, DEC)a
0h 20m 28.5s ,
59◦ 17′ 06.08′′
0h 20m 18.515s,
59◦ 18′ 31.61′′
Radius of
Radii of Local
Aperture Background Rings
(◦ )
(◦ )
0.0145
0.017 – 0.02075
0.009
0.01075 – 0.0145
Number of Pixels
in Aperture
105.683
40.715
right ascension, declination
To calculate the integrated intensities within the two apertures, we used a modified IDL routine from the Astrolib library, that takes the aperture radii, coordinates
and background rings as the main inputs and returns the flux contained within the
given aperture with error, as well as the mean background in the ring with error.
We do not use the error calculated by the program, but rather a combination of
uncertainties we evaluated, which are described in the next section. The values we
obtained for the integrated flux are listed in Tables 2.7 and 2.8 along with all associated uncertainties. Next we will discuss the other uncertainties we must take into
account when determining the total error for each aperture.
2.8
Error analysis
There are several steps required in order to properly evaluate the errors that are
present in our images. There is an error associated with our background evaluation
as mentioned above in Section 2.5, which is the noise in the image. There is also a
calibration error associated with each instrument itself, and for some wavelengths an
aperture correction was also necessary. Lastly, we evaluate the non-dust contributions
to the submillimetre bands, as well as the radio continuum contributions at each
CHAPTER 2. DATA REDUCTION AND ANALYSIS
55
waveband. We will discuss each source of error or contribution, and our methods to
deduce them below.
2.8.1
Background noise
The noise in each image is due to the small fluctuations in the background value.
Recall in Section 2.5 we measured the background values of the original images using the “Gaussian method”, which demonstrated that these small fluctuations exist
through the distribution itself. To evaluate the noise present in our convolved images,
we need to propagate the noise errors in our background subtracted images. To do
this we first create artificial noise maps containing a Gaussian distribution of pixel
values with a standard deviation equal to that of the noise in the original image. This
is accomplished by scaling the distribution (created with the “Randomn” function in
IDL) by the standard deviation. Each noise image generated has the same dimensions
as the corresponding original, and maintains the overall background characteristics
of the original map. The next step is to convolve the noise maps following the same
procedure as for the original images (see Section 2.6). This is required as it is the
only way to properly propagate the noise errors and correctly measure the noise in
the convolved images. After convolving the images, we regrid each image as was done
for the original convolved images, and finally obtain a noise map for each wavelength
treated identically as its corresponding original image. From these noise images it
is now a simple matter of evaluating the standard deviation of the convolved noise
maps, which gives us the noise present in one pixel. These errors must be adjusted by
multiplying the noise per pixel by the square root of the number of pixels contained
within each aperture.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
56
One caveat with the 160 µm, 450 µm, and 850 µm images is an increase in the
magnitude of the noise in the vicinity of IC 10 NW (see Figures 3.1m, 3.1n and
3.1o). As we felt that the noise level calculated using the method just described was
not sufficiently large enough to accommodate this increase, we estimated the noise
based on a comparison of the source flux of IC 10 NW to the background flux in the
immediate vicinity. As a result we conservatively set the noise at 40 % of the total
flux within IC 10 NW for the 160 µm, and 50 % of the total flux for the 450 µm and
850 µm images.
2.8.2
Calibration errors and aperture corrections
The calibration errors are related to the telescope and observing instrument used
during observations. Most of the calibration corrections were applied to the data
before we obtained them; however, two further corrections were necessary. The first
requires an aperture correction by applying a multiplicative factor to the aperture
fluxes from the 450 µm image to correct for the flux from the error beams (Dr. Wilson;
private communication). The error beams are the side lobes of the light diffraction
pattern seen by the detector. Most of the light falls within the main beam (recall
in Section 2.6 we defined the beam size as the FWHM of the PSF); however, some
light is detected on either side of the main beam due to the constructive interference
of the light (see Figure 2.7). If an object has an angular size that is larger than
the width of the main beam, these side lobes will measure flux external to the main
beam, which is then added to the flux measured by the main beam, overestimating
the true flux as a result. The response of the detectors can be studied to model this
pattern and corrections can be applied to the data to account for the flux in the side
CHAPTER 2. DATA REDUCTION AND ANALYSIS
57
Table 2.5: Multiplicative factors for aperture correction.
Wavelength
(µm)
3.6
4.5
5.8
8.0
450
a
b
Aperture Correction
Multiplication Factor
0.944a
0.937a
0.772a
0.737a
0.86 (IC 10 SE)b
0.95 (IC 10 NW)b
Reach et al. (2005)
Dr. Wilson; private communication
lobes. In addition, Reach et al. (2005) suggest applying multiplication factors for
aperture corrections to the IRAC data as well. The multiplication factors we used
are presented in Table 2.5.
The other calibration correction we applied to our data dealt with absolute calibration errors, since we are using observations taken with six different instruments.
Publications such as Rieke et al. (2008) and Reach et al. (2005) give some comparisons
between a few instruments, but it is difficult to extend this to all of the instruments
we are using. Given the information we have from these two papers, as well as information from the various instrument manuals we have estimated the calibration errors.
Note that these errors are necessary in order to compare data from numerous telescopes but they do not affect the variations from pixel to pixel in the images. These
values are shown in Tables 2.7 and 2.8 and comparing them to the other sources of
error, they are the dominant source in the majority of cases.
CHAPTER 2. DATA REDUCTION AND ANALYSIS
2.8.3
58
Waveband contamination
As we are specifically studying the dust SED of IC 10 rather than the entire spectrum,
we have to remove any contribution to our images that is not accounted for by the
SED model to be used to fit our observations (see Chapter 3). More specifically,
at 850 µm there is radiation present due to the J = 3 → 2 rotational transition
of carbon monoxide (CO). CO emission contributes to a large fraction of the total
molecular mass within a galaxy, and is often used as a tracer of H2 , the dominant
source of molecular mass. It has been detected in IC 10 through several emission
lines such as J = 1 → 0 transition or C ii, and numerous groups have mapped out
the distribution of CO within the galaxy (e.g. Wilson & Reid, 1991; Madden et al.,
1997; Leroy et al., 2006). As a result of its strong presence within IC 10, we need to
determine the contribution from the CO(J = 3 → 2) transition since it falls within
the 850 µm band, and adjust our flux values if necessary (i.e. we need to compare the
energy of the CO(J = 3 → 2) line with the total energy within the 850 µm band).
To estimate the CO(J = 3 → 2) contribution to the 850 µm waveband emission,
we refer to studies of CO carried out by Bayet et al. (2006) and Leroy et al. (2006).
From the survey of Bayet et al. (2006) we were able to determine the ratio of the
intensities of to the J = 3 → 2 to J = 1 → 0 transitions, finding that I3−2 /I1−0 =
0.56. Next, we use the intensity distribution map for the CO(J = 1 → 0) transition
from Leroy et al. (2006) to determine the intensity of that line within IC 10 SE and
IC 10 NW. Since the beam size of the telescope used in this survey (the Arizona
Radio Observatory (ARO)) is 55′′ , it is approximately the diameter of the aperture
we use for IC 10 NW and we were able to use the intensity at this location directly.
However, the aperture we use for IC 10 SE is larger than the area of the beam by
CHAPTER 2. DATA REDUCTION AND ANALYSIS
59
a factor of 3.6, so we need to increase the intensity measured within the telescope’s
beam accordingly. We find that the intensity of the CO(J = 1 → 0) emission at
the position of IC 10 SE is approximately 8.1 K km s−1 for the ARO beam size,
which corresponds to an intensity of 4.5 K km s−1 for the CO(J = 3 → 2) emission.
This translates to an intensity of approximately 16.3 K km s−1 within the aperture
for IC 10 SE, assuming a uniform intensity distribution. For IC 10 NW we find an
intensity of 1.0 K km s−1 for the CO(J = 1 → 0) emission, corresponding to an
intensity of 0.56 K km s−1 for the CO(J = 3 → 2) emission.
Next we convert these intensities to units of Jy km s−1 using a conversion factor
of 25 Jy/K determined specifically for the ARO, finding intensities of 408 Jy km s−1
and 14 Jy km s−1 for IC 10 SE and IC 10 NW, respectively. To make a comparison
of these values to our measured flux at 850 µm we have to multiply our flux values
by the width of the 850 µm filter in units of km s−1 . From Table 2.1 we find that the
width of this filter is 70 µm, which is equivalent to 2.5×104 km s−1 using the relations
∆ν = ∆λc/λ2 and ∆v = ∆νc/ν, where ∆λ, ∆ν and ∆v are the filter bandwidth in
terms of wavelength, frequency and velocity, respectively. Using the flux measured
within IC 10 SE and IC 10 NW from Tables 2.7 and 2.8 and the bandwidth in terms
of velocity, we find intensities of 1.4 × 104 Jy km s−1 and 1.22 × 103 Jy km s−1
for IC 10 SE and IC 10 NW, respectively. Comparing these values to the emission
contribution of the CO(J = 3 → 2) transition, we find that the CO(J = 3 → 2)
emission is negligible, contributing only 3 % and 1 % to the total flux at 850 µm for
IC 10 SE and IC 10 NW, respectively.
We also have to remove any radio continuum that has extended into our submillimetre images. In order to quantify the flux in these images from the radio continuum,
CHAPTER 2. DATA REDUCTION AND ANALYSIS
60
we evaluated it first assuming that the continuum included both non-thermal and
thermal emission, but was dominated by non-thermal emission, and then assuming
only thermal emission. Non-thermal emission is generally in the form of synchrotron
radiation. This radiation mostly stems from free electrons travelling at very high
speeds in the presence of a magnetic field. The electrons spiral around the field lines,
and are accelerated as a result. Eventually, the accelerated electron will emit a photon. Thermal emission tends to occur most often in regions where a plasma of free
electrons and positive ions exists, such as an H ii region. This radiation is called
Bremsstrahlung radiation. When an electron approaches an ion it is accelerated into
a new orbit around the ion, subsequently emitting a photon to compensate for the
change in energy required to alter its orbit. The energy of the electrons involved in
Bremsstrahlung radiation reflects the temperature of the gas it resides in, which is
why it is considered to be thermal emission.
For the combined continuum we needed to determine the spectral index associated
with it. The radiation follows the relation
F = Cλα ,
(2.10)
where F is the flux from the radio continuum, and α is the spectral index that includes
both thermal and non-thermal emission. It is assumed to be described by the slope
between 3.55 cm and 6.2 cm, where we know that non-thermal emission dominates
the total. The variable C is a constant. Since we have two different fluxes for two
different radio wavelengths we can solve for C and α. In Table 2.6 we present the
data used to determine Equation (2.10) for both regions and the resulting equations
61
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Table 2.6: Radio data points used to extract radio continuum equation.
Wavelength,
λ (µm)
3.55 × 104
6.2 × 104
log(λ)
IC 10
(µm)
Flux, F (Jy)
4.55023
0.04933
4.79239
0.0681
SE
log(F) (Jy)
-1.30689
-1.16685
IC 10 NW
Flux, F (Jy) log(F) (Jy)
0.01639
-1.78542
0.02071
-1.68382
are
FSE = (1.1537 × 10−4 )λ0.5782
(2.11)
FNW = (2.0217 × 10−4 )λ0.4195
(2.12)
for IC 10 SE and
for IC 10 NW.
Wielding these two equations, we can now calculate the non-thermal radio continuum contribution for all wavelengths. The non-thermal radio continuum contributions
are shown in Tables 2.7 and 2.8.
The continuum due to solely thermal emission can be approximated by Equation (2.10) with α = 0.1. Using data only from the 3.55 × 104 µm radio image, we can
determine the value of C for each aperture. As already stated we know that at 3.55 cm
the emission is dominated by non-thermal radiation which falls off more rapidly than
for the thermal emission. Therefore, extrapolating the thermal emission from this
point will give us the upper limit on the total emission at shorter wavelengths. Thus,
we obtain
FSE = (1.73 × 10−2 )λ0.1
(2.13)
FNW = (5.75 × 10−3 )λ0.1
(2.14)
for IC 10 SE and
CHAPTER 2. DATA REDUCTION AND ANALYSIS
for IC 10 NW. The contribution due to the thermal continuum is also shown in
Tables 2.7 and 2.8. Comparing these values at each wavelength with those obtained
from the combined continuum we see that the contribution from a solely thermal
continuum is higher because we extrapolated it to shorter wavelengths, whereas the
value of α for the total emission assumes that the thermal continuum falls off rapidly
and the non-thermal radiation dominates at all wavelengths. The important thing to
note here is that regardless of the type of continuum, the total contribution due to
radio continuum is negligible to the total flux in the apertures.
Tables 2.7 and 2.8 present the integrated flux as measured by our routine, all individual error contributions, and finally the net flux with associated error. In Chapter 3
we will introduce the program we used to model the dust SEDs of each region, along
with our best-fitting models.
62
Wavelength
(µm)
1.25
1.65
2.17
3.6
4.5
5.8
6.75
8.0
11.4
15.0
24.0
70.0
160.0
450
850
3.55 ×104
6.2 ×104
Flux
Noise
(Jy)
0.339
0.447
0.401
0.280
0.198
0.433
0.668
0.870
1.130
1.115
3.957
33.651
39.384
3.526
0.561
0.049
0.068
(Jy)
8.438 × 10−5
1.290 × 10−4
1.512 × 10−4
9.914 × 10−6
6.934 × 10−6
4.865 × 10−5
3.949 × 10−4
9.880 × 10−5
5.646 × 10−4
5.645 × 10−4
6.698 × 10−5
3.354 × 10−3
1.408 × 10−1
3.315 × 10−2
2.082 × 10−3
2.089 × 10−5
9.904 × 10−6
Calibration
Error
(%; Jy)
2%; 0.007
2%; 0.009
2%; 0.008
5%; 0.014
5%; 0.010
5%; 0.022
15%; 0.100
5%; 0.044
15%; 0.169
15%; 0.167
5%; 0.198
10%; 3.365
10%; 3.938
25%; 0.881
10%; 0.056
5%; 0.002
5%; 0.003
Error from Local
Background
(Jy)
0.003
0.004
0.004
0.002
0.001
0.005
0.007
0.008
0.008
0.007
0.013
0.248
0.813
0.090
0.010
0.0003
0.0004
Non-thermal Radio
Contribution
(Jy)
0.0001
0.0002
0.0002
0.0002
0.0003
0.0003
0.0004
0.0004
0.0005
0.0006
0.0007
0.0014
0.0022
0.0040
0.0057
0.0493
0.0681
Thermal Radio
Contribution
(Jy)
0.0177
0.0182
0.0187
0.0197
0.0201
0.0206
0.0209
0.0213
0.0221
0.0227
0.0238
0.0265
0.0287
0.0319
0.0340
0.0493
—
Net Flux
(Jy)
0.339 ± 0.007
0.447 ± 0.009
0.401 ± 0.008
0.28 ± 0.01
0.20 ± 0.01
0.43 ± 0.03
0.7 ± 0.1
0.87 ± 0.06
1.1 ± 0.2
1.1 ± 0.2
4.0 ± 0.2
34 ± 3
39 ± 4
4±1
0.56 ± 0.06
0.049 ± 0.002
0.068 ± 0.003
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Table 2.7: Flux in apertures and associated error contributions for IC 10 SE.
63
Wavelength
(µm)
1.25
1.65
2.17
3.6
4.5
5.8
6.75
8.0
11.4
15.0
24.0
70.0
160.0
450
850
3.55 ×104
6.2 ×104
Flux
Noise
(Jy)
0.141
0.193
0.171
0.113
0.080
0.138
0.175
0.258
0.366
0.450
2.242
11.168
11.369
0.355
0.048
0.016
0.021
(Jy)
5.237 × 10−5
8.008 × 10−5
9.386 × 10−5
6.153 × 10−6
4.304 × 10−6
3.020 × 10−5
2.451 × 10−4
6.133 × 10−5
3.505 × 10−4
3.504 × 10−4
4.157 × 10−5
2.082 × 10−3
8.741 × 10−2
2.058 × 10−2
1.292 × 10−3
1.297 × 10−5
6.147 × 10−6
Calibration
Error
(%; Jy)
2%; 0.003
2%; 0.004
2%; 0.003
5%; 0.006
5%; 0.004
5%; 0.007
15%; 0.026
5%; 0.013
15%; 0.055
15%; 0.067
5%; 0.0112
10%; 1.117
10%; 1.137
25%; 0.089
10%; 0.005
5%; 0.0008
5%; 0.001
Error from Local
Background
(Jy)
0.004
0.006
0.006
0.003
0.002
0.004
0.004
0.006
0.007
0.005
0.022
0.170
0.273
0.057
0.003
0.0002
0.0003
Non-thermal Radio
Contribution
(Jy)
0.0002
0.0003
0.0003
0.0004
0.0004
0.0004
0.0005
0.0005
0.0006
0.0006
0.0008
0.0012
0.0017
0.0026
0.0034
0.0164
0.0207
Thermal Radio
Contribution
(Jy)
0.0059
0.0060
0.0062
0.0065
0.0067
0.0069
0.0070
0.0071
0.0073
0.0075
0.0079
0.0088
0.0096
0.0106
0.0113
0.0164
—
Net Flux
(Jy)
0.141 ± 0.003
0.193 ± 0.004
0.171 ± 0.003
0.113 ± 0.006
0.080 ± 0.004
0.138 ± 0.009
0.18 ± 0.03
0.26 ± 0.02
0.37 ± 0.05
0.45 ± 0.07
2.2 ± 0.1
11 ± 1
11 ± 5
0.4 ± 0.2
0.05 ± 0.02
0.016 ± 0.001
0.021 ± 0.001
CHAPTER 2. DATA REDUCTION AND ANALYSIS
Table 2.8: Flux in apertures and associated error contributions for IC 10 NW.
64
Chapter 3
Results
In this chapter, we present the 17 images of IC 10 at their highest resolution and
describe the various morphological characteristics of each image and how they change
with wavelength. The Spectral Energy Distribution (SED) model we used to fit our
observational data is introduced, and the results for various models are presented.
3.1
Morphology of IC 10
The background subtracted images at their original resolution are presented in Figures 3.1a to 3.1q. They are presented in order of increasing wavelength from 1.24 µm
to 6.2 cm to emphasise the change in morphology IC 10 undergoes as we look from
the near infrared (NIR) to radio wavelengths. At near-infrared (NIR) wavelengths
IC 10 reveals its older, cool stellar population. Note that point sources in these images are foreground stars from our own Galaxy. In the J-band (1.24 µm), H-band
(1.66 µm) and K-band (2.16 µm) images, IC 10 looks like a compact elliptical galaxy,
65
CHAPTER 3. RESULTS
66
surrounded by extended emission which extends farther out with increasing wavelength. At 3.6 µm we are looking at primarily the older stellar population of the
galaxy (Hunter et al., 2006), and it is in this image we begin to see faint, extended
structure with emission likely from very hot dust, which is in close proximity to the
hot young stars at the hearts of these star forming regions (SFRs). In addition, the
bandwidth of the 3.6 µm filter also detects emission from the 3.3 µm PAH line. Moving to the 4.5 µm image, emission here corresponds to hot dust as well, in addition
to some contribution from stars. IC 10 SE is now resolved into two separate smaller
regions, while IC 10 NW is also starting to take shape in the arc to the northwest
(see Figure 1.10 for positions of IC 10 SE and IC 10 NW). A second, much fainter
arc is barely visible extending far up to the north, above the first arc.
In the mid-infrared (MIR) images 5.8, 6.75, 8.0 and 11.4 µm we are seeing emission dominated by polycyclic aromatic hydrocarbons (PAHs). There is significant
structure in these images, as IC 10 SE and IC 10 NW are now very well defined, with
more diffuse emission in between. The arcs extending up and to the northeast have
now almost completely closed to form loops of material. It has been observed that in
the regions within these loops are very hot O and B-type stars, and an unusually high
density of Wolf-Rayet (WR) stars which all possess stellar winds capable of blowing
out material and causing it to build up around the edges (Hunter, 2001). The 15 µm
image primarily picks up continuum due to the warm dust, with the strongest diffuse structure located in between IC 10 SE and IC 10 NW, which are both still very
prominent.
The MIPS 24 µm image shows an extensive distribution of warm dust. In this
image we see smaller regions of strong emission, most distinctly in the upper northwest
CHAPTER 3. RESULTS
67
Figure 3.1a: Background subtracted images with original resolution, in order of increasing wavelength. Contours are overlaid for clarity with the lowest contour in each
image corresponding to the 3σ level. For all images, North is upwards and East is
to the left, and the greyscale and contours are in units of MJy/sr. The blue circles
and crosses mark the aperture sizes and centres of IC 10 SE and IC 10 NW. J-band
(1.24 µm): Contours are from 0.6 MJy/sr to 3.0 MJy/sr in increments of 0.6 MJy/sr
(3σ).
CHAPTER 3. RESULTS
68
Figure 3.1b: H-band (1.66 µm): Contours are from 0.9 to 5.4 MJy/sr in increments
of 0.9 MJy/sr (3σ).
CHAPTER 3. RESULTS
69
Figure 3.1c: K-band (2.16 µm): Contours are from 1.2 to 5.2 MJy/sr in increments
of 2.5 MJy/sr.
CHAPTER 3. RESULTS
70
Figure 3.1d: 3.6 µm: Contours are from 0.06 to 2.46 MJy/sr in increments of
0.3 MJy/sr.
CHAPTER 3. RESULTS
71
Figure 3.1e: 4.5 µm: Contours are from 0.06 to 3.06 MJy/sr in increments of
0.5 MJy/sr.
CHAPTER 3. RESULTS
Figure 3.1f: 5.8 µm: Contours are 0.3, 1.3, 3.3, 5.3, 7.3 and 9.3 MJy/sr.
72
CHAPTER 3. RESULTS
73
Figure 3.1g: 6.75 µm: Contours are from 0.9 to 9.9 MJy/sr in increments of
1.5 MJy/sr.
CHAPTER 3. RESULTS
74
Figure 3.1h: 8 µm: Contours are from 0.6 to 20.6 MJy/sr in increments of 4.0 MJy/sr.
CHAPTER 3. RESULTS
75
Figure 3.1i: 11.4 µm: Contours are from 1.5 to 21.5 MJy/sr in increments of
4.0 MJy/sr.
CHAPTER 3. RESULTS
76
Figure 3.1j: 15 µm: Contours are from 1.5 to 26.5 MJy/sr in increments of 6.0 MJy/sr.
CHAPTER 3. RESULTS
77
Figure 3.1k: 24 µm: Contours are 0.3, 5.3, 15.3, 30.3, 50.3, 100.3, and 200.3 MJy/sr.
CHAPTER 3. RESULTS
78
Figure 3.1l: 70 µm: Contours are 6.0, 12.0, 24.0, 48.0, 96.0, 192.0, and 384.0 MJy/sr.
CHAPTER 3. RESULTS
79
Figure 3.1m: 160 µm: Contours are from 21.0 to 291.0 MJy/sr in increments of
30.0 MJy/sr.
CHAPTER 3. RESULTS
80
Figure 3.1n: 450 µm: Contours are from 90.0 to 180.0 MJy/sr in increments of
30.0 MJy/sr.
CHAPTER 3. RESULTS
81
Figure 3.1o: 850 µm: Contours are from 6.0 to 16.0 MJy/sr in increments of
2.0 MJy/sr.
CHAPTER 3. RESULTS
82
Figure 3.1p: 3.55 cm: Contours are from 0.75 to 5.25 MJy/sr in increments of
0.75 MJy/sr.
CHAPTER 3. RESULTS
83
Figure 3.1q: 6.2 cm: Contours are from 0.39 to 1.43 MJy/sr in increments of
0.26 MJy/sr.
CHAPTER 3. RESULTS
84
part of the galaxy, with some smaller isolated pockets of emission located between the
two most prominent emission features. Moving to the 70 µm image our field of view is
significantly reduced so only the central region is visible. At this wavelength we have
very strong emission in both IC 10 SE and IC 10 NW; however we cannot infer the
structure of IC 10 in the extended regions as we do not have the spatial coverage, and
also because of the low resolution of the image. The outlying structure of IC 10 in
the western part is also missing from the 160 µm, again due to a field-of-view smaller
than the the size of IC 10, and its low resolution.
The SCUBA 450 µm and 850 µm images both trace cold dust in the galaxy. There
is some weak emission and structure visible in the 450 µm image; however, it is more
distinct in the 850 µm image. In the latter, it is possible to see a part of the arc
containing IC 10 NW. Diffuse emission is very difficult to see in these images due
to the magnitude of the noise, but there is some present in between the two main
regions.
Lastly, in the radio images we see strong non-thermal emission due to synchrotron
radiation from both IC 10 SE and IC 10 NW (recall from Section 2.8.3 that nonthermal emission dominates the total radio emission at these wavelengths), with
weaker diffuse emission extending in between both peaks and farther to the northwest
of IC 10 NW. This is an interesting result. Although there are H ii regions present,
which are generally dominated by thermal Bremsstrahlung emission, it means we are
looking at star forming regions within IC 10 SE and IC 10 NW containing hot young
stars. As a result, supernovae must have existed in these regions and perhaps still do.
While we do not observe them directly, meaning we do not observe the shells that
form from the blown out stellar ejecta of these supernovae, the non-thermal radiation
CHAPTER 3. RESULTS
85
we detect at radio wavelengths is indicative of this activity. It so happens that this
non-thermal radiation is stronger than the thermal Bremsstrahlung radiation. In the
6.2 cm image we see significant extended emission extending west of IC 10 SE, with
some isolated pockets of strong emission also present in the western part of the galaxy.
3.2
SED modelling
The Spectral Energy Distribution (SED) model we use to fit our observational SEDs
is a simple model based on that of Dale et al. (2001), with the dust properties of
Zubko et al. (2004) described in Section 3.2.1. The model incorporates several other
programs to aid in modelling the various aspects of the SED, such as the stellar
population and dust, using the most up-to-date data possible. The main components of the model are the dust composition (in this case we consider only silicates,
graphites and PAHs), dust grain size distribution, stellar population, extinction and
the interstellar radiation field (ISRF). The overall model is fit to the data using a
Levenberg-Marquardt least-squares fitting routine taking into consideration the uncertainties in the data. Individual SEDs are created for a variety of ISRF intensities,
and then combined using the power-law distribution (Dale et al., 2001)
dMd (U) ∝ U −α dU, 0.01 < U < 105 ,
(3.1)
where U is the radiation density or heating intensity, Md (U) is the mass of dust
heated by an ISRF with intensity U, and α is the index of a power-law distribution
describing the relative contributions of ISRFs with different intensities. While the
code allows a range of U between 0.01 and 105 , the range of U is generally narrower.
86
CHAPTER 3. RESULTS
The total dust SED, in terms of integrated luminosity per unit frequency (in Solar
units), is therefore
(1 − α)
Lν =
1−α
U+ − U−1−α
Z
U+
U−
dLν −α
Md dU,
U
dMd
(3.2)
with Md the total mass of dust. The derivative dLν /dMd multiplied by the total dust
mass, Md gives a summation of the luminosity contributions due to each dust or PAH
component, with
dLν
=
dMd
MPAH, tot
Md
MPAH+
1−
MPAH, tot
Lν, PAH +
MPAH+
MPAH, tot
Lν, PAH+ + Lν, g + Lν, s .
(3.3)
The luminosities of the PAH, graphite and silicate dust components are Lν, PAH , Lν, g
and Lν, s , respectively, and MPAH, tot /Md and MPAH+ /MPAH, tot are the PAH to total
dust mass ratio (normalised to the Galactic value of 0.046) and ionised PAH to
total PAH ratio, respectively. Note that Lν, g and Lν, s are already normalised to the
total dust mass, Md and are therefore not attenuated by 1/Md in Equation (3.3). A
description of these components follows in Section 3.2.1.
3.2.1
Model components
As stated already, the overall model makes use of several other models to describe
the various galactic components/environments. Here we describe each component in
more detail.
CHAPTER 3. RESULTS
87
Dust and PAH component
The size distribution of dust grains and PAHs for the SED model is based on the work
of Zubko et al. (2004). They created numerous dust size distribution models based
on different composition combinations using an analytical approximation constrained
with observational data. The authors use three different sets of abundances based on
solar, F and G star and B star observations (see their Table 1 for more details) to
help constrain their models in addition to infrared emission observations of the diffuse
interstellar medium (ISM) in our Galaxy, and interstellar extinction information.
The SED model we use takes for its dust composition the PAH, bare graphite and
silicate class of models from Zubko et al. (2004), with their grain size ranges listed
in Table 3.1. While the optical properties of the graphites and silicates such as the
extinction and absorption cross sections, Qext (λ, a) and Qabs (λ, a), are taken from
Zubko et al. (2004), the absorption cross sections, Qabs, PAH and Qabs, PAH+ , of the
neutral and singly positively ionised PAHs, respectively, are taken from Draine & Li
(2007). Draine & Li (2007) determine these parameters with up-to-date observational
data from the Spitzer Space Telescope. In addition, they adopt a PAH and large grain
shape of a sphere of radius a, which has the same volume of a grain with mass, mg
and density, ρ. The density for each component as assumed by Zubko et al. (2004)
is listed in Table 3.1. For reference, the smallest PAH molecule considered by Draine
& Li (2007) has 20 carbon atoms which corresponds to a sphere with a radius equal
to the minimum radius stated in Table 3.1.
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CHAPTER 3. RESULTS
Table 3.1: The size ranges for each dust component as determined by the model of
Zubko et al. (2004), along with their mass densities for each component.
Dust
Component
Graphite
Silicate
PAH
Minimum Size,
amin (µm)
0.00035
0.00035
0.00035
Maximum Size,
amax (µm)
0.33
0.37
0.005
Mass density,
ρ (g cm−3 )
2.24
3.5
2.24
Interstellar radiation field (ISRF)
The interstellar radiation field is the integrated mean radiation intensity of the ISM,
IISRF =
ZZ
Jλ dλdΩ = 4π
Z
Jλ dλ,
(3.4)
where Jλ is the mean radiation intensity per unit wavelength1 , and Ω represents a solid
angle. The ISRF in the solar neighbourhood was determined by Mathis et al. (1983) to
be 2.17×10−2 erg cm−2 s−1 , using a four-component model. These components include
ultraviolet (UV) emission from young hot stars, two components representing the
stellar population of the Galactic disk and a fourth component representing emission
due to red giant stars. While the UV component is created with a piecewise function
(see Mezger et al. (1982) for details), the other three components are blackbodies at
different temperatures modified by dilution factors, W . The total ISRF is then
IISRF = IUV + 4π[W2 Bλ (T2 ) + W3 Bλ (T3 ) + W4 Bλ (T4 )],
(3.5)
where IUV is the UV component of the ISRF, Bλ is a blackbody function, and the
values of the dilution factors Wi , and the temperatures Ti are given in Table 3.2. The
1
Equivalently we can define an intensity per unit frequency, Jν
89
CHAPTER 3. RESULTS
Table 3.2: The dilution factors and temperatures of the four-component ISRF model
by Mathis et al. (1983).
Component Number
1
2
3
4
Temperature, T (K)
0
7500
4000
3000
Dilution Factor W
0
1 × 10−14
1 × 10−13
4 × 10−13
equation for a blackbody curve is
1
2hc2
,
Bλ (T ) = 5
λ exphc/λkT −1
(3.6)
where T is the temperature of the star, h = 1.38 × 10−16 erg K−1 is the Planck
constant and c is the speed of light.
The ISRF component of our SED model makes use of this same ISRF function
for the Solar neighbourhood, but the ISRF for the model is allowed to vary using a
scale factor, U. We can express the ISRF in terms of an energy density defined as
4π
u=
c
Z
Jλ dλ.
(3.7)
The scale factor, U, is then defined as in Draine & Li (2007) by
uν = Uu⊙
ν,
(3.8)
with uν the energy density per unit frequency, and u⊙
ν the ISRF for the Solar neighbourhood, as determined by Mathis et al. (1983). Thus, U is a dimensionless radiation
density, normalised to the local ISRF. Recall that we introduced this parameter earlier in Equation (3.1) where dMd /dU is the mass of dust heated by a radiation field
CHAPTER 3. RESULTS
90
of intensity, U. The variable α in that equation ranges between 1 and 2.5 due to heat
intensity variations, depending on what kind of environment is being studied (Dale
et al., 2001). For a diffuse medium, α ≈ 2.5 since the intensity falls off as r −2 , where
r is the distance from the heating source. For more dense environments α ≈ 1, as the
heating intensity decreases linearly by dust absorption.
We note here that the general function (i.e. shape) representing the local ISRF in
Equation (3.5) may not ideally represent the ISRF for IC 10. In fact, Galliano et al.
(2005) compared models of the ISRF of four different dwarf galaxies (NGC 1569,
II Zw 40, He 2-10 and NGC 1140) with a model of the Galaxy’s ISRF and found
that the dwarf galaxies contain harder ISRFs and different overall shapes than that
of the Galaxy. For this SED model we have assumed that the shape of the ISRF of
IC 10 with respect to λ is the same as that of the Milky Way; however, the energy
density, u, is integrated over all wavelengths so U is actually a scaling factor of the
total ISRF. Therefore, U can give us an indication of the total integrated intensity
of the ISRF with respect to the Solar value, but not the overall shape of the ISRF.
This is acceptable for our SED model as we are not focusing on the general shape of
the ISRF of IC 10, but rather its total intensity.
Next we discuss the incorporation of stochastic heating into the SED model.
Stochastic heating
The heat capacity of a dust grain will vary with size, as it is proportional to its
volume. For certain small grains which possess internal energies less than or equal to
the average photons in the ISRF, absorption of a single photon can temporarily heat
them to very high temperatures, higher than the ambient dust temperatures. Their
91
CHAPTER 3. RESULTS
subsequent emission of an infrared (IR) photon causes their temperature to decrease
with time, until it absorbs another photon and the process is repeated (Draine &
Li, 2001). This process is dependent on the ISRF in which the dust grains reside,
as stronger fields mean more photons, which means less time for the grains to cool
before another photon is absorbed.
Stochastic heating is a very important factor in the ISM, as a large fraction of the
dust grains undergo this process. Only larger dust grains are assumed to maintain
thermal equilibrium with their surroundings, as they have a larger heat capacity
(Galliano et al., 2003). In the SED model we use, stochastic heating is accounted
for by creating synthetic spectra for each of the silicate grains, graphite grains, and
ionised and neutral PAHs. The temperature fluctuations are computed using the
method of Guhathakurta & Draine (1989). Once these spectra are created, the total
luminosity per unit frequency for each type of dust grain is evaluated.
Older stellar population
The evolution of the older star population is simulated using the PEGASE program
(Fioc & Rocca-Volmerange, 1997). The stellar population is assumed to have undergone a starburst 5 × 103 Myr ago, with instantaneous star formation. This means
that the older stellar population evolved together, with most of the star formation
occurring over a short period of time. The Initial Mass Function (IMF) which governs
the distribution of stellar masses of a particular stellar population is assumed to be
the Salpeter IMF (Salpeter, 1955),
ξ(M) ∝ (M)−1.35 ,
(3.9)
92
CHAPTER 3. RESULTS
where M is the stellar mass in Solar units.
The stellar population is allowed to evolve and the luminosity per unit mass is
determined. This value must then be multiplied by the total stellar mass Moldstar
to obtain the total luminosity per unit frequency Lν, star , of the older stellar population. Next the model will combine all the components to create the SED and apply
extinction and instrument colour corrections to it.
3.2.2
SED creation
The SED model fit is constrained by eight parameters, namely the total dust mass
Md , the PAH to total dust mass ratio MPAH, tot /Md , the fraction of all PAHs which
are ionised MPAH+ /MPAH, tot , the limits of the radiation density scale factor U− and
U+ , the power-law exponent α, the total V-band extinction AV , and the total stellar
mass Moldstar . The limits and initial values of each parameter are listed in Table 3.3.
The luminosity due to the dust and PAH component is calculated using Equations (3.2) and (3.3), which, when combined, becomes
Lν, PDR
1−α
= 1−α
U+ − U−1−α
Z
U+
U−
MPAH
{
Md
MPAH+
MPAH+
1−
Lν, PAH +
Lν, PAH+
MPAH, tot
MPAH,tot
+Lν, g + Lν, s } U −α dU Md .
(3.10)
This luminosity is then added to the luminosity due to the older stellar population,
Lν, star to obtain the total SED in units of Solar luminosities,
Lν = Lν, PDR + Lν, star .
(3.11)
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CHAPTER 3. RESULTS
Table 3.3: The eight parameters supplied as constraints for the model fit, their lower
and upper limits and their starting values.
Parameters
Dust Mass, Md (M⊙ )
Lower
Limit
0.0
Upper
Limit
–
Initial
Value
max(νLν )/(2 × 1010 )
×1 × 107
0.0
–
1.0
0.0
1.0
0.5
1.0
0.01
1.0
0.0
2.5
1.0 × 104
1.0 × 105
100.0
2.0
1.0
1.0 × 104
1.0
0.0
–
max(νLν )*10.0
PAH to Dust Mass
Ratio, MPAH, tot /Md
Ionised PAH to Neutral PAH Mass
Ratio, MPAH+ /MPAH, tot
Global SED power-law
exponent, α
ISRF scale factor, UISRF scale factor, U+
Extinction, Aν (mag)
Total Stellar Mass,
Moldstar (107 M⊙ )
The next step in the model is to apply the interstellar extinction corrections to the
total SED.
The total interstellar extinction law of a star or stellar population is defined as
A(λ) = −2.5 log
Iλ
Iλ0
,
(3.12)
where Iλ0 is the intrinsic intensity of the source for a given wavelength, λ0 , and Iλ
is the intensity we observe. For a medium which only absorbs and does not emit
radiation, Iλ /Iλ0 = exp(−τλ ), therefore
A(λ) = 2.5 log e · τλ = 1.086τλ .
(3.13)
CHAPTER 3. RESULTS
The reduced luminosity can be expressed as
Lν = Lν, 0 e−τλ = Lν, 0 e−Aλ /1.086 ,
(3.14)
where Lν, 0 is the uncorrected luminosity, as the dust extinguishes the light exponentially.
One final correction has to be applied to the SED to account for the different filters
used for the observations. Data obtained with a given instrument is calibrated against
a theoretical source that has a certain characteristic spectrum (in general, a constant
spectrum is assumed), such that, a measured flux density using observational data
is accurate for such a source. However, this simulated spectrum will not be accurate
for all types of observed objects, so a colour correction appropriate for the observed
object is often necessary to obtain photometry that is more accurate for that type
of object. Our model applies colour corrections to the derived SED to simulate the
observed photometry. The model’s synthetic photometry is then compared with the
observed photometry for each data point and the differences between the two are
minimised by the fitting routine. In the SED model, discrete points are plotted in
green, which represent the model photometry for each filter.
The SED model is iterative, and will continue iterating until the relative error in
the sum of squares is below some tolerance level.
In the next section we discuss the results of fitting this model to the observed
SEDs of IC 10 SE and IC 10 NW.
94
CHAPTER 3. RESULTS
3.3
Model fitting results
We ran the SED fitting routine for both IC 10 SE and IC 10 NW. In Figure 3.2 we
present the model SED fit to the observational data for IC 10 SE. The open black
circles with error bars are our observational data, the red line is the contribution
from dust and PAHs, the yellow line is the contribution from the evolved stellar
population, the blue line is the total SED without extinction corrections, and the
dark grey line is the final SED fit with extinction corrections. The green dots are the
synthetic photometry corresponding to each observational data point.
In Figure 3.3 we present the best fitting model SED for IC 10 NW. The lines and
circles have the same meaning as described above for the model of IC 10 SE.
In Table 3.4 we present the final values for each of the eight parameters as determined by the fitting routine for IC 10 SE and IC 10 NW. Errors on these parameters
were determined by running models for the limiting values of our initial data based on
the extremes of their uncertainties. The differences between these limiting cases and
our best-fit model are calculated and we assigned the average of the two differences
to the error if they were similar, or we took both limits in cases where the differences
were significantly different. We realise that this is a very conservative method of
evaluating the errors on these parameters, but this method does give us an idea as to
how the model responds when fitting the extreme limiting cases.
In the next chapter we examine the results of our models and conduct a spatial
analysis on the entire galaxy.
95
CHAPTER 3. RESULTS
96
Figure 3.2: The model SED for IC 10 SE. black circles with error bars: our calculated flux values; red : contribution
from dust and PAHs; yellow : contribution due to older stellar population; blue: total SED without extinction
corrections; dark grey: extinction corrected total SED; green dots: interpolated values of luminosity for each input
wavelength.
CHAPTER 3. RESULTS
97
Figure 3.3: The model SED for IC 10 NW. black circles with error bars: our calculated flux values; red : contribution
from dust and PAHs; yellow : contribution due to older stellar population; blue: total SED without extinction
corrections; dark grey: extinction corrected total SED; green dots: interpolated values of luminosity for each input
wavelength.
98
CHAPTER 3. RESULTS
Table 3.4: The values of the eight parameters determined by the best-fitting model,
for both IC 10 SE and IC 10 NW.
Parameters
Dust Mass, Md (104 M⊙ )
PAH to Dust Mass
Ratio, MPAH, tot /Md
Ionised PAH to total PAH Mass
Ratio, MPAH+ /MPAH, tot
Global SED power-law
exponent, α
ISRF scale factor, UISRF scale factor, U+ (103 )
Extinction, Aν (mag)
Total Stellar Mass,
Moldstar (107 M⊙ )
IC 10 SE
6.7 ± 0.7
IC 10 NW
0.5 ± 0.2
0.48 ± 0.03
0.45 ± 0.01
0.54 ± 0.08
0.59 ± 0.08
2.11 ± 0.02
0.85 ± 0.03
20.7 ± 0.8
0.91 ± 0.03
1.8+0.1
−0.8
2±1
9+6
−9
1.25 ± 0.06
10.15 ± 0.02
4.6 ± 0.1
Chapter 4
Analysis and discussion
In Chapter 3 we presented our 17 images of IC 10 at their highest resolution, introduced the Spectral Energy Distribution (SED) model we used to fit our observational
data (see Tables 2.7 and 2.8 in Chapter 2 for details about the observational data),
and presented our best-fitting models of both IC 10 SE and IC 10 NW. Here we
present key overlays1 which highlight some of the physical correlations between the
different components of these two regions, followed by an analysis on the best-fit
models and the implications they might have on our knowledge of IC 10.
4.1
Spatial analysis of IC 10
In this section we present several overlays which highlight the spatial correlation
between certain components of IC 10 on a global scale. In order to make these new
comparisons, we convolved the image with the higher resolution of the pair to match
that of the other image, following the same method described in Section 2.6. This is
1
An overlay consists of two separate images stacked on one another in order to see how the
emission at different wavelengths correlates.
99
CHAPTER 4. ANALYSIS AND DISCUSSION
100
to ensure we are not using images with a resolution that is lower than it needs to be
to make a meaningful comparison.
We begin with Figure 4.1, which shows contours of 24 µm emission overlaid on the
8 µm image in greyscale. Both the contours and greyscale are set to a minimum value
equivalent to 3σ for the 24 µm and 8 µm data, respectively. We see a tight spatial
correlation between the 24 µm and 8 µm emission which correspond to emission
from warm dust and PAHs, respectively. In addition to the strong emission from
both IC 10 SE and IC 10 NW, we also see small pockets of emission to the west
of IC 10 SE in between the two primary star forming regions. Much more diffuse
emission extends significantly to the west in 24 µm; however, the full extent of the
emission at 8 µm in this region is not known, as the coverage of that image does not
extend far enough west. Thus, both IC 10 SE and IC 10 NW contain photodissociation
regions (PDRs) surrounding the central star forming regions (SFRs) we know to exist
at these locations, as PDRs emit strongly through PAH lines and through the farinfrared (FIR) dust continuum (Tielens, 1995; Tielens et al., 2004). The central stars
heat up the surrounding dust and excite the PAHs which then emit photons upon
relaxing. The diffuse region between IC 10 SE and IC 10 NW, where we see faint
structure in 8 µm greyscale but no detail in the 24 µm. Small pockets of dust far
away from SFRs and strong FUV photons may not increase in temperature as much
as the dust near the SFRs, while PAHs are easily ionised by weaker FUV photons
and can still emit radiation upon recombination.
In Figure 4.2 we now show the 24 µm contours tracing warm dust overlaid on
the 850 µm emission in greyscale, which traces cold dust. While the 850 µm is quite
noisy, it is still apparent that there is a spatial correlation with at least the strongest
CHAPTER 4. ANALYSIS AND DISCUSSION
101
Figure 4.1: 24 µm contours overlaid onto the 8 µm image. The apertures of IC 10 SE
and IC 10 NW and their central positions are shown in blue. Contour levels are 0.3
(3σ), 5.3, 15.3, 30.3, 50.3, 100.3, and 200.3 MJy/sr.
CHAPTER 4. ANALYSIS AND DISCUSSION
102
Figure 4.2: 24 µm contours overlaid onto the 850 µm image. Contour levels range
from 0.5 MJy/sr to 10.5 MJy/sr in increments of 2 MJy/sr.
emission in IC 10 SE and IC 10 NW between the two components; however, the
24 µm appears more uniformly distributed in the extended areas surrounding these
two regions. It is possible that the extent of warm dust is more expansive than
the cold dust; however, it is more likely that this discrepancy between cold dust
and warm dust is a consequence of the low signal-to-noise in the 850 µm image, in
comparison with the 24 µm image. This makes it difficult to trace fainter emission
at 850 µm. We also see a correlation between the 8 µm emission and the 850 µm
emission in Figure 4.3, emphasising a link between cold dust, PAHs and warm dust
in the proximity of young stellar populations. The broader extent of 8 µm emission
CHAPTER 4. ANALYSIS AND DISCUSSION
103
Figure 4.3: 8 µm contours overlaid onto the 850 µm image. Contour levels range from
1.0 MJy/sr to 25.0 MJy/sr in increments of 4 MJy/sr.
is likely due to the fact that the 850 µm data are very noisy. Therefore, we cannot
conclude from this image whether or not the 8 µm emission is truly more expansive
than the 850 µm.
We will now investigate the correlations between these various components of the
interstellar medium by analysing the two model SEDs we presented in Chapter 3.
CHAPTER 4. ANALYSIS AND DISCUSSION
4.2
4.2.1
104
IC 10 SE
Best fit SED Model
In Figure 3.2 we show the best fit SED to the observational data. All the data points
are well constrained to the simulated photometry (green dots), which is the most
important result of the fit. Note that the 5.8 µm and 6.75 µm data points do not
lie on the total SED line (dark grey). We believe this is due to the fact that colour
corrections were applied to the discrete simulated photometry to match the observed
photometry, while the continuous SED emphasises the details of the PAH emission
lines in the near-infrared (NIR), which are lost in the broad-band photometry.
The peak of this SED occurs around 70 µm, which suggests that there is a large
component of warm dust in the region.
In Table 3.4 we show the values of the eight parameters corresponding to our best
fit. The total dust mass is (6.7 ± 0.7) × 104 M⊙ , and the fraction of this mass due to
PAHs is nearly one half (0.48) of the Galactic value of 0.046, giving the PAHs a total
mass of approximately (1.5 ± 0.2) × 103 M⊙ . This is only about 2 % of the total dust
mass, meaning that the vast majority of the dust mass is comprised of silicate and
graphite dust grains.
In addition, the fraction of PAHs that are ionised is 0.54 ± 0.08, suggesting that
the photoelectric effect is moderately efficient at heating the gas in this region, as it
is most efficient when the PAHs are neutral and can be easily ionised.
The power-law index, which describes the relative contributions of the individual
ISRF intensities to the overall SED, α (recall Equation (3.1)), is 2.11 ± 0.02, and the
limits of U are very broad, ranging from 0.85 to 2.04 × 104 u⊙ . When α ∼ 2.5, the
CHAPTER 4. ANALYSIS AND DISCUSSION
105
environment is more diffuse and the heating intensity, U, is dependent on the distance
from a central stellar source. Therefore, based on the value of α and the range of U,
we infer that the overall SED is weighted more towards individual SEDs for diffuse
regions, where the ISRF has a larger effect on the environment.
The extinction, AV , as determined by the model is (0.91 ± 0.03) magnitudes. To
compare this result with those in the literature, we convert this value to the colour
excess E(B − V ) using the relation
E(B − V ) = AV /RV ,
(4.1)
where AV is the visual extinction and RV is the total-to-selective extinction ratio.
Typically the adopted value of RV is ∼ 3.1 for the diffuse ISM in our Galaxy (e.g.
Schultz & Wiemer, 1975; Sneden et al., 1978; Clayton & Cardelli, 1988), therefore
with Equation (4.1) we find E(B − V ) = 0.29 ± 0.01. Values of the global E(B − V )
previously determined for IC 10 have ranged anywhere from 0.4 mag to > 1 mag
(see Demers et al. (2004) for a list of previously determined values for E(B − V ));
however, a value of ∼ 0.75 − 0.80 mag, as determined by Massey & Armandroff
(1995) is generally accepted by several authors for the global colour excess. However, Hunter et al. (2006) find a E(B − V ) = 0.4 ± 0.3 for a smaller aperture of
IC 10 SE than we have although it is within our aperture (their Region 3: Right
Ascension (RA) = 00h 20m 27.1s , Declination (DEC) = 59◦ 17′ 06′′ , compared to our
central position of RA = 0h 20m 28.5s , DEC = 59◦ 17′ 06.08′′ ), which is in good agreement with our determined value.
The mass of the older stellar population in IC 10 SE is (1.015 ± 0.002) × 108 M⊙ .
Jarrett et al. (2003) determined that the total stellar population of IC 10 is 3×108 M⊙
CHAPTER 4. ANALYSIS AND DISCUSSION
106
using 2MASS images (adjusted to our adopted distance of 0.82 Mpc), suggesting that
about one third of the total stellar mass is due to older stars in IC 10 SE. Recall from
Section 3.2.1 the model assumed a starburst occurred 5 × 103 Myr ago and underwent
instantaneous star formation. Therefore, this is the primary factor in obtaining such
a high fraction of the mass from older stars. Note that this fraction does not include
the stellar remnants of O and B stars that would have formed during the more recent
starburst thought to have occurred only 4–30 Myr ago (Hunter, 2001).
We have estimated the total mass of H i within IC 10 SE using a column density2
map from Wilcots & Miller (1998). The total H i mass is
MH i
mH NH i A
=
,
M⊙
M⊙
(4.2)
where mH is the mass of a hydrogen atom, 1.67 × 10−24 g, NH i is the column density
of H i, A is the area of the aperture, and M⊙ = 1.989 × 1033 g. At a distance of
0.82 Mpc, one arcsecond is equivalent to ∼ 4 pc, therefore the area of IC 10 SE is
∼ 0.1353 kpc2 or 1.29 × 1042 cm2 . From the column density map of Wilcots & Miller
(1998), the column density within IC 10 SE is ∼ 4 × 1021 cm−2 , therefore we find that
the total H i mass of IC 10 SE is approximately 4.3 × 106 M⊙ .
In order to determine the total mass of hydrogen, we also have to determine the
amount of H2 in the region of IC 10 SE, given by
mH NH2 A
MH2
=2
,
M⊙
M⊙
2
(4.3)
Column density is a measure of the surface density of atoms or molecules and is in units of
cm . Equivalently, it gives the total number of particles within a column of unit radius extending
vertically through the galaxy.
−2
CHAPTER 4. ANALYSIS AND DISCUSSION
107
where NH2 is the column density of molecular hydrogen. Using the same integrated
intensity map of CO from Leroy et al. (2006) that we used in Section 2.8.3, we estimate
an integrated intensity within IC 10 SE of ∼ 29 K km s−1 . Using the Galactic CO-toH2 conversion factor of 2 × 1020 cm−2 (K km s−1 )−1 adopted by Leroy et al. (2006),
we find the column density of H2 to be ∼ 5.8 × 1021 cm−2 , and therefore the mass
contributed by H2 molecules is ∼ 1.24 × 107 M⊙ . Combining this total with that for
H i map we find a total gas mass of 1.67 × 107 M⊙ . Note that the CO-to-H2 is known
to vary; however, Leroy et al. (2006) examined this factor and concluded that while
it is possible it may be slightly higher than the Galactic value in IC 10, they adopt
the Galactic value for their study as they deem it much more reliable.
We can now determine the gas-to-dust ratio for IC 10 SE. From Table 3.4, the
total dust mass is approximately 6.7 × 104 M⊙ . This gives a gas-to-dust mass ratio of
250 ± 30 which is higher than the Galactic value of ∼ 113 (measured with respect to
the total hydrogen mass); however, it is significantly lower than other low-metallicity
galaxies which have gas-to-dust mass ratios varying between 330 and 2000 (Galliano
et al., 2005). As the authors calculated the total gas mass to include the mass
of helium (He) which they assumed made up 25 % of the total, we need to multiply
their ratios by a factor of 0.75 to obtain the ratio just including the mass of hydrogen.
We then obtain a gas-to-dust mass ratio range of 248–1500, for which the lower end
of the range agrees with that for IC 10 SE. We will discuss this result in more detail
in Section 4.5.
We can also calculate the mass abundance of the PAHs, YPAH , which is the ratio
of the mass of PAHs to the total gas mass. The total mass of PAHs within IC 10 SE
is (1.5 ± 0.2) × 103 M⊙ , therefore the abundance of PAHs is (9 ± 1) × 10−5 . This is
108
CHAPTER 4. ANALYSIS AND DISCUSSION
similar to values derived for other dwarf galaxies, and we will compare these numbers
in Section 4.5.
One other value we can obtain is the fraction of the total dust mass that has
a temperature of . 25 K. This is approximately the characteristic temperature of
silicate or graphite dust grains in radiative equilibrium with their surroundings (the
temperature range for a silicate is between 20 and 30 K depending on size, while the
temperature range for a graphite grain is approximately 19 to 29 K (Tielens, 2005)).
These cold dust grains reflect the heating intensity they are exposed to, estimated to
be U . 8.5u⊙ . We can determine the fraction of cold dust with the following integral,
which is similar to that of Equation (3.2),
fc =
Mc
Md
1−α
= 1−α
U+ − U−1−α
Z
UT ∼25
K
U −α dU,
(4.4)
U−
where fc is the mass fraction of the total dust mass which has a temperature of less
than approximately 25 K, Mc is the mass of the cold dust, Md is the total dust mass,
and UT ∼25 K ∼ 8.5. Using the results summarised in Table 3.3, we find that the
fraction of cold dust in IC 10 SE is approximately (92 ± 10) %. This means that
the vast majority of the dust radiates with a temperature of less than approximately
25 K.
CHAPTER 4. ANALYSIS AND DISCUSSION
4.3
4.3.1
109
IC 10 NW
Best fit SED model
The best fit model SED for IC 10 NW is shown in Figure 3.3. There is a discrepancy
between the synthetic photometry (green dots) and the observed photometry (open
circles) at 6.75 µm. Aside from this one data point, the model fits well to the observed
data in this case, although in the FIR, namely the 70 µm and 160 µm data points,
the fit just passes through the error bars.
The peak of the SED is between 40 and 50 µm, and is somewhat asymmetric. With
the peak at this wavelength, we infer that a large fraction of the dust in IC 10 NW is
heated to higher temperatures than in IC 10 SE (for which the SED peaked around
70 µm), giving rise to the peak at 50 µm. The total dust mass in this region is
(5 ± 2) × 103 M⊙ , and following the same method as for IC 10 SE, we determine that
the PAH mass is only about (97 ± 41) M⊙ (see Table 3.4), or 2 % of the total dust
mass, which agrees with the mass fraction of PAHs in IC 10 SE. The fraction of PAHs
that are ionised is 0.59 ± 0.08, which is also equal to the fraction of ionised PAHs in
IC 10 SE within error.
The value of α determined by the model is 1.8+0.1
−0.8 , and the heating intensity varies
3
between 2 ± 1 and (9+6
−9 ) × 10 . The value of α is slightly less than that of IC 10 SE,
though within error they agree, and the range of U has narrowed significantly in
comparison to the range of U for IC 10 SE. The lower limits of U are the same for
both regions, while the upper limit has decreased by a factor of two, suggesting a more
uniform weighting of the various ISRF intensities for IC 10 NW. Using Equation (4.4)
and the results from Table 3.3, we find that the fraction of cold dust in IC 10 NW is
CHAPTER 4. ANALYSIS AND DISCUSSION
110
about (70 ± 50) %.
The visual extinction is 1.25 magnitudes, while the total mass due to evolved
stars is 4.61 × 107 M⊙ . Using Equation (4.1) we find the colour excess E(B − V ) of
this region to be approximately (0.40 ± 0.02) mag, which is slightly higher than in
IC 10 SE. This is lower than the adopted global colour excess for IC 10; however, no
previous study has examined the colour excess within IC 10 NW alone, therefore we
are the first to report a local extinction for IC 10 NW.
The gas-to-dust ratio can be evaluated in the same manner as it was for IC 10 SE.
From Wilcots & Miller (1998) we estimate the column density within IC 10 NW to be
2 × 1021 cm−2 . Since the area of IC 10 NW is 4.98 × 1041 cm2 , we find that the total
H i mass of 8.4 × 105 M⊙ . From Leroy et al. (2006) we find an integrated intensity
from CO of 1 K km s−1 , which corresponds to a H2 column density of 2 × 1020 cm−2 .
Therefore, the mass of H2 is approximately 1.67 × 105 M⊙ . Combining the H i and
H2 masses we obtain a total gas mass of ∼ 1 × 106 M⊙ . From Table 3.4, the dust
mass in IC 10 NW is 5 × 103 M⊙ , giving us a gas-to-dust mass ratio of approximately
200±80 which agrees with that of IC 10 SE within error. This result will be discussed
in more detail in Section 4.5.
Lastly, the PAH abundance by mass, YPAH , can now be calculated. The total PAH
mass is 97 M⊙ , therefore we find a relative abundance of (10 ± 4) × 10−5 .
4.4
Comparing IC 10 SE and IC 10 NW
Now that we have examined the model SEDs for IC 10 SE and IC 10 NW individually,
we will proceed to comment on the notable similarities and differences between these
two environments. Looking at wavelengths longer than 15 µm in Figures 3.2 and 3.3,
111
CHAPTER 4. ANALYSIS AND DISCUSSION
Table 4.1: A comparison between derived values for IC 10 SE and IC 10 NW.
Parameter
Dust mass surface density,
Σd (M⊙ arcsec−2 )
Stellar mass surface density,
Σstar (104 M⊙ arcsec−2 )
Fraction of dust with
T . 25 K, fc
Gas-to-dust mass ratio
PAH mass abundance, YPAH (10−5 )
IC 10 SE
IC 10 NW
7.8 ± 0.8
1.5 ± 0.6
1.186 ± 0.002 1.39 ± 0.03
0.92 ± 0.01
250 ± 30
9±1
0.7 ± 0.5
200 ± 80
10 ± 4
we see a few distinct differences. The most obvious difference is in the peaks of the
SEDs. For IC 10 SE we see that the peak has a fairly shallow curve around 70 µm,
while for IC 10 NW the peak is narrowed and is positioned at about 45 µm. We
conclude from this that the average dust temperature for IC 10 NW is warmer than
for IC 10 SE. This, in turn leads us to conclude that either the typical dust grain
sizes in IC 10 NW are smaller than in IC 10 SE, or the stronger ISRF of IC 10 NW
could be heating the dust grains to higher temperatures, or both.
In Table 4.1 we present a comparison of the derived properties between IC 10 SE
and IC 10 NW. We find that the fraction of dust with a temperature of . 25 K is
equal for both IC 10 SE and IC 10 NW, within errors; however, the errors on the
value for IC 10 SE are much smaller than for the fraction of cold dust in IC 10 NW.
Therefore, it is possible that there is indeed a difference in the amount of cold dust
present in these regions, but we cannot discern a difference given the large error on
this fraction for IC 10 NW. If this were the case, the lower fraction of cold dust in
IC 10 NW would support our conclusion that the average dust temperature in that
region is warmer than for IC 10 SE. Future work with the model may confirm this.
Comparing the values for the parameters for both regions in Tables 3.4 and 4.1,
CHAPTER 4. ANALYSIS AND DISCUSSION
112
we see that IC 10 SE and IC 10 NW share an equal abundance of PAHs with respect
to both the total dust mass and to the total gas mass, within errors. In addition,
they also have the same ratio of ionised to neutral PAHs. This implies that the
same physical processes lending to these ratios is taking place in both IC 10 SE and
IC 10 NW. The presence of PAHs within these regions suggests the degree of ionisation
for all molecules and atoms within these regions will be affected. According to Tielens
et al. (2004), a number abundance of PAHs with respect to the number of hydrogen
atoms > 10−7 is considered high. Converting our mass abundance, YPAH , to a number
abundance, assuming the mass of one PAH is equal to 50 times the mass of one carbon
atom (since a typical PAH molecule comprises ∼ 50 carbon atoms), we find a PAH
number abundance of (1.5 ± 0.2) × 10−7 for IC 10 SE and a PAH number abundance
of (1.7 ± 0.7) × 10−7 for IC 10 NW. Therefore, we conclude that relative to the total
gas, the abundance of PAHs in IC 10 SE and IC 10 NW is high. These neutral and
ionised PAHs are combining with free electrons to create negatively charged ions and
neutral PAHs, respectively, which leads to an environment in which the degree of
ionisation is low. In addition, the ionised PAHs contribute to a reduction in efficiency
of the photo-electric effect, which in turn, affects the temperature of the surrounding
gas.
The total visual extinction, AV is slightly higher in IC 10 NW than IC 10 SE. As
we look along the same line of sight to both regions, we would assume the foreground
extinction due to our own galaxy would be the same for both regions. Therefore, we
believe that the discrepancy lies in the internal extinction of the galaxy.
To make a meaningful comparison of the dust and stellar masses between IC 10 SE
and IC 10 NW it is necessary to convert the total masses to a surface density in Solar
CHAPTER 4. ANALYSIS AND DISCUSSION
113
masses per arcsecond (arcsec) squared, because the areas of the two regions differ. The
area of IC 10 SE is 8.56×103 arcsec2 , therefore from Table 3.4 and assuming a uniform
mass distribution, the surface density of the dust mass is (7.8 ± 0.8) M⊙ arcsec−2
while the surface density of the stellar mass is (1.186 ± 0.002) × 104 M⊙ arcsec−2 .
The area of IC 10 NW is 3.30 × 103 arcsec2 , therefore from Table 3.4 we find a dust
mass surface density of 1.5 ± 0.6 M⊙ arcsec−2 and a stellar mass surface density of
(1.39 ± 0.03) × 104 M⊙ arcsec−2 . The surface density of stellar mass is thus higher in
IC 10 NW by only a factor of ∼ 1.2, while the surface density of dust mass is higher
in IC 10 SE by a factor of ∼ 5. This implies that the concentration of dust is higher
in IC 10 SE than in IC 10 NW, but they have the same gas-to-dust mass ratio, within
error. This would imply that the amount of gas in IC 10 SE should be higher than
that of IC 10 NW, which we do not see. This may be a result of the dust simply
blocking more stellar light in IC 10 SE than in IC 10 NW, or it is possible that our
assumption of a uniform distribution of stars and dust is not a very good one within
these regions.
The upper limit on the range of ISRF intensities for IC 10 NW is weaker than that
of IC 10 SE; however, the power-law exponent, α, is the same for both regions. This
means that the distribution of ISRF intensities is the same for both IC 10 SE and
IC 10 NW and therefore, comparing the integrated value of U between the limits can
tell us the relative strengths of the fields in these regions. This leads to the conclusion
that the ISRF in IC 10 NW is weaker than in IC 10 SE, but still much stronger than
the ISRF in the Solar vicinity. The fact that our SEDs show that the average dust
temperature is warmer in IC 10 NW suggests that the dust is likely heated mostly by
the FUV photons emitted by stars at the heart of the star forming region, and not
CHAPTER 4. ANALYSIS AND DISCUSSION
114
by the ambient ISRF.
The fact that IC 10 SE and IC 10 NW share the same physical characteristics
with the exception of the dust temperature and ISRF, may be an indication that the
episodes of star formation occurring in these regions may have begun at approximately
the same time, leading to an initial mass function that is coeval for the higher mass
O and B stars formed in the recent starbursting episode. This would agree with
the conclusions of Hunter (2001), who identified a number of stellar associations of
intermediate mass stars (6.3–18 M⊙ ) which likely formed within the past 4–30 Myr
with a typical initial mass function (IMF).
4.5
A comparison with other galaxies
In this section we attempt to put our results into context by comparing the SEDs
of IC 10 SE and IC 10 NW with SEDs modelled for the Large Magellanic Cloud
(LMC), dwarf galaxy NGC 1569 and the Milky Way (MW). The LMC is a satellite
dwarf galaxy of our own galaxy, along with the Small Magellanic Cloud (SMC), and
is located at a distance of approximately 51 kpc (Keller & Wood, 2006). It has a low
metallicity of Z ∼ 0.3–0.5 Z⊙ (Bernard et al., 2008, and references therein) so it is
an ideal candidate for comparison to the regions of IC 10, which has a metallicity of
1/6 Z⊙ . We also compare our model SED to the dust SED of NGC 1569, modelled
by Galliano et al. (2003). It too, is an ideal dwarf galaxy to compare to IC 10 as its
metallicity is about 0.2 Z⊙ (Gonzalez Delgado et al., 1997). Lastly we will compare
the SED for IC 10 with two model SEDs of the Milky Way as modelled by Bernard
et al. (2008) and Dwek et al. (1997).
In Figure 4.6 we present four model SEDs of the LMC developed by Bernard et al.
CHAPTER 4. ANALYSIS AND DISCUSSION
115
Figure 4.4: Our model SED for IC 10 SE in units of L⊙ Hz−1 .
(2008). The model in the top left corner is a global SED while the top right, bottom
left and bottom right are for a particular H i region, and H i emission associated with
clouds CO-154 and CO-21, respectively. In order to compare the general shape of
their SED we have to convert the units of our SED from νLν to Lν . These figures
are shown in Figures 4.4 and 4.5. Note that we have not normalised our SED to the
number of hydrogen atoms in the region, as has been done for the LMC; however,
this is only a scaling factor and will not change the overall shape of the SED.
Comparing the SED of IC 10 SE with all four SEDs for the LMC, we see that
they all peak at approximately the same wavelength, though the peak in IC 10 SE
is at a slightly shorter wavelength (∼ 120 µm) than all of LMC SEDs, which peak
at approximately 150 µm. This implies that there is a deficit of FIR emission in
IC 10 SE with respect to the LMC, which is expected since we are only considering a
star-forming region within IC 10 SE. The LMC SEDs represent the global trend, and
CHAPTER 4. ANALYSIS AND DISCUSSION
116
Figure 4.5: Our model SED for IC 10 NW in units of L⊙ Hz−1 .
sample H i regions and CO clouds. If we compare the SED of IC 10 NW in Figure 4.5
with the four LMC SEDs, the only significant difference is between the peaks, as the
peak of IC 10 NW is at approximately 70 µm. From this we conclude that the largest
fraction of dust in IC 10 NW is warmer than that in the LMC because of its proximity
to a star forming region.
The results of the SED modelling of Bernard et al. (2008) also include values
for the PAH abundance, interstellar radiation field, and the gas-to-dust ratio. In
Table 4.2 we summarise these properties for all four regions of the LMC. We see that
the gas-to-dust ratios of IC 10 SE and IC 10 NW are in fairly good agreement with
those of the LMC. The metallicity of IC 10 is lower than that of the LMC, which
suggests a lower abundance of metals. If we assume that most metals are locked
up in dust, then this suggests that IC 10 has a lower dust mass and therefore the
gas-to-dust mass ratio should be higher.
CHAPTER 4. ANALYSIS AND DISCUSSION
117
Figure 4.6: The model SEDs for four different regions within the LMC (Bernard
et al., 2008). Top left: The entire LMC SED less the stellar contribution. Top
right: The SED for a selected H i region. Bottom left: The model SED of the H i
associated emission around cloud CO-154. Bottom right: The model SED of the H i
associated emission around cloud CO-216. Observational data points are black dots
while the model’s predictions are squares. The various components making up the
total SED (solid line) are the NIR continuum (long dash), PAHs (dashed line), very
small grains (dotted line) and big grains (dash-dotted line). All values are normalized
to NH = 1020 H cm−2 .
CHAPTER 4. ANALYSIS AND DISCUSSION
118
Table 4.2: A comparison of the important physical parameters derived for IC 10 SE
and IC 10 NW with those of several other galaxies.
Galaxy,
Region
IC 10, SEa
IC 10, NWa
LMC, globalb
LMC, H ib
LMC, CO-154b
LMC, CO-216b
NGC 1569c
MW, planeb
MW, diffuseb
Metallicity,
Z (Z⊙ )
0.17
0.17
0.3–0.5
0.3–0.5
0.3–0.5
0.3–0.5
0.25
1.0
1.0
Gas-to-Dust PAH Abundance,
Ratio
YPAH (10−4 )
250
0.9
215
0.97
333
0.98
250
1.58
260
1.78
186
2.69
555–1200
∼ 0 − 0.01
128
3.11
172
4.83
ISRF Scale
Factor, U
0.85–2.04 × 104
2.1–9.43 × 103
1.83
1.19
2.59
1.91
–
1.46
0.80
a
this thesis
Bernard et al. (2008)
c
Galliano et al. (2003), Galliano et al. (2005). Note that the ISRF was modelled for this galaxy
and a scale factor range was not determined explicitly. Note that we have adjusted the gas-to-dust
ratio to reflect a total gas mass excluding helium.
b
Figure 4.7 shows the model SED for NGC 1569 by Galliano et al. (2003). The
peak of this SED is approximately 60 µm, which is similar to the peak of IC 10 SE
but farther towards the FIR than that of IC 10 NW (as shown in Figures 3.2 and 3.3),
suggesting NGC 1569 and IC 10 SE share a common dominant warm dust component.
The metallicity of NGC 1569 is slightly higher than that of IC 10; however, we see
that it has a lower abundance of PAHs, which was determined by the model to be
. 1.0 × 10−6 . IC 10 SE has a PAH abundance that is larger than NGC 1569 by a
factor of ∼ 1000. This would suggest that IC 10 is bathed by a much weaker ISRF
than NGC 1569, if we assume that the PAHs are destroyed by the hard ISRF photons.
We know that IC 10 is undergoing strong star formation activity, and that it has a
large population of O and B stars (Hunter, 2001); however, NGC 1569 is thought to
have undergone an episode of star formation in its recent past. Therefore, we would
CHAPTER 4. ANALYSIS AND DISCUSSION
119
Figure 4.7: The modelled dust SED of NGC 1569 as presented in Galliano et al.
(2003). The components contributing to the overall SED are big grains (BGs; dashdotted line) of dust, very small grains (VSGs; dotted line) of dust, polycyclic aromatic
hydrocarbons (PAHs; dashed line) and very cold dust grains (VCGs; dash-dot-dot-dot
line). Observed data are shown as crosses with error bars, where the horizontal error
bars represent the filter bandwidth for a given wavelength, not physical error).
expect this result to be true if the photons emitted from the young stars in NGC 1569
are presently ubiquitous, while those in IC 10 are still primarily absorbed by dust or
photodissociate molecules.
In addition, Galliano et al. (2003) determined a gas-to-dust ratio of 550–1200,
which is significantly higher than that of either IC 10 SE or IC 10 NW. This could
imply that either IC 10 SE has an unusually high dust mass, or unusually low gas
mass, though it is likely an effect of the fact that that the ratio for NGC 1569 is a
global value and not for solely a SFR.
Lastly we compare IC 10 SE with two model SEDs of the Milky Way (MW;
CHAPTER 4. ANALYSIS AND DISCUSSION
120
Bernard et al., 2008). On the left-hand side of Figure 4.8 is a model SED for the
plane of the MW while on the right is a model for the diffuse regions of the MW.
Referring again to our models in Figures 4.4 and 4.5, we see that both modelled
SEDs of the MW peak at approximately 170 µm implying that both the plane and
diffuse regions of the MW have a similar warm dust content to IC 10 SE; however,
this component is cooler than that of IC 10 NW. The gas-to-dust ratios are 128 and
172 for the plane and diffuse areas, respectively, both of which are lower than those
of IC 10 SE and IC 10 NW. This is expected, as the Milky Way is at a later stage of
evolution than IC 10 and therefore will have depleted more of its gas reservoir.
The abundance of PAHs in the plane of the MW is approximately 3.11 × 10−4
while in the diffuse region it is higher at 4.83×10−4 , whereas the abundances of PAHs
in IC 10 SE and IC 10 NW are 0.9 × 10−4 and 0.97 × 10−4 , respectively. We find
that the ISRF in IC 10 SE is stronger overall than both the plane of the MW and the
diffuse regions which have scale factors of 0.80 and 1.46, respectively. We assume that
the lower PAH abundance in IC 10 is again due to a stronger ISRF than that of the
Milky Way, which leads us back to the question of whether or not the Galactic form
of the ISRF is suitable for low-metallicity galaxies. In this case, we conclude that it
is not, and it would be useful to be able to model the SEDs again with a different
ISRF to see how they vary.
Overall, we find that IC 10 SE has similar physical characteristics to the LMC,
but differs from NGC 1569, in that IC 10 SE has a higher PAH abundance and
ISRF but a much lower gas-to-dust mass ratio. One reason for this discrepancy
may be that the values for NGC 1569 are global values and therefore encompass
numerous different environments, while we are focusing on two star forming regions.
CHAPTER 4. ANALYSIS AND DISCUSSION
121
Figure 4.8: Two model SEDs for the Milky Way, one for the plane (Bernard et al.,
2008) and one for the diffuse ISM (Dwek et al., 1997). Observational data points
are black dots while the model’s predictions are squares. The various components
making up the total SED (solid line) are the NIR continuum (long dash), PAHs
(dashed line), very small grains (dotted line) and big grains (dash-dotted line). All
values are normalized to NH = 1020 H cm−2 .
As expected, IC 10 SE differs from the Milky Way, with a higher gas-to-dust ratio
and lower abundance of PAHs, although the lower limit on the heating intensity
for IC 10 SE is comparable to that of the diffuse Milky Way. In general, we also
find similar trends between these galaxies and IC 10 NW, although it has a slightly
stronger ISRF than IC 10 SE and a larger component of warm dust. These results
suggest that both star forming regions we studied in IC 10 reflect the fact that IC 10
is at an earlier stage of evolution than the Milky Way, and is, in fact, similar to other
dwarf irregular galaxies.
Chapter 5
Summary and Conclusions
We have presented seventeen images of the dwarf irregular galaxy IC 10, ranging in
wavelength from 1.24 µm to 6.2 cm. Data were obtained from the archives of the
2MASS survey, the Infrared Space Observatory (ISO), the Spitzer Space Telescope,
and the Very Large Array (VLA) at the National Radio Astronomy Observatory
(NRAO). In addition, we present new observations at 450 µm and 850 µm, taken
with the Submillimeter Common-User Bolometer Array (SCUBA) mounted on the
James Clerk Maxwell Telescope (JCMT).
We have modelled the observed spectral energy distributions (SEDs) of IC 10 SE
and IC 10 NW from 1.24 µm to 850 µm. We are the first to present such wellconstrained models of two individual star-forming regions within IC 10. The model we
used is based on that of Dale et al. (2001), and the premise is a power-law distribution
measuring the total dust mass (including silicate and graphite grains, and PAHs) as
a function of the interstellar radiation fields (ISRFs) in which the dust is located.
Individual, localised SEDs are created and then combined to obtain the total SED
following this distribution of mass. The dust properties of the model are from Zubko
122
CHAPTER 5. SUMMARY AND CONCLUSIONS
123
et al. (2004) while characteristics of the PAHs are from Draine & Li (2007). The
interstellar radiation field is based on the Galactic ISRF in the Solar neighbourhood
of Mezger et al. (1982), and our SED model allows for a range of ISRF intensities
between 0.01 and 105 times the ISRF in the Solar vicinity. The stochastic heating
model is from Guhathakurta & Draine (1989), and the older stellar population is
allowed to evolve using the program PEGASE, by (Fioc & Rocca-Volmerange, 1997).
The SED model incorporates all of these components into its evaluation of the
total luminosity from dust and PAHs, and old stars. We constrain the model with
eight parameters, which are allowed to vary in obtaining the best fit to the observed
data. These parameters are the total dust mass, Md , the PAH to total dust mass
ratio MPAH, tot /Md , the fraction of all PAHs which are ionised MPAH+ /MPAH, tot , the
limits of the radiation density scale factor U− and U+ , the power-law exponent α,
the total V-band extinction AV , and the total stellar mass Moldstar . We ran the SED
model for the regions IC 10 SE and IC 10 NW and obtained two well constrained fits
to the observed data.
Our most important conclusions are as follows:
• The structure of IC 10 changes dramatically as we look at observations of
the galaxy at progressively longer wavelengths. At near-infrared (NIR) wavelengths we see emission primarily from older stellar populations and hot dust
distributed in a relatively uniform elliptical shape. Looking at IC 10 at midinfrared (MIR) wavelengths we see strong emission from polycyclic aromatic
hydrocarbons (PAHs) concentrated in IC 10 SE and IC 10 NW, as well as more
extended emission in the western part of the galaxy, and in two arcs to the
north of IC 10 NW. Warm dust is apparent in the far-infrared (FIR), and the
CHAPTER 5. SUMMARY AND CONCLUSIONS
124
cold dust component of IC 10 is visible in the submillimetre images. Lastly,
we found strong emission due to non-thermal synchrotron radiation in our two
radio images.
• There are tight spatial correlations amongst emission at 8 µm, 24 µm, and
850 µm in IC 10 SE and IC 10 NW (i.e. the correlation between PAHs, warm
dust and cold dust), which is important as they are associated with star forming regions. In addition, there was some spatial correlation between certain
extended regions of IC 10, the arc to the north of IC 10 NW in particular.
• The model SEDs reveal a difference in the temperatures of the primary dust
components between IC 10 SE and IC 10 NW, as the SED of IC 10 SE peaks
around 70 µm while the SED of IC 10 NW peaks around 50 µm. IC 10 NW
thus appears to have a warmer dominant dust component than IC 10 SE which
may be due to the proximity of the dust to the hot stars at the centre of that
region.
• The total dust mass of IC 10 SE is (6.7 ± 0.7) × 104 M⊙ , and the fraction of the
dust mass contributed by PAHs is only 2 %, giving a relative PAH abundance
of 0.9 × 10−4 . This is similar to the relative PAH abundance of other dwarf
irregular galaxies. We also find that ∼ 92 % of the total dust mass radiates at
a temperature of . 25 K.
• The gas-to-dust mass ratio of IC 10 SE is 250±30, which is similar to that for the
Large Magellanic Cloud (LMC), but significantly lower than for NGC 1569. We
believe that the difference between these two gas-to-dust mass ratios is likely due
to the fact that the ratio for NGC 1569 encompasses the entire galaxy, including
CHAPTER 5. SUMMARY AND CONCLUSIONS
125
the various environments within the interstellar medium (ISM), whereas for
IC 10 SE we are looking primarily at a star forming region. We also find that
the gas-to-dust mass ratio of IC 10 SE is higher than the value for the Milky
Way of ∼ 113. This is expected as the Milky Way is at a later stage of evolution
than IC 10 SE and therefore has depleted more gas into the formation of stars.
The distribution of ISRF intensities for IC 10 SE is very broad and is comprised
primarily of ISRFs likely found in quiescent regions of the galaxy.
• The total dust mass of IC 10 NW is (0.5 ± 0.2) × 104 M⊙ , and the fraction
of PAHs by mass is the same as for IC 10 SE, within error. The fraction of
cold dust by mass is 0.7 ± 0.5, while the gas-to-dust ratio for IC 10 NW is
approximately 200 ± 80. The lower limit of the ISRF is slightly stronger in
IC 10 NW than in IC 10 SE; however, the range of intensities is more narrow
than for IC 10 SE which leads us to conclude that the ISRF is more moderate
with less extreme intensities in IC 10 NW.
• The two star forming regions of IC 10 are the same in most respects, within error,
and their characteristics reflect conditions in other dwarf irregular galaxies.
The two star forming regions of IC 10 may be similar as a result of star formation
episodes in these regions beginning simultaneously and evolving together. Studies of
the H i content by Wilcots & Miller (1998) show evidence of material being blown
out by the stellar winds of massive stars or supernova events, leaving holes which are
relatively empty of H i and increasing the density in regions surrounding the holes.
While the stars responsible for these holes likely formed very recently, as their lifetimes
are short in comparison to stars of lower mass, it is possible that the population of
stars which created the holes in H i formed earlier in the galaxy’s evolution than the
CHAPTER 5. SUMMARY AND CONCLUSIONS
126
stars currently forming in IC 10 SE and IC 10 NW. It would be beneficial for us to
obtain data for the H i distribution in order to make an accurate spatial comparison
between the holes and regions of ongoing star formation to see if and how they are
related.
Our results show that the star forming regions are not out of character for dwarf
irregular galaxies; however, we know that on a global scale IC 10 is unique with
its abundance of Wolf-Rayet stars and complicated distribution of H i. It would be
interesting to obtain maps in the FIR which cover a larger field-of-view than those we
have, so that we could investigate the more diffuse regions of IC 10 and see how they
compare with the two star forming regions we have studied for this project. With
the upcoming launch of the European Space Agency’s Herschel Space Observatory,
we may obtain maps that will allow us to carry out such an investigation. Modelling
SEDs of the more diffuse regions of IC 10 could give us a better idea of how the star
forming regions of the galaxy are different from the more diffuse regions and examine
how the physical characteristics differ and how these two environments interact with
each other. This, in turn, can give us more details about the star formation history of
the galaxy, and therefore will also allow us to better examine the evolution of IC 10
as a whole.
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Appendix A
List of Acronyms
2MASS Two Micron All-Sky Survey
BCD Blue Compact Dwarf
dE Dwarf Elliptical
dI Dwarf Irregular
FIR Far-Infrared
FITS Flexible Image Transport System
FUV Far-Ultraviolet
HST Hubble Space Telescope
IMF Initial Mass Function
IR Infrared
IRAC Infrared Array Camera
137
APPENDIX A. LIST OF ACRONYMS
ISRF Interstellar Radiation Field
ISM Interstellar Medium
ISO Infrared Space Observatory
JCMT James Clerk Maxwell Telescope
MIPS Multiband Imaging Photometer for Spitzer
MIR Mid-Infrared
NIR Near-Infrared
NaN Not a Number
NRAO National Radio Astronomy Observatory
PAH Polycyclic Aromatic Hydrocarbon
PDR Photodissociation Region
SCUBA Submillimeter Common-User Bolometer Array
SED Spectral Energy Distribution
SF Star Formation
SFR Star Formation Rate
VLA Very Large Array
138
Appendix B
Box Method IDL Code
B.1
“bkgrd box overplot.pro”
;; NAME: bkgrd_box_overplot
;; This is a program to calculate the mean and sigma for three
;; different box samples on a given image using bkgrd_box_method, and
;; then plot empty boxes onto the image to show where the samples came
;; from.
;; Tara Parkin
;; 2007
PRO bkgrd_box_overplot, image, header
;; Assume an image has already been loaded into IDL
139
140
APPENDIX B. BOX METHOD IDL CODE
yn = ’’
fn = ’’
read, yn, prompt = ’Would you like to save the $
final image as a postscript file?
Answer yes/no: ’
IF (yn EQ ’yes’) THEN BEGIN
read, fn, prompt = ’Please enter a filename, $
in the format "filename.ps": ’
set_plot, ’ps’
device, filename = fn ;optional keyword /color removed
ENDIF
;; Plot the image using pli:
i = image
h = header
nl = double(0)
READ, nl, PROMPT = ’Please select the number of levels $
to show on plot: ’
pli, i, h, nlevels = nl, charthick = 2.0
;; Determine the mean and sigma of three boxes,
;; and create arrays for plotting the box:
APPENDIX B. BOX METHOD IDL CODE
;; Define the data type of the coordinates:
x0 = double(0)
x1 = double(0)
y0 = double(0)
y1 = double(0)
FOR i=0, 2 DO BEGIN
READ, x0, x1, y0, y1, PROMPT = ’Please enter two corner $
coordinates (in pixel units) to create a box, $
using the format x0, x1, y0, y1: ’
;; Call program to calculate mean and variance (sigma)
;; of each sample:
bkgrd_box_method, image, x0, x1, y0, y1
;; Convert units of pixels to world coordinate system:
xyad, h, x0, y0, a0, d0
xyad, h, x1, y0, a1, d1
xyad, h, x1, y1, a2, d2
xyad, h, x0, y1, a3, d3
x_array_i = [a0, a1, a2, a3, a0]
y_array_i = [d0, d1, d2, d3, d0]
141
APPENDIX B. BOX METHOD IDL CODE
oplot, x_array_i, y_array_i, color=200
ENDFOR
;; Close ps device if open and set plot back to xwindow:
device, /close
set_plot, ’x’
END
B.2
“bkgrd box method.pro”
;; Program to calculate the mean and sigma of a small sample of
;; background from an image
;; Tara Parkin
;; 2007
PRO bkgrd_box_method, image, x0, x1, y0, y1
;; Assume an image has already been loaded into IDL
;; Define sub-array:
142
APPENDIX B. BOX METHOD IDL CODE
sub_array = image[x0:x1, y0:y1]
;; Determine mean and variance of selected region:
result = moment(sub_array)
mean = result[0]
sigma = sqrt(result[1])
middle = median(sub_array)
;; Now print mean, and sigma to the screen:
print, "The mean of the selected region is: ",mean," units."
print, ’The sigma of the selected region is: ’,sigma, ’ units.’
print, ’The median of the selected region is: ’, middle, ’units.’
END
143
Appendix C
Gaussian Method IDL Code
;;+
;; NAME: bkgrd_gauss_method
;;
;; PURPOSE: to estimate the background flux of an image by
;; analysing the LHS of a fitted gaussian to the histogram
;; corresponding to the image.
;;
;; CATEGORY: image analysis (background)
;;
;; CALLING SEQUENCE: bkgrd_gauss_method, image, header
;;
;; INPUTS:
;;
image = 2D array containing image pixel values
;;
header = fits header containing information about image
;;
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APPENDIX C. GAUSSIAN METHOD IDL CODE
;; MODIFICATION HISTORY:
;;
Began August 29, 2007 by Tara Parkin
;;
Modified September 24, 2007 by TP
;;
Modified April 24, 2008 by TP
;;
;; Note: This program assumes that the user has already read
;;in the fits file to be analysed.
;;-
PRO bkgrd_gauss_method, image, header, $
locations = locations, $
nbins = nbins, $
max = max, $
min = min
;; First, create and plot a histogram of number vs.
;; flux value.
;; Useful optional keywords for histogram include
;; locations, nbins (initially unspecified),
;; and max/min (initially unspecified).
;; Check if user defined a variable for locations,
;; and set default if not:
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APPENDIX C. GAUSSIAN METHOD IDL CODE
IF (n_elements(locations) EQ 0) THEN BEGIN
num_den = histogram(image,locations=flux, nbins=nbins,$
max=max, min=min, /nan)
ENDIF ELSE BEGIN
flux = locations
num_den = histogram(image,locations=flux, $
nbins=nbins,max=max, min=min, /nan)
ENDELSE
plot, flux, num_den, psym = 10
;; Check resulting histogram
ans = ’’
read, ans, prompt = ’Are you satisfied with this histogram? $
Answer "yes" to continue, or "no" to edit histogram $
parameters: ’
IF ans EQ ’no’ THEN BEGIN
WHILE (ans EQ ’no’) DO BEGIN
read, nbins, prompt = ’Enter value for nbins: ’
read, max, prompt = ’Enter value for max: ’
read, min, prompt = ’Enter value for min: ’
num_den = histogram(image,locations=flux, nbins=nbins,$
max=max, min=min)
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APPENDIX C. GAUSSIAN METHOD IDL CODE
plot, flux, num_den, psym=10
read, ans, prompt = ’Are you satisfied with this $
histogram?
Answer "yes" to continue, or "no" to $
edit histogram parameters: ’
ENDWHILE
ENDIF
;; Once histogram is satisfactory, the flux with the
;;highest count must be determined.
max_count = max(num_den)
max_x = where(num_den EQ max_count)
max_flux = flux[max_x]
;print, ’Max flux value: ’, max_flux
num_max_bins = n_elements(max_x)
;print, num_max_bins
;; Create new flux and num_den arrays.
flux_array = flux
flux_array_1 = flux_array[0:(max_x-1)]
flux_array_2 = flux_array[0:max_x]
f2_size = n_elements(flux_array_2)
const_array = dblarr(f2_size)
FOR k = 0, f2_size-1 DO BEGIN
const_array[k] = max_flux
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APPENDIX C. GAUSSIAN METHOD IDL CODE
ENDFOR
flux_array_2 = (const_array-flux_array_2) + const_array
;print, ’part two: ’, flux_array_2
;; Ensure second half of flux_array is increasing
;; (only use for fluxes less than 0):
IF flux_array_2[0] GT flux_array_2[f2_size-1] THEN BEGIN
flux_array_2 = reverse(flux_array_2)
ENDIF
new_flux_array = [flux_array_1,flux_array_2]
;print, ’Flux values: ’, new_flux_array
new_count_array = [num_den[0:(max_x-1)], $
reverse(num_den[0:max_x])]
;print, new_count_array
plot, new_flux_array, new_count_array, psym = 10
;; Check if any further modifications are necessary:
;User entered element number to change if necessary:
el_num = double(0)
;User entered value to replace old value in given element:
el_val = double(0)
yn = ’’ ;Answer
read, yn, prompt = ’Do you need to modify any bins? $
Answer yes/no: ’
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APPENDIX C. GAUSSIAN METHOD IDL CODE
IF yn EQ ’yes’ THEN BEGIN
print, ’The number of elements in the new flux $
array is: ’, n_elements(new_flux_array)
ENDIF
WHILE (yn EQ ’yes’) DO BEGIN
read, el_num, el_val, prompt = ’Enter the subscript of $
the element to change and its new value, $
in the format "element, value": ’
new_count_array[el_num] = el_val
read, yn, prompt = ’Do you need to modify any bins? $
Answer yes/no: ’
ENDWHILE
;; Plot final histogram to be fitted:
plot, new_flux_array, new_count_array, psym = 10
;; Fit a gaussian to the histogram:
fit_hist = gaussfit(new_flux_array, new_count_array, $
coefficients, nterms = 3)
oplot, new_flux_array, fit_hist, color = 110
print, ’The background estimate is approximately: ’, $
coefficients[1]
print, ’The sigma value is approximately: ’, coefficients[2]
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APPENDIX C. GAUSSIAN METHOD IDL CODE
yn2 = ’’ ;Answer
read, yn2, prompt = ’Do you want to save data from $
this run? Answer yes/no: ’
IF yn2 EQ ’yes’ THEN BEGIN
;; Save variables for original and modified histograms,
;; and gaussian parameters:
des=’’
read, des, prompt=’Please enter a sentence describing $
the image this analysis was conducted on: ’
fn=’’
read,fn, prompt = ’Please enter the filename for this $
data using the format "filename.sav": ’
save, flux, num_den, new_flux_array, new_count_array, $
fit_hist, coefficients, description = description, $
filename = fn
ENDIF
END
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