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MULTI-FREQUENCY TIME VARIABILITY
OF ACTIVE GALACTIC NUCLEI
RITABAN CHATTERJEE
Dissertation submitted in partial fulfillment
of the requirements for the degree of
&
Doctor of Philosophy
BOSTON
UNIVERSITY
%
BOSTON UNIVERSITY
GRADUATE SCHOOL OF ARTS AND SCIENCES
Dissertation
MULTI-FREQUENCY TIME VARIABILITY
OF ACTIVE GALACTIC NUCLEI
by
RITABAN CHATTERJEE
M.Sc., Indian Institute of Technology, Kanpur, India, 2003.
B.Sc., University of Calcutta, India, 2001
Submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
2010
Approved by
First Reader
Alan P. Marscher, PhD
Professor of Astronomy
Second Reader
Kenneth Brecher, PhD
Professor of Astronomy
Acknowledgments
We often say that mankind’s most fundamental questions are, “Where did I come
from? What am I doing? And where am I going from here?” It seems to me that these
apply perfectly to graduate students as well. This written thesis and the defense-talk
finally answer the second question (or so we hope!), the answer of the third question
is simple (post-doc, teaching, other jobs, ..., simply home to take a break) and this,
the acknowledgment, tries to answer the first question. But this is tricky because it’s
probably not uncommon toward the later stage of a PhD that one finds it confusing
to pinpoint where it all started. Who are the folks I am indebted to? After all, we
learn little things from even the strangers in the subway and those lessons may not be
any less valuable than how to numerically integrate a power-law-like function most
efficiently! So whom should I mention and whom should I take for granted? I have
decided to start from my first day of class at Boston University and trace it forward
and backward from there.
I can never forget my first day of class here at Boston University. There was a sense
of achievement in the realization that I was accepted to study here and eventually
contribute to the field of Astrophysics in a foreign land only because of my scientific
abilities and nothing else. That gave me an enormous amount of encouragement.
From that perspective I should start by thanking the Astronomy department as a
whole. There was not much in common except science. But the way I always felt
welcome, surrounded by friends and supportive people, was overwhelming. So, fellow
graduate students, professors and administrative staff, here is to you.
Talking about welcome, I still remember the reply that Prof. Alan Marscher gave
iii
me after I wrote an email asking if I could work with him in the summer (of 2004)
and “may be also after that.” It read, “Welcome to the Blazar group, Ritaban”, and
in the next five years I never hesitated to knock on his door. He was always there. At
first, to answer my questions, then, as time went by, to direct me to the idea instead
of giving a simple answer, and toward the end, as a sounding board to my ideas. He
usually starts answering a question assuming a level of knowledge that I may or may
not have (with the latter being the majority!). Often times I had to think about what
he said after coming back to my desk and sometimes I had to ask him again. But
then, as I said, he was always there. My knowledge of AGNs, my streams of thought
about time variability, my scientific writing and a part of my scientific philosophy
will always be largely influenced by him and I’m happy that it will. Thank you, Prof.
Marscher, for sharing your wisdom, your time and your philosophy with me.
This PhD was not possible without Dr. Svetlana Jorstad. The first project I
did for my thesis was very computational and statistics-intensive, and I was learning
FORTRAN at the time. I remember that I’d go to her with an error message or lines
of code and she’d patiently explain the trivial mistakes I made. We had hours of
discussion on statistical analysis and how the statistical results fit into AGN physics.
On the other side of the spectrum, I talked to her about numerous personal issues,
starting from homework deadlines to the imminent qualifier exam to how it is almost
impossible to keep track of all the AGN related papers in the Astro-ph archive. In research, whenever I hit an obstacle that seemed immovable or I felt really frustrated at
the slow pace of my progress at the time, her words were of immense encouragement.
Thank you, Dr. Jorstad, for being a true friend, philosopher and guide.
I also thank the other members of my PhD committee, Profs. Kenneth Brecher,
Nathan Schwadron, and David Thompson for valuable suggestions. At BU, I have
learned a lot of Astrophysics specifically from Profs. Tereasa Brainerd, Kenneth
iv
Brecher, Dan Clemens and James Jackson through courses, journal club and personal discussion. If I teach a class one day, parts of it will be designed based on
how they taught classes. I have also learned a lot from my discussion with fellow
graduate students including Ned Douglass, Loren Anderson, Ed Chambers, Suwicha
Wannawichian, Francesca D’Arcangelo, Monica Young and Tyler Chapmann. Ned
deserves a special thanks for familiarizing me with the social details of this foreign
country. There was a time when I used to ask him all my questions. I am also grateful
to Prof. Supriya Chakrabarti for his concern about my well-being throughout the last
six years. I am indebted to Prof. Phil Uttley of University of Southampton, UK for
his advice about the power spectral density calculations in my thesis. I also thank
my roommate Ayan Pal and Aritra Mandal (who is almost a roommate) for making
my life in Boston way more cheerful than it would have been without them.
In this work, I have used multi-waveband data from various sources. I thank
Haruki Oh, Alice Olmstead, and Benjamin Chicka (Boston University), Ian McHardy
(University of Southampton, UK), Margo Aller, and Hugh Aller (University of Michigan), Thomas Balonek (Colgate University), H. Richard Miller, Wesley Ryle, and
Kevin Marshall (Georgia State University), Gino Tosti (University of Perugia, Italy),
Omar Kurtanidze, and Maria Nikolashvili (Abastumani Astrophysical Observatory,
Georgia), Valeri Larionov, and Vladimir Hagen-Thorn (St. Petersburg State University, Russia), Anne Lähteenmäki, Merja Tornikoski, and Talvikki Hovatta (Metsähovi
Radio Observatory, Finland), and C. Martin Gaskell (University of Texas, Austin)
for providing and/or reducing the data used in this work. I also thank Martin Gaskell
for providing me the ICCF routine. Svetlana Jorstad reduced some of the optical as
well as VLBA data used in this thesis and made some of the VLBA images. She also
did much of the modeling of the VLBA data to derive the ejection times and apparent speeds of knots which have been presented and interpreted in this work. Alan
v
Marscher reduced the RXTE data and some of the VLBA data, and supervised the
collection and reduction of all the data that have been analyzed in this dissertation.
Now tracing backwards from my first day at BU, I thank the faculty at the Physics
Department of IIT Kanpur for giving me the preliminary lessons to be a tough professional in the field of Physics. I thank Prof. Alok Gupta of ARIES, India (who was
at HRI, India at the time) for giving me a chance to work on my first Astronomy
research project. Presidency College, Calcutta is where I learned to love Physics.
There were some excellent professors such as Profs. Debapriya Shyam, Pradip Kumar Dutta and Dipanjan Roy Chaudhuri. Moreover, the atmosphere in the Physics
department taught me to see Physics as something special. Fellow students in my
own class, those in the senior classes, professors, laboratory assistants and even the
inanimate instruments in the lab seemed to ooze out an essence of pride and timelessness and it seemed very natural to choose Physics as my profession. I shall always
be proud that I went to Presidency College. I am indebted to Dipankar Maitra, who
was a senior student at Presidency and IITK, for his valuable advice and suggestions
throughout these years. Before that, teachers at Ramakrishna Mission, Rahara and
Belur were very inspiring. I thank these institutions for teaching me discipline, hard
work and a love for learning. I am also grateful to my teacher, Mr. Nrisingha Prasad
Ghosh, for always inspiring me to stay with Physics and advising me not to be discouraged by temporary inconveniences. I can’t help singling out one aspect of my
school days: “additional Physics” classes at the ninth grade taught by Mr. Prasanta
Kundu. Those classes single-handedly changed how I see Physics (or science for that
matter), how I envision my future and how I understand nature. Thank you, Sir, for
your gift. I dedicate this thesis to you.
I remember that my elder brother taught me my first programming language. At
the time, little did we know that some day computer programming would be one
vi
of the main resources I’d use for my research. But, more importantly, my parents
and my brother helped me build my character. A PhD degree, I think, is a test of
character more than anything else. So, thank you for that and the constant support.
Being so far away for the last six years, I understand your value more than ever.
It’s absurd to acknowledge Suchetana’s contribution to this thesis and my life in
a line or two. She did all that I said above. She made me feel welcome, she taught
me specific topics, she is my friend and philosopher, she helped mold my scientific
philosophy, she shaped my character, she is my “truth, beauty and charm”. I look
forward to spending the rest of my life with you as much as making contributions to
the field of Astrophysics.
Boston, MA
Ritaban Chatterjee
07-23-09
vii
MULTI-FREQUENCY TIME VARIABILITY
OF ACTIVE GALACTIC NUCLEI
(Order No.
)
RITABAN CHATTERJEE
Boston University, Graduate School of Arts and Sciences, 2010
Major Professor: Alan P. Marscher, Professor of Astronomy.
ABSTRACT
In an active galactic nucleus (AGN), the central region of a galaxy is brighter
than the rest of the galaxy and sometimes ∼10,000 times as bright as an average
galaxy. The extremely high luminosities of AGNs are thought to be produced by
the accretion of matter onto a supermassive black hole (1 million - 10 billion solar
masses). In many cases AGNs produce two oppositely directed jets of magnetized
plasma moving at near-light speed that are luminous over a large range of wavelengths.
Understanding the structure and ongoing physical processes of AGNs has important
implications in cosmology, galaxy formation theory, black hole physics and other areas
of astronomical interest. Due to their large distances, AGNs are not spatially resolved
with current and near-future technologies except by radio interferometry. However,
we can use time variability, one of the defining properties of AGNs, to probe the
location and physical processes related to the emission at resolutions even finer than
provided by very long baseline interferometry (VLBI).
This dissertation employs extensive multi-frequency monitoring data of the blazar
3C 279 (over >10 years) and the radio galaxies 3C 120 and 3C 111 (>5 years) at Xviii
ray, optical, and radio wave bands, as well as monthly VLBI images. The study
develops and applies a set of statistical tools to characterize the time variability of
AGNs, including power spectral density (PSD), discrete cross-correlation functions
and decomposition of light curves to compare the properties of contemporaneous
flares in multiple wave bands. The significance of cross-correlation is determined
using random light curves simulated from the previously calculated PSDs.
This dissertation also develops numerical models of the time variable emission
spectrum of the jets and accretion disk-corona system to relate the variability to the
physics and locations of the various emission regions of the AGN. The analysis leads
to the inferences that (1) multiple nonthermal emission zones occur in the jet, (2)
acceleration of the highest energy electrons in the jet is often gradual, (3) optical
emission from the radio galaxies arises mainly in the accretion disk, (4) the X-ray
emitting hot electrons above the disk lie within about 50 gravitational radii from the
black hole, (5) X-ray emission from these radio galaxies contain a characteristic time
scale similar to that seen in Galactic X-ray binaries, and (6) A physical connection
exists between the radiative state of the accretion disk and events in the jet in these
radio galaxies.
ix
Contents
1 Introduction
1
1.1
Probing AGN Jets Using Time Variability . . . . . . . . . . . . . . .
1
1.2
Disk-jet connection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.3
Statistical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.4
Numerical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.4.1
Emission from Relativistic Jets . . . . . . . . . . . . . . . . .
7
1.4.2
Emission from the Disk-Corona System . . . . . . . . . . . . .
7
2 Radiative Processes and Jet Physics
9
2.1
Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.2
Matter Content and Magnetic Field . . . . . . . . . . . . . . . . . . .
10
2.3
Relativistic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.4
Emission Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.4.1
Black Body (Thermal) Radiation . . . . . . . . . . . . . . . .
15
2.4.2
Synchrotron Radiation . . . . . . . . . . . . . . . . . . . . . .
16
2.4.3
Inverse Compton Scattering . . . . . . . . . . . . . . . . . . .
17
2.5
Acceleration Mechanism: Shock acceleration . . . . . . . . . . . . . .
18
2.6
Contribution of this Dissertation toward the Understanding of AGNs
18
3 Observational Data
20
3.1
3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.2
3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.3
3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
x
4 Statistical Techniques Developed and Used in this Study
4.1
52
Power Spectral Density (PSD) . . . . . . . . . . . . . . . . . . . . . .
52
4.1.1
Results: 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4.1.2
Results: 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . .
57
4.1.3
Results: 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . .
60
Cross-correlation Function . . . . . . . . . . . . . . . . . . . . . . . .
62
4.2.1
Significance of Correlation . . . . . . . . . . . . . . . . . . . .
63
4.2.2
Uncertainties in Cross-correlation Coefficients and Time Delay
64
4.2.3
Results: 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . .
64
4.2.4
Results: 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . .
65
4.2.5
Results: 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . .
71
Time Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.3.1
Results: 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4.3.2
Results: 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . .
75
4.3.3
Results: 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . .
75
4.4
Comparison of DCCF and ICCF . . . . . . . . . . . . . . . . . . . . .
78
4.5
Light Curve Decomposition: Characterizing individual flares . . . . .
78
4.5.1
Results: 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.5.2
Results: 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4.5.3
Results: 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . .
93
4.2
4.3
5 Theoretical Modeling
5.1
5.2
94
Emission from Relativistic Jets . . . . . . . . . . . . . . . . . . . . .
94
5.1.1
Single Zone Model . . . . . . . . . . . . . . . . . . . . . . . .
95
5.1.2
Multi-Zone Model . . . . . . . . . . . . . . . . . . . . . . . . .
97
Emission from the Disk-Corona System . . . . . . . . . . . . . . . . . 104
xi
6 Discussion of Results
6.1
6.2
6.3
111
3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1.1
Red Noise Behavior and Absence of a Break in the PSD . . . 111
6.1.2
Correlation between Light Curves at Different Wavebands . . 112
6.1.3
Quantitative Comparison of X-ray and Optical Flares . . . . . 115
3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.1
PSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.2
Disk-Jet Connection . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.3
Source of Optical Emission . . . . . . . . . . . . . . . . . . . . 121
3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.3.1
PSD Break-BH Mass Relation . . . . . . . . . . . . . . . . . . 127
6.3.2
X-ray/Optical Correlation . . . . . . . . . . . . . . . . . . . . 128
6.3.3
Variation of X-ray/Radio Correlation . . . . . . . . . . . . . . 128
7 Conclusions
131
7.1
3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.2
3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3
3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.4
Implications for the General Population of Radio-Loud AGNs . . . . 136
References
141
Curriculum Vitae
149
xii
List of Tables
3.1
Start and end times of observations of 3C 279 presented in this study.
3.2
Ejection times, apparent speeds, and position angle of superluminal
21
knots in 3C 279. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.3
Parameters of the light curves of 3C 120. . . . . . . . . . . . . . . . .
34
3.4
Time, area and width of the X-ray Dips and 37 GHz Flares, and Times
of Superluminal Ejections of 3C 120. . . . . . . . . . . . . . . . . . .
44
3.5
Parameters of the Light Curves of 3C 111. . . . . . . . . . . . . . . .
46
3.6
Times of X-ray Dips and Superluminal Ejections in 3C 111. . . . . .
50
4.1
Parameters of the light curves of 3C 279 for calculation of PSD. . . .
54
4.2
Total energy output (area) and widths of flare pairs of 3C 279. . . . .
87
6.1
Theoretical expectation about the comparison of SSC and EC flares
following a synchrotron flare. . . . . . . . . . . . . . . . . . . . . . . . 116
xiii
List of Figures
1·1 Optical and VLBA images of the quasar 3C 279 . . . . . . . . . . . .
2
2·1 kpc scale jets of AGN 1 . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2·2 kpc scale jets of AGN 2 . . . . . . . . . . . . . . . . . . . . . . . . . .
10
2·3 Pc-scale jet of AGNs . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2·4 SED of 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
3·1 kpc-scale jet of 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . .
22
3·2 X-ray data of 3C 279 on different time-scales . . . . . . . . . . . . . .
24
3·3 Optical data of 3C 279 on different time-scales . . . . . . . . . . . . .
26
3·4 Radio data of 3C 279 on different time-scales . . . . . . . . . . . . . .
27
3·5 Distance versus epoch of VLBA knots of 3C 279 . . . . . . . . . . . .
28
3·6 X-ray, optical, radio and position angle variation of the jet in 3C 279
from 1996 to 2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3·7 VLBA images of the pc-scale jet of 3C 279 at one epoch during each
year of 11-year monitoring . . . . . . . . . . . . . . . . . . . . . . . .
30
3·8 VLBA core light curve of 3C 279 . . . . . . . . . . . . . . . . . . . .
32
3·9 kpc-scale jet of of 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . .
32
3·10 X-ray light curves of 3C 120 . . . . . . . . . . . . . . . . . . . . . . .
36
3·11 V and R band flux conversion for 3C 120 . . . . . . . . . . . . . . . .
38
3·12 Combined V and R band light curve of 3C 120 . . . . . . . . . . . . .
38
3·13 VLBA images of 3C 120: 1 . . . . . . . . . . . . . . . . . . . . . . . .
40
3·14 VLBA images of 3C 120: 2 . . . . . . . . . . . . . . . . . . . . . . . .
41
xiv
3·15 VLBA images of 3C 120: 3 . . . . . . . . . . . . . . . . . . . . . . . .
42
3·16 X-ray, optical, and Radio light curves of 3C 120 . . . . . . . . . . . .
43
3·17 kpc-scale jet of 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3·18 X-ray light curves of 3C 111 . . . . . . . . . . . . . . . . . . . . . . .
47
3·19 X-ray, optical and radio light curves of 3C 111 . . . . . . . . . . . . .
48
3·20 VLBA image of 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . .
49
4·1 PSD Results of 3C 279 . . . . . . . . . . . . . . . . . . . . . . . . . .
58
4·2 Success fraction vs. slope for 3C 279 PSD calculation . . . . . . . . .
59
4·3 X-ray PSD of 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
4·4 X-ray PSD of 3C 111 . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
4·5 Multi-wavelength correlation functions of 3C 279 . . . . . . . . . . . .
66
4·6 X-ray flux versus position angle of the jet cross-correlation . . . . . .
67
4·7 3C 120 X-ray/radio cross-correlation . . . . . . . . . . . . . . . . . .
68
4·8 3C 120 X-ray/optical cross-correlation . . . . . . . . . . . . . . . . .
70
4·9 3C 120 X-ray/optical cross-correlation of well-sampled subset . . . . .
70
4·10 X-ray/radio cross-correlation of 3C 111 . . . . . . . . . . . . . . . . .
72
4·11 Discrete cross-correlation function (DCCF) of the X-ray and 230 GHz
monitor data of 3C 111 between 2007 April and 2008 August. 230 GHz
variations lead those in the X-rays by 5 ± 7 days. . . . . . . . . . . .
73
4·12 X-ray/optical cross-correlation of 3C 111 . . . . . . . . . . . . . . . .
74
4·13 Correlation time window of 3C 279 . . . . . . . . . . . . . . . . . . .
76
4·14 Correlation time window of 3C 120 . . . . . . . . . . . . . . . . . . .
77
4·15 3C 120 X-ray/optical cross-correlation using ICCF . . . . . . . . . . .
79
4·16 3C 120 X-ray/optical cross-correlation (June 2004 to May 2005) using
ICCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
79
4·17 3C 120 X-ray/optical cross-correlation (June 2005 to May 2007) using
ICCF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
4·18 3C 120 X-ray/optical cross-correlation of well-sampled subset using ICCF 80
4·19 3C 120 X-ray/radio cross-correlation . . . . . . . . . . . . . . . . . .
81
4·20 3C 120 X-ray/radio cross-correlation excluding the major flare at 37
GHz in 2006-07 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4·21 Light curve decomposition of 3C 279 . . . . . . . . . . . . . . . . . .
84
4·22 X-ray/core flux correlation of 3C 279 . . . . . . . . . . . . . . . . . .
85
4·23 Baseline of the X-ray light curve of 3C 120 . . . . . . . . . . . . . . .
89
4·24 Light curve decomposition of 3C 120 . . . . . . . . . . . . . . . . . .
90
4·25 Comparison of dips and flares in 3C 120 . . . . . . . . . . . . . . . .
91
4·26 X-ray dip/superluminal ejection connection in 3C 111 . . . . . . . . .
92
5·1 Synchrotron spectrum in case of a single-zone model. . . . . . . . . .
95
5·2 Synchrotron self-Compton spectrum in case of a single-zone model. .
97
5·3 Simulated light curves from the time variable single zone model along
with segments of real light curves . . . . . . . . . . . . . . . . . . . .
98
5·4 Time variability of the synchrotron spectrum of the multi-zone model
100
5·5 Time variability of the SSC spectrum of the multi-zone model . . . . 101
5·6 Fraction of total emission at different energies versus the zone number
starting at the downstream end. . . . . . . . . . . . . . . . . . . . . . 102
5·7 Cumulative fraction of total emission at different energies versus the
zone number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5·8 Total intensity of different annuli of an accretion disk versus the annular
radii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5·9 The emission spectrum radiated by the annulus at a radius of 50 rg . 106
5·10 The emission spectrum radiated by the annulus at a radius of 1000 rg
xvi
107
5·11 The temperatures of flares in the accretion disk at different radii caused
by the propagation of a disturbance . . . . . . . . . . . . . . . . . . . 108
5·12 Simulated X-ray and optical light curves from the accretion disk-corona
model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5·13 Simulated X-ray and optical light curves from the accretion disk-corona
model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6·1 Model synchrotron and SSC flares 1 . . . . . . . . . . . . . . . . . . . 117
6·2 Model synchrotron and SSC flares 2 . . . . . . . . . . . . . . . . . . . 118
6·3 Discrete cross-correlation function (DCCF) of the soft and hard longlook X-ray data of 3C 120. . . . . . . . . . . . . . . . . . . . . . . . 124
6·4 Sketch of the accretion disk-corona system as derived in this work. . . 125
6·5 Intensely sampled dips in X-ray and optical light curves . . . . . . . . 126
xvii
List of Abbreviations
AGN
Active galactic nuclei
BHXRB
Black hole X-ray binary
BLR
Broad line region
DCCF
Discrete cross-correlation function
EC
External Compton
FR-RSS
Flux Randomization and Random Subset Selection
HWHM
Half-width at half maximum
kpc
Kilo-parsec
LT
Liverpool Telescope
M
Solar mass
mas
Milli arcsecond
PSD
Power spectral density
PSRESP
Power Spectrum Response
SED
Spectral Energy Distribution
SMBH
Super-massive black hole
SSC
Synchrotron self-Compton
VLBA
Very Long Baseline Array
VLBI
Very long baseline interferometry
XRB
X-ray binary
xviii
1
Chapter 1
Introduction
1.1
Probing AGN Jets Using Time Variability
Considerable progress has been made in our understanding of the nature of active
galactic nuclei (AGNs) over the last three decades (see Brecher (1976) for a summary
of early observational properties and theoretical ideas and Elvis (2001) for a recent
review). The extremely high luminosities of AGNs are thought to be produced by the
accretion of matter onto a supermassive black hole (SMBH, 106 − 1010 M ). In many
cases two oppositely directed jets of magnetized plasma are propelled at near-light
speed along the rotation axis of the accretion disk. One of the prominent theories
of jet production asserts that the jet plasma is driven by twisted magnetic field lines
threading the accretion disk or the black hole’s ergosphere, with the flow collimated
and accelerated along the poles (Meier, Koide, & Uchida 2001; Begelman 1995; Blandford & Payne 1982; Blandford & Znajek 1977; Lovelace, Berk, & Contopoulos 1991).
In some cases, the jets are luminous over a wide range of wavelengths from radio
to γ-rays. Radio to optical (and in some cases X-ray) emission from the jets is due
to synchrotron radiation (Impey & Neugenbauer 1988; Marscher 1998) and X-rays
and γ-rays are due to inverse Compton scattering of seed photons from within (synchrotron self-Compton, SSC) or outside the jet (radiation from broad emission line
region or BLR, accretion disk, or dusty torus; external Compton or EC) (e.g. Mause
et al. 1996; Romanova & Lovelace 1997; Coppi & Aharonian 1999; Blażejowski et al.
2000; Sikora et al. 2001; Chiang & Böttcher 2002; Arbeiter et al. 2005; Blażejowski
2
et al. 2000). High energy electrons required for the above-mentioned emission may
be produced in the jet by a moving shock wave (Marscher & Gear 1985), presumably produced by events near the SMBH, such as instabilities in the accretion disk.
Turbulence present in the jet can also energize the electrons.
The above-mentioned theoretical ideas about the launching and collimation of the
jet are incomplete, while the high-energy emission mechanisms are not well-tested
by observations. This is mainly because, due to their large distances, AGNs are
not spatially resolved with current and near-future technologies, except by very long
baseline radio interferometry (VLBI). However, we can use time variability—one of
the defining properties of AGNs—to probe the location and physical processes related
to the emission at resolutions even finer than provided by VLBI.
Fig. 1·1.— Left Panel: 3C 279 and its surroundings in optical wavelength. The kpc
scale jet and the inner structures of the quasar are all contained in the point source
(From STScI Digital Sky Survey Website). Right Panel: VLBA images of the jet
of the quasar 3C 279. Contours and color (grayscale) denote total and polarized
intensity, respectively. The VLBA, with its sub-milliarcsecond (mas) resolution, can
probe the parsec-scale features of the jet.
3
Figure 1, left panel, shows the optical image of 3C 279 and its surroundings in the
sky. It is a point source in this image. In 3C 279 (z=0.538), 1 arcsec is equivalent
to 6 kilo-parsecs (kpc). Therefore, with the best possible resolution in optical, ∼0.1
arcsec, we can not resolve the parsec (pc) scale jet. The point source contains the kpc
scale jet and the inner structures of the quasar. At even higher energy observations,
e.g., X-rays, γ-rays, the best possible angular resolution is also insufficient to resolve
the pc-scale features of AGN jets. The right panel shows a VLBA image of the
jet of 3C 279 at one epoch in 2008. The VLBA, with its sub-milliarcsecond (mas)
resolution, can probe the parsec-scale features of the jet. But even finer structures
need to be explored to investigate the acceleration and collimation processes involved.
This can be achieved by the investigation of the time variability properties of multiwaveband emission from AGNs. For example, the possible models of emission in
AGNs may be distinguished by measuring time lags between the flux variations in
multiple frequencies. Comparison of the amplitudes and times of peak flux of flares
at different wavebands may be used to identify the location of relevant emission
regions. For this reason, long-term multi-frequency monitoring programs are crucially
important. This dissertation uses such a program that has followed the variations in
emission of the blazar 3C 279 over a time span of ∼10 yr, and radio galaxies 3C 120
and 3C 111 (∼5 yr) with closely-spaced observations in X-ray (2-10 keV), optical (R
and V band) and radio (14.5 GHz, 37 GHz) wavebands as well as monthly observation
with the VLBA.
1.2
Disk-jet connection
Time variability can also be used in establishing the connection between the AGNs
and X-ray binaries. Stellar mass black hole X-ray binaries (BHXRBs) and AGNs are
both powered by accretion onto a black hole (BH). In many cases these systems emit
4
radiation over several decades of frequency and possess relativistic jets (Mirabel &
Rodriguez 1994, 1998; Greiner, Cuby, & McCaughrean 2001; Meier, Koide, & Uchida
2001). The above similarities in the basic generation of energy and observational
properties have led to the paradigm that these two systems are fundamentally similar
with characteristic time and size scales linearly scaled by the mass of the central BH
(∼10 M for BHXRBs and 106 to 109 M for AGNs). Although this paradigm has
given rise to the expectation that we might test models of AGNs with observations
of the BHXRBs, such an approach is unjustified until detailed, possibly quantitative
connections between BHXRB systems and AGNs become well-established. The comparison of BHXRBs and AGNs is complicated by the fact that a single AGN usually
does not show the whole set of properties that we wish to compare. For example,
Seyfert galaxies are the AGNs that most resemble BHXRBs, but their radio jets tend
to be weak and non-relativistic (e.g. Ulvestad et al. 1999). On the other hand, in radio
loud AGNs with strong, highly variable nonthermal radiation (blazars), the Doppler
beamed emission from the jet at most wavelengths dominates over thermal emission
from the accretion disk or its nearby regions.
One well-established property of BHXRBs is the connection between accretion
state and events in the jet. In these objects, certain well-defined changes in X-ray
states are associated with very bright features subsequently moving down the radio
jet (Mirabel & Rodriguez 1998; Fender & Belloni 2004). No accretion disk-jet connection was established in AGNs until Marscher et al. (2002) reported a relationship
between X-ray and radio events in the radio galaxy 3C 120. During three years of
monitoring of this object, they found that dips in the X-ray emission, accompanied
by spectral hardening, are followed by the appearance of bright superluminal knots
in the radio jet. Since the superluminal knots are disturbances propagating down the
jet, a connection between decreases in X-ray production and the emergence of new
5
superluminal components demonstrates the existence of a disk-jet connection.
Another similarity between the BHXRB and Seyfert galaxies is in their X-ray
power spectral densities (PSDs). The PSD corresponds to the power in the variability
of emission on different timescales. The X-ray PSDs of both Seyfert galaxies and
BHXRBs can be fit by piecewise power laws with one or more breaks. The PSD
“break frequency” scales with the mass of the central black hole (Belloni & Hasinger
1990; Nowak et al. 1999; Uttley et al. 2002; McHardy et al. 2004; Markowitz et al.
2003; Pounds et al. 2001; Edelson & Nandra 1999). Therefore, it is important to
investigate whether the X-ray PSD of AGNs such as 3C 120 also has a break and if it
does then whether that is consistent with the “break timescale-BH mass” relationship
given by McHardy et al. (2006) (break timescale is the inverse of break frequency) .
On the other hand, it is unclear a priori what the shape of the PSD of nonthermal
emission from the jet should be, a question which can be answered by calculating the
PSD of the X-ray variation of 3C 279, where most of the emission originates in the
jet.
1.3
Statistical Techniques
Detailed analysis of the time variable emission from AGNs is therefore instrumental
to the goal of establishing a model of AGN activity by constraining the physics of relativistic jets and the accretion disk-jet connection. To investigate the time variability
properties of AGNs, a set of robust and objective statistical tools is required so that
the deduced results are consistent and significant. This thesis develops such a set
of analysis techniques including power spectral density, discrete cross-correlation and
light curve decomposition, and employs them to extract physical information from
the observational data. The raw PSD calculated from a light curve combines two
aspects of the data set: (1) the intrinsic variation of the object and (2) the effects
6
of the temporal sampling pattern of the observations. In order to remove the latter,
we apply a Monte-Carlo type algorithm based on the “Power Spectrum Response
Method” (PSRESP) of Uttley et al. (2002) to determine the intrinsic PSD and its associated uncertainties. The cross-frequency time lag relates to the relative locations
of the emission regions at the different wavebands, which in turn depends on the
high-energy radiation mechanism(s). Similar complications affect the determination
of correlations and time lags of variable emission at different wavebands. Uneven
sampling, as invariably occurs, can cause the correlation coefficients to be artificially
low. In addition, the time lags can vary across the years owing to physical changes
in the source. In light of these issues, we use simulated light curves, based on the underlying PSD, to estimate the significance of the derived correlation coefficients. This
thesis also develops a technique similar to Valtaoja et al. (1999) to decompose the
light curves into individual (sometimes overlapping) flares. This is used to compare
the properties of contemporaneous flares at multiple wave bands.
1.4
Numerical Modeling
Application of the statistical analysis techniques on the long-term monitor data mentioned in the previous section gives us characteristic timescales of variability, crossfrequency time delays, and properties of the longterm flares in the light curves. To
connect these results with the physical variables in the jet, e.g., the magnetic field,
number density and energy distribution of electrons, and bulk velocity, numerical
modeling of the emission mechanisms in the jet is necessary. Similarly, modeling of
the emission processes in the accretion disk-corona system is required to deduce limits
on the the physical size of the corona, distance of the emission regions from the BH
and the relevant emission mechanisms.
7
1.4.1
Emission from Relativistic Jets
This thesis develops a model for the emission processes in the relativistic jets of
AGNs. I model the jet as an elongated box having 64 × 2 × 2 cells with magnetic
field and particle density decreasing with the distance from one side as is expected
from a conical jet. I assume that the electrons are energized by the passing of a shock
front (Marscher & Gear 1985) such that they form a power-law energy distribution. I
calculate the non-thermal radiation emitted by this distribution of electrons as they
lose energy via synchrotron and synchrotron self-Compton processes. Finally, I obtain
the time variable emission spectrum from the jet as the shock is passing through it and
also from the steady jet when the shock has already passed. Comparing the results of
the simulation and the application of the above-mentioned statistical procedures on
the real data, I draw conclusions about the location of the emission regions of these
objects and identify the ongoing emission mechanisms and implications regarding the
physics of jets.
1.4.2
Emission from the Disk-Corona System
I perform a theoretical calculation to produce multi-wavelength light curves from an
accretion disk-corona system. I use a computer code to simulate this disk-corona
system and then introduce a disturbance in the temperature of the accretion disk
that propagates from the center toward the outside or vice versa. As the disturbance
passes, the temperature at a given annulus increases and decreases with a Gaussian
profile. This causes a flare in the emission of the entire system at all wavelengths,
although the flare starts and peaks at different times at different wavelengths. I
produce these light curves at X-ray, UV, and optical wavelengths, including delays
from internal light travel time. From the comparison of the temporal properties of
the simulated light curves to those of the observed variability, I draw conclusions
8
about the physical size of the emitting regions and their relative distance, and put
constraints on the important parameters of the ongoing emission processes.
9
Chapter 2
Radiative Processes and Jet Physics
Accretion on to a compact object is often accompanied by a narrow bipolar outflow
— jets — perpendicular to the plane of accretion. Different classes of AGNs, which
are all powered by accretion onto a compact object, show a wide variety of jets. FR
II radio galaxies and radio loud quasars have highly relativistic, focused and very
powerful jets; FR I radio galaxies and BL Lac objects have less focused jets with
lower power than for the FR II sources, and Seyfert galaxies have weak and relatively
slow jets.
2.1
Morphology
0827+243
1222+216
D
C2
C1
C1
C2
2"
C5
3"
C3
C6
C4
Fig. 2·1.— kilo-parsec scale jet of AGNs. The grayscale and contours denote the
X-ray and radio intensity, respectively. Figure courtesy: Svetlana Jorstad.
Figures 2·1 and 2·2 show the kpc scale jets of 4 AGNs. Usually the jet broadens
10
with distance from the nucleus with a small (1◦ −5◦ ) opening angle. Its emission
structure consists of a series of knots (as seen in the figures). Figure 2·3 shows the
evolution of the pc scale jet of 3C 120 over 6 months. These VLBA images consist
of an apparently stationary bright spot called the “core” at the upstream end and
a series of knots downstream. In the figure, individual moving knots are marked at
selected epochs. Jets have a generally similar appearance on different length scales,
indicating self-similarity.
2209+080
1317+520
C
2"
3"
C1
C2
C3
Fig. 2·2.— kilo-parsec scale jet of AGNs. The grayscale and contours denote the
X-ray and radio intensity, respectively. Figure courtesy: Svetlana Jorstad.
2.2
Matter Content and Magnetic Field
Observation of synchrotron radiation from jets implies that the material in the jet is
a magnetized plasma. The content of the plasma may be electrons and protons or
electrons and positrons or a mixture of these. Recently, Homan et al. (2009), using
polarization properties of the pc scale jet of the quasar 3C 279 derived from VLBA
observations, determined the lower limit of the fraction of electron-proton plasma
to be 75%. The power-law emission spectrum indicates that the emitting particles
11
Fig. 2·3.— VLBA image of the pc-scale jet of the radio galaxy 3C 120 at 43 GHz at
seven epochs in 2002. The contours and color (grayscale) show the total and polarized
intensity, respectively. Individual moving knots are marked at selected epochs. In this
object knots move at an apparent speed of ∼ 4c. The core is the bright, stationary
feature on the left of each image.
12
(mostly electrons) have a power-law energy distribution given by
N(γ) = N0 γ −s ,
(2.1)
where γ is the electron Lorentz factor, s is a positive number in the range 1 − 4, and
N0 is the number density parameter. The average number density and energy density
of electrons are given by
n=
Z
N(E)dE
(2.2)
Z
EN(E)dE,
(2.3)
E
and
nE =
E
respectively. Since the jet broadens with distance r from the core, the magnetic field
B and the density parameter N0 decrease as B(r) ∝ r −b and N0 (r) ∝ r −a , where the
exponent a and b are positive numbers. Königl (1981) proposed that B ∝ r −1 and
N0 ∝ r −2 , i.e., a = 2 and b = 1. Subsequently it has been shown that in the jet of 3C
120, the above values of a and b are maintained over several orders of magnitude in
length scale (Walker et al. 1987). Marscher et al. (2008) showed that within a few pc
from the central engine of the AGN BL Lac, the jet contains a helical magnetic field
and beyond that region the ambient magnetic field has a chaotic structure.
2.3
Relativistic Effects
As shown in Fig 2·3, the pc-scale jet is made of a presumably stationary core and
a series of knots moving at apparent superluminal speeds. In case of blazars, the
apparent speeds of knots are between 5c − 50c and this occurs because the axis of the
jet is aligned very close to our line of sight (within a few degrees) and the emitting
material is approaching the observer at near light speed. The apparent velocity of
13
the emitting material in this case is given by
vapp =
βcsinθ
,
1 − βcosθ
(2.4)
where θ is the angle between the direction of motion of the emitting material and our
line of sight and β = v/c, where v is the actual velocity of the jet plasma.
Due to the motion of the emitting material, the “Doppler effect” causes the observed timescales and the observed wavelength of the emission to be shorter. The
Doppler factor
δ = [Γ(1 − βcosθ)]−1 ,
(2.5)
where Γ is the Lorentz factor of the flow, given by
Γ = (1 − β 2 )−1/2 .
(2.6)
The observed flux density of the plasma from a moving knot
Fν ∝ δ 3+α ,
(2.7)
where α is the spectral index. In the above expression, one factor of δ 2 occurs because the emission from a relativistically moving knot is not isotropic but is instead
emitted within a cone of half opening angle ∼ Γ−1 . Another factor of δ results from
compression of the timescale. The remaining δ α factor is added since the frequency
also increases by a factor of δ and Fν ∝ ν −α .
2.4
Emission Mechanisms
AGNs emit radiation at a broad range of frequencies from radio to γ-rays. This
is evident in the spectral energy distribution (SED) of the blazar 3C 279 shown in
Figure 2·4. This object is bright over 15 decades of frequency. Such a broad spectrum
14
Fig. 2·4.— The spectral energy distribution of the blazar 3C 279. The Y axis is in the
units of νLν so that it shows the total energy emitted at a given frequency interval.
Figure courtesy: Alan Marscher.
15
occurs because AGNs emit a mixture of thermal and non-thermal emission from both
the accretion disk-corona system and the jets. The low frequency radio emission
is synchrotron radiation from the large (kpc) scale jet, the high frequency radio to
optical emission is the same from the small (pc) scale jet, the accretion disk emits
thermal optical-UV radiation and the X-rays and γ-rays are produced in the small
scale jet through inverse Compton scattering of the synchrotron photons and seed
photons from outside the jet (accretion disk, broad emission line region etc.).
2.4.1
Black Body (Thermal) Radiation
Ultra violet emission from AGNs is dominated by blackbody radiation from the accretion disk (Malkan & Sargen 1982). The accretion disk is assumed to behave like
a blackbody where the temperature changes as a function of the radial distance from
the center as T ∝ r −3/4 (Shakura & Sunyaev 1973). Therefore, the accretion disk is
a “multi-color” blackbody where each annulus radiates following Planck’s Law, given
by
Fν =
2hν 3 /c2
exp(hν/kT (r)) − 1
(2.8)
where h, c, and k are Planck’s constant, the speed of light in vacuum and the Boltzmann’s constant, respectively, and T (r) is the temperature of the black body. After
integrating over r, the emission spectrum of the accretion disk as a whole is given by
Fν ∝ ν 1/3 exp(−
hν
),
kT (rmax )
(2.9)
where rmax is the radius at which the maximum dissipation per unit area occurs.
rmax is somewhat outside the marginally stable orbit (Krolik 1999). The wavelength
(λmax ) at which the intensity peaks is determined by Wien’s Displacement Law:
λmax T = 0.29 cmK
(2.10)
16
The temperature of the accretion disk in AGNs vary between ∼4000 to 40000 K,
hence it emits optical-UV radiation. The temperature (T) depends on the mass of
−1/4
the central BH (MBH ) as T ∝ MBH . The temperature of the accretion disk is given
by (Krolik 1999)
−1/4
1/4
T = 6.8 × 105 η −1/4 (L/LE )1/2 L46 RR (r/rg )−3/4 K,
(2.11)
where η is efficiency of converting accreted rest-mass energy into radiation, LE is the
Eddington luminosity, L46 is the bolometric luminosity in the units of 1046 ergs/sec,
RR is a factor which denotes the General Relativistic effects and gravitational radius
rg = GM/c2 , G and M being the gravitational constant and the mass of the central
BH, respectively.
2.4.2
Synchrotron Radiation
Synchrotron radiation is emitted by charged particles with relativistic energies in the
presence of a magnetic field. Jets of AGNs containing magnetized relativistic plasma
emit synchrotron radiation at radio to optical (sometimes X-ray) frequencies. The
critical frequency, near which most of the synchrotron luminosity occurs, is given by
νc = k1 γ 2 , while the synchrotron energy loss rate is given by dγ/dt = −k2 γ 2 . Both k1
and k2 are functions of B and are given by k1 = 2.8 × 106 B and k2 = 1.3 × 10−9 B 2 ,
where B is in Gauss. The spectrum of emission from a single electron is given by,
P (ν) = c1 F (x),
(2.12)
Z+∞
F (x) = x
K 5 (ξ) dξ,
(2.13)
where c1 is a constant and
3
x
17
where x = ν/νc and K 5 is the modified Bessel function of the second kind of order
3
5
.
3
The synchrotron emission coefficient is given by
γZmax
N0 γ −s F (x)dγ.
(2.14)
jν (ν) ∝ N0 B (s+1)/2 ν −(s−1)/2 ,
(2.15)
jν (ν) =
γmin
This can also be written as
where ν νc (γmax ).
2.4.3
Inverse Compton Scattering
Inverse-Compton (IC) scattering is another process through which electrons in an
AGN jet can emit high energy photons. In this process, a (seed) photon gains energy
when it scatters off a high energy electron. The seed photons may be synchrotron
photons produced by the same electron distribution in the jet or photons external
to the jet coming from the accretion disk, emission line clouds or the dusty torus.
The former process is termed synchrotron self-Compton (SSC) and the latter is called
external Compton (EC). The IC energy loss rate is dEIC /dt ∝ γ 2 Uph , where Uph is
the energy density of the seed photon field. The frequency of the scattered photon
(νf ) is approximately given by
νf ∼ γ 2 νi ,
(2.16)
where νi is the frequency of the incident photon. The inverse Compton emission
coefficient for a power-law electron energy distribution is given by
jνIC ∝
γZmax νZmax
N0 γ −s γ 2 Uph dγdν
γmin νmin
(2.17)
18
2.5
Acceleration Mechanism: Shock acceleration
Broadband nonthermal emission from radio to X-ray wave bands from kpc scale AGN
jets implies that a powerful particle acceleration mechanism is at work. Particles accelerated to very high energies in AGNs have been considered as a prime candidate
source of extragalactic cosmic rays (e.g. Brecher & Burbidge 1972). It is generally believed that shock fronts propagating down AGN jets are associated with such particle
acceleration. The electrons are energized along the shock front and then move away
at a speed close to c as they lose energy via synchrotron and IC processes (Marscher
& Gear 1985). The formation of jets in AGNs is tied to the accretion disk, so the
shock waves may be produced by disturbances that originate there. It is possible that
the process of jet production is punctuated by dramatic events due to instabilities
occurring in the accretion disk, and these events may inject high energy plasma into
the jet causing a shock wave to form and move through the jet. When some particles
are overtaken by a shock front their energy increases. Then, scattering by plasma
waves may cause some of the particles to change their velocity such that they overtake the shock front. In this process, energy of the particles increase as well since
between successive shock-crossing, their velocity distribution becomes isotropic with
respect to the flow due to internal scattering. By crossing the shock front multiple
times, particles can be accelerated to a high energy before they leave the acceleration
region. For a recent discussion of diffusive shock acceleration, see Schwadron, Lee &
McComas (2008) and McComas & Schwadron (2006).
2.6
Contribution of this Dissertation toward the Understanding of AGNs
Analysis and modeling of the time variable emission from AGNs can advance the
physical understanding of these systems. The variability timescale at high energies
19
(which is not affected by opacity in the jet) can be used to put constraints on the
source size, bulk velocity of the jet plasma and its angle to our line of sight. The nature
of the emission mechanism(s), e.g., the synchrotron flux, inverse Compton flux and
their relative amplitude, will inform us about the magnetic field and particle density
at different positions in the AGN jet. These will have direct implication regarding the
geometry and relative distances of the accretion disk and broad and narrow emission
line clouds. VLBI images of AGN jets along with polarization information can be
used to identify shocks in the jet. The efficiency of the shock acceleration mechanism
will be related to the typical variability timescale of the high energy emission. A large
set of well-sampled short timescale X-ray/optical flares may be used to investigate
the nature of the electron acceleration due to turbulence which is commonly assumed
to be the cause of such flares. The level of turbulence can be determined using the
ratio of observed fractional polarization to that for a uniform magnetic field (∼70%)
in the jet (Jorstad et al. 2007). We may probe deep into the accretion disk or even
closer to the black hole by investigating the larger amplitude variability, since this is
produced by changes deep inside the AGN, e.g., in the energy input or mass loading
in the jet presumably due to instabilities in the accretion disk.
Modeling of the time variable emission of AGNs is considered one of the prominent
challenges in contemporary astrophysics. This dissertation adds to the knowledge of
physical conditions deep inside the jet to put stringent constraints on the models. Jets
are observed in stellar-mass black hole and neutron star binary systems, star formation regions, and pulsar powered remnants of supernova explosions as well as AGNs.
Understanding the physical nature of jets, therefore, is necessary to understand all of
these astronomically interesting objects.
20
Chapter 3
Observational Data
In recent years, multi-wavelength monitoring of AGNs has been achieved using the
VLBA, a multitude of mm, submm, and radio telescopes and arrays such as CARMA,
SMA, and JCMT, numerous optical telescopes, the Rossi X-ray timing explorer
(RXTE), Swift, and XMM-Newton for X-rays, and Cherenkov detectors such as VERITAS and HESS over 0.05-10 TeV energies. Such monitoring is now being expanded
to a wide range of γ-ray energies (20 MeV to 300 GeV) through the Fermi Gamma-ray
Space Telescope, which was launched in June 2008. By analyzing a combination of
these data as well as VLBI imaging, more stringent tests on models for the nonthermal emission and jet physics in AGNs will be possible. In this chapter, I describe the
objects that have been studied in this thesis and discuss the observational data that
have been used for the study.
3.1
3C 279
The quasar 3C 279 (z=0.538; Burbidge & Rosenburg 1965) is one of the most prominent blazars owing to its high optical polarization and variability of flux across the
electromagnetic spectrum. Very long baseline interferometry (VLBI) reveals a onesided radio jet featuring bright knots (components) that are “ejected” from a bright,
presumably stationary “core”. The measured apparent speeds of the knots observed
in the past range from 4c to 16c (Jorstad et al. 2005), superluminal motion that
results from relativistic bulk velocities and a small angle between the jet axis and
21
Table 3.1 Start and end times of observations of 3C 279 presented in this study.
X-ray
Optical
Radio
data set
Start
End
Start
End
Start
End
Longlook Dec 96 Jan 97 Mar 05 Jun 05
Medium Nov 03 Sep 04 Jan 04 Jul 04 Mar 05 Sep 05
Monitor Jan 96 Jun 07 Jan 96 Jun 07 Jan 96 Sep 07
line of sight. Relativistic Doppler boosting of the radiation increases the apparent
luminosity to ∼ 104 times the value in the rest frame of the emitting plasma.
Table 3.1 summarizes the intervals of monitoring at different frequencies for each
of the three wavebands in our program. We term the entire light curve “monitor
data”; shorter segments of more intense monitoring are described below.
X-ray Monitoring
The X-ray light curves are based on observations of 3C 279 with the Rossi X-ray
Timing Explorer (RXTE) from 1996 to 2007. We observed 3C 279 in 1222 separate
pointings with the RXTE, with a typical spacing of 2-3 days. The exposure time
varied, with longer on-source times—typically 1-2 ks—after 1999 as the number of
fully functional detectors decreased, and shorter times at earlier epochs. For each exposure, we used routines from the X-ray data analysis software FTOOLS and XSPEC
to calculate and subtract an X-ray background model from the data and to model the
source spectrum from 2.4 to 10 keV as a power law with low-energy photoelectric absorption by intervening gas in our Galaxy. For the latter, we used a hydrogen column
density of 8 × 1020 atoms cm−2 . There is a ∼ 1-year gap in 2000 and annual 8-week
intervals when the quasar is too close to the Sun’s celestial position to observe.
In 1996 December and 1997 January we obtained, on average, two measurements
per day for almost two months. We refer to these observations as the “longlook”
22
Fig. 3·1.— VLA 15 GHz image showing the kpc-scale radio jet of 3C 279 and a radio
lobe extending to the northwest. The inset is a zoomed-in view of the nucleus. The
HST FOC V-band image (color/gray scale) is shown with a MERLIN+VLA 5 GHz
image overlaid. The 15 GHz fluxes are plotted logarithmically in steps of factor 2
beginning at 1.05 mJy beam−1 . This figure is from Figure 1 of Cheung (2002).
23
data. Between 2003 November and 2004 September, we obtained 127 measurements
over 300 days (the “medium” data). Figure 3·2 presents these three data sets. The
X-ray spectral index αx , defined by fx ∝ ν αx , where fx is the X-ray flux density and
ν is the frequency, has an average value of −0.8 with a standard deviation of 0.2 over
the ∼ 10 years of observation, and remained negative throughout.
Optical Monitoring
We monitored 3C 279 in the optical R band over the same time span as the X-ray
observations. The majority of the measurements between 1996 and 2002 are from the
0.3 m telescope of the Foggy Bottom Observatory, Colgate University, in Hamilton,
New York. Between 2004 and 2007, the data are from the 2 m Liverpool Telescope
(LT) at La Palma, Canary Islands, Spain, supplemented by observations at the 1.8
m Perkins Telescope of Lowell Observatory, Flagstaff, Arizona, 0.4 m telescope of the
University of Perugia Observatory, Italy, 0.7 m telescope at the Crimean Astrophysical
Observatory, Ukraine, the 0.6 m SMARTS consortium telescope at the Cerro Tololo
Inter-American Observatory, Chile, and the 0.7 m Meniscus Telescope of Abastumani
Astrophysical Observatory in Abastumani, Republic of Georgia. We checked the
data for consistency using overlapping measurements from different telescopes, and
applied corrections, if necessary, to adjust to the LT system. We processed the data
from the LT, Perkins Telescope, Crimean Astrophysical Observatory, and Abastumani
Astrophysical Observatory in the same manner, using comparison stars 2, 7, and 9
from Gonzalez-Perez et al. (2001) to determine the magnitudes in R band. The
frequency of optical measurements over the ∼ 10-year span presented here is, on
average, 2-3 observations per week. Over a three-month period between 2005 March
and June, we obtained about 100 data points, i.e., almost one per day (“longlook”
data). Another subset (“medium”) contains ∼ 100 points over 200 days between 2004
January and July. Figure 3·3 displays these segments along with the entire 10-year
24
Flux (10-11 erg cm-2 s-1)
6
Monitor
5
4
3
2
1
0
Flux (10-11 erg cm-2 s-1)
Flux (10-11 erg cm-2 s-1)
1996
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
2003.8
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1996.94
1998
2000
2002
2004
2006
2008
Medium
2004
2004.2
2004.4
2004.6
Longlook
1996.98
1997.02
1997.06
1997.1
YEAR
Fig. 3·2.— X-ray (2-10 keV) data of 3C 279 on different time-scales. In the upper
panel, the arrows show the times of superluminal ejections and the line segments
perpendicular to the arrows show the uncertainties in the times of ejection.
25
light curve.
Radio Monitoring
We have compiled a 14.5 GHz light curve (Figure 3·4) with data from the 26 m
antenna of the University of Michigan Radio Astronomy Observatory. Details of the
calibration and analysis techniques are described in Aller et al. (1985). The flux scale
is set by observations of Cassiopeia A (Baars et al. 1977). The sampling frequency was
usually of order once per week. An exception is a span of about 190 days between 2005
March and September when we obtained 60 measurements, averaging one observation
every ∼ 3 days (“medium” data).
VLBA Monitoring: Ultra-high Resolution Images
Starting in 2001 May, we observed 3C 279 with the Very Long Baseline Array (VLBA)
at roughly monthly intervals, with some gaps of 2-4 months. The sequence of images
from these data provides a dynamic view of the jet at an angular resolution ∼ 0.1
milliarcseconds (mas). We processed the data in the same manner as described in
Jorstad et al. (2005). For epochs from 1995 to 2001, we use the images and results of
Lister et al. (1998), Wehrle et al. (2001), and Jorstad et al. (2001, 2005). We model
the brightness distribution at each epoch with multiple circular Gaussian components
using the task MODELFIT of the software package DIFMAP (Shepherd 1997). At
each of the 80 epochs of VLBA observation since 1996, this represents the jet emission
downstream of the core by a sequence of knots (also referred to as “components”), each
characterized by its flux density, FWHM diameter (a circular Gaussian brightness
distribution is used), and position relative to the core. Figure 3·5 plots the distance
vs. epoch for all components brighter than 100 mJy within 2.0 mas of the core. We
use the position vs. time data to determine the projected direction on the sky of the
inner jet, as well as the apparent speeds and birth dates (or “ejection times,” defined
26
35
Monitor
Flux Density (mJy)
30
25
20
15
10
5
0
1996
1998
2000
2002
2004
2006
2008
2004.3
2004.4
2004.5
2004.6
10
Flux Density (mJy)
Medium
8
6
4
2
0
2004
10
2004.1
2004.2
Flux Density (mJy)
Longlook
8
6
4
2
0
2005.2 2005.24 2005.28 2005.32 2005.36 2005.4 2005.44 2005.48
YEAR
Fig. 3·3.— Optical (R-band) data of 3C 279 on different time-scales.
27
35
Monitor
Flux Density (Jy)
30
25
20
15
10
1996
1998
2000
2002
2004
2006
2008
18
Medium
Flux Density (Jy)
17
16
15
14
2005.2
2005.3
2005.4
2005.5
2005.6
2005.7
YEAR
Fig. 3·4.— Radio (14.5 GHz) data of 3C 279 on different time-scales.
2005.8
28
below) of new superluminal knots.
Fig. 3·5.— Angular separation from the core vs. epoch of all knots brighter than 100
mJy within 2.0 mas of the core of 3C 279. The solid lines indicate the motion of each
knot listed in Table 3.2. A knot is identified through continuity of the trajectory from
one epoch to the next. The diameter of each symbol is proportional to the logarithm
of the flux density of the knot, as determined by model fitting of the VLBA data.
We define the inner-jet position angle (PA) θjet with respect to the core as that
of the brightest component within 0.1-0.3 mas of the core. As seen in Figure 3·6,
θjet changes significantly (∼ 80◦ ) over the 11 years of VLBA monitoring. Figure 3·7
displays a sampling of the VLBA images at epochs corresponding to the circled points
in the lower panel of Figure 3·6.
Flux Density (mJy)
Flux (10-11 erg cm-2 s-1)
29
6
X-ray, Monitor
5
4
3
2
1
0
35
Optical, Monitor
30
25
20
15
10
5
0
35
Position Angle (Degree)
Flux Density (Jy)
14.5 GHz, Monitor
30
25
20
15
10
-80
-90
-100
-110
-120
-130
-140
-150
-160
-170
-180
1996
1998
2000
2002
2004
2006
2008
YEAR
Fig. 3·6.— Variation of X-ray flux, optical flux, radio flux and position angle of the
jet from 1996 to 2008. The circled data points in the bottom panel are the epochs
shown in Fig. 3·7.
30
Fig. 3·7.— VLBA images of the pc-scale jet of 3C 279 at one epoch during each year
of 11-year monitoring. The images are convolved with the beam of the size 0.38 ×0.14
mas at PA = −9◦ . The map peak is 17.0 Jy/Beam. The contour levels are 0.15, 0.3,
0.6, ...,76.8 % of the peak. The angular scale given at the bottom is in milliarcseconds
(mas). The circled points in Fig. 3·6 (bottom panel) correspond to these images.
31
We determine the apparent speed βapp of the moving components using the same
procedure as defined in Jorstad et al. (2005). The ejection time T0 is the extrapolated
epoch of coincidence of a moving knot with the position of the (presumed stationary)
core in the VLBA images. In order to obtain the most accurate values of T0 , given
that non-ballistic motions may occur (Jorstad et al. 2004, 2005), we use only those
epochs when a component is within 1 mas of the core, inside of which we assume its
motion to be ballistic. The values of θjet , T0 , and βapp between 1996 and 2007 are
shown in Table 3.2. These values of T0 do not significantly differ from any previously
published times of ejection, for example, for components C8-C16 in Jorstad et al.
(2005). We have also made “super-resolved” maps with a restoring circular Gaussian
FWHM beam size of 0.1 × 0.1 mas, corresponding to the resolution of the longest
VLBA baselines along the direction of the jet, in order to measure more precisely
the locations of components near the core. (The actual interferometer synthesized
beam is typically fit by a Gaussian of FWHM dimensions 0.38 × 0.14 mas along
PA−9◦ .) Table 3.2 gives the values of T0 and βapp of all identified knots, following
the component naming scheme of Jorstad et al. (2005). For the calculation of βapp
we use a ΛCDM cosmology, with Ωm = 0.3, ΩΛ = 0.7, and Hubble constant H0 =
70 km s−1 Mpc−1 (Spergel et al. 2007). As part of the modeling of the images, we
have measured the flux density of the unresolved core in all the images, and display
the resulting light curve in Figure 3·8.
3.2
3C 120
The broad line radio galaxy 3C 120 (z=0.033) has a prominent relativistic radio jet
with apparent superluminal motion at ∼5c that displays strong variability in flux
and jet structure (Gomez et al. 2001; Walker et al. 2001). It is Fanaroff-Riley class
I (Fanaroff & Riley 1974) radio galaxy. The jet lies at an angle ∼ 20◦ to our line
32
16
Core Flux Density (Jy beam-1)
14
12
10
8
6
4
2
1996
1998
2000
2002
YEAR
2004
2006
2008
Fig. 3·8.— Light curve of the VLBA core region of 3C 279 at 43 GHz. The jagged
line through the data points is drawn solely to aid the eye to follow the variability.
Statistical and systematic uncertainty in each measurement is difficult to determine
accurately, but typically 10-20%.
Fig. 3·9.— 5 GHz VLA image of 3C 120 showing the kpc-scale jet (from Figure 4 of
Walker et al. (1987)).
33
Table 3.2 Ejection times, apparent speeds, and position angle of superluminal knots
in 3C 279.
Knot
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
1
2
T0
1996.09±
1996.89±
1997.24±
1997.59±
1998.56±
1998.98±
1999.50±
1999.85±
2000.27±
2000.96±
2001.40±
2002.97±
2003.39±
2004.75±
2005.18±
2006.41±
0.10
0.12
0.16
0.11
0.09
0.07
0.09
0.05
0.05
0.12
0.16
0.12
0.10
0.05
0.06
0.15
T0 (MJD1)
115± 36
407± 44
536± 58
662± 40
1016± 33
1174± 26
1360± 33
1487± 18
1642± 18
1895± 44
2054± 58
2648± 44
2781± 44
3280± 18
3434± 22
3888± 55
MJD = Julian date minus 2450000
Average position angle of knot within 1 mas of the core.
βapp
θ (deg)2
5.4± 0.7 −130± 3
12.9± 0.3 −131± 5
9.9± 0.5 −132± 6
10.1± 1.2 −135± 4
16.9± 0.4 −129± 3
16.4± 0.5 −130± 4
18.2± 0.7 −135± 6
17.2± 2.3 −131± 7
16.9± 3.5 −140± 8
6.2± 0.5 −133± 12
4.4± 0.7 −150± 8
6.6± 0.6 −133± 7
6.0± 0.5 −155± 10
16.7± 0.3 −147± 7
12.4± 1.2 −102±17
16.5± 2.3 −114± 5
34
of sight, significantly wider than is the case for blazars (Jorstad et al. 2005). The
Doppler factor is therefore lower than in blazars. Because of this, at optical and Xray frequencies 3C 120 possesses properties similar to Seyfert galaxies and BHXRBs,
e.g., a prominent iron emission line at a rest energy of 6.4 keV (Grandi et al. 1997;
Zdziarski & Grandi 2001). Hence, most of the X-rays are produced in the immediate
environment of the accretion disk—the corona, a hot wind, or the base of the jet.
The bulk of the optical and UV continuum in such AGNs is thought to emanate from
the disk as well (Malkan & Sargen 1982; Malkan 1983).
Table 3.3 summarizes the intervals of monitoring at different frequencies for each
of the three wave bands in our data set. We term the entire light curve “monitor
data”; shorter segments of more intense monitoring are described below.
Table 3.3 Parameters of the light curves of 3C 120.
X-ray
Optical
Radio
Data set
Start
Longlook 2002 December 13
Medium
2006 November
Monitor
2002 March
Monitor
2004 August
Monitor
2002 March
End
T(days)
2002 December 14
1.5
2007 January
60.0
2007 May
1910.0
2008 January
1250.0
2008 January
2167.0
∆T (days)
0.01
0.25
15.0
-
X-ray Monitoring
The X-ray light curves are based on observations of 3C 120 with the Rossi X-ray
Timing Explorer (RXTE) from 2002 March to 2007 May. We observed 3C 120 with
the RXTE PCA instrument with typical exposure times of 1-2 ks. For each exposure,
we used routines from the X-ray data analysis software FTOOLS and the program
XSPEC to calculate and subtract an X-ray background model from the data and to fit
the X-ray spectrum from 2.4 to 10 keV as a power law with low-energy photoelectric
35
absorption by intervening gas in our Galaxy. For the latter, we used a hydrogen
column density of 1.23 × 1021 atoms cm−2 (Elvis, Lockman, & Wilkes 1989).
The sampling of the X-ray flux varied. Normally, observations were made 2-3
times per week except during 8-week intervals each year when the radio galaxy is too
close to the Sun’s celestial position to observe safely. In order to sample shorter-term
variations, between 2006 November and 2007 January, we obtained, on average, four
measurements per day for almost two months. We refer to these observations as the
“medium” data. XMM-Newton observed 3C 120 quasi-continuously for about 130 ks
on 2002 December 13 and 14, during which all instruments were operating normally.
The data were processed with the latest software (SAS version 5.3.3). Light curves
were extracted in two energy bands, 0.3-10 keV and 4-10 keV, and were backgroundsubtracted and binned to 100 s time intervals. The 4-10 keV light curve, re-binned to
an interval of 0.01 day, were used as the “longlook” data. We use the 4-10 keV data
since the energy range is similar to that of our RXTE data (2.4-10 keV). Figure 3·10
presents these three data sets.
Optical Monitoring
We also monitored 3C 120 in the optical R and V bands over a portion of the time span
of the X-ray observations. The majority of the measurements in R band are from the
2 m Liverpool Telescope (LT) at La Palma, Canary Islands, Spain, supplemented by
observations at the 1.8 m Perkins Telescope of Lowell Observatory, Flagstaff, Arizona.
The V-band photometry was obtained with the 0.4-m telescope of the University of
Nebraska. On each night a large number of one-minute images (∼ 20) were taken
and measured separately. Details of the observing and reduction procedure are as
described in Klimek, Gaskell, & Hendrick (2004). Comparison star magnitudes were
calibrated as done by Doroshenko et al. (2006). To minimize the effects of variations
in the image quality fluxes were measured through an aperture of 8 arcseconds radius.
Flux (10-11 erg cm-2 s-1)
36
9
Monitor
8
7
6
5
4
3
2
1
Flux (10-11 erg cm-2 s-1)
2003
2004
2005
2006
Medium
4
3
2
2006.9
2006.94
2006.98
0.9
counts sec-1
2007
2007.02
Longlook
0.7
0.5
0.3
2002.956
2002.957
2002.958
2002.959
YEAR
Fig. 3·10.— X-ray light curves of 3C 120 with different sampling rates.
37
The errors given for each night are the errors in the means. The Miller Observatory
observations were taken with a 0.4-m telescope in Nebraska and reduced similarly to
the University of Nebraska observations. Observations at the Shanghai Astronomical
Observatory were obtained with the 1.56-m telescope at Sheshan Station. Standard
Johnson-Cousins V, R, and I filters were used, and all the magnitudes were scaled
to the V passband. The reductions were as for the Nebraska observations. Early
observations (2002 to 2004) carried out at the Perkins Telescope were in V-band. For
these measurements, we used stars D, E, and G from Angione (1971) to calculate the
V-magnitudes. We use three comparison stars in the field of 3C 120 to calculate the
R-magnitude. We determined the R-magnitudes of these three stars based on ∼20
frames obtained within 2 yr. We use the flux-magnitude calibration of Mead et al.
(1990) and correct for Galactic extinction for both R and V bands.
Since the optical sampling is not as frequent as the X-ray sampling in R or V band
individually, we construct a better-sampled optical light curve by combining these two
bands. We find that the R and V band light curves have 38 data points that were
measured within 0.5 day of each other. These data are shown in Figure 3·11. The
equation of the best-fit line is FR = 0.96FV + 1.96, where FV and FR are the fluxes
in V and R band, respectively. We convert the V band fluxes into R band using this
equation. We present the combined light curve in Figure 3·12.
Radio Monitoring
We have compiled a 37 GHz light curve with data from the 13.7 m telescope at
Metsähovi Radio Observatory, Finland. The flux density scale is set by observations
of DR 21. Sources 3C 84 and 3C 274 are used as secondary calibrators. A detailed
description on the data reduction and analysis is given in Teräsranta et al. (1998).
We also monitored 3C 120 at 14.5 GHz with the 26 m antenna of the University
of Michigan Radio Astronomy Observatory. Details of the calibration and analysis
38
10
9.5
R-Band Flux (mJy)
9
8.5
8
7.5
7
6.5
6
5.5
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
V-Band Flux (mJy)
Fig. 3·11.— Filled circles show the 38 data points for 3C 120 that we measured within
0.5 day of each other in V and R band, along with the respective uncertainties. The
dashed line represents the best fit straight line through these points, which is used
for the V band to R band flux conversion.
11
Flux Density (mJy)
10
9
8
7
6
5
2003
2004
2005
2006
2007
2008
Year
Fig. 3·12.— Light curve of 3C 120 constructed by combining the V and R band light
curves.
39
techniques are described in Aller et al. (1985). At both frequencies the flux scale was
set by observations of Cassiopeia A (Baars et al. 1977).
VLBA Monitoring
Starting in 2001 May, we observed 3C 120 with the Very Long Baseline Array (VLBA)
at 43 GHz at roughly monthly intervals, with some gaps of 2-4 months. The sequence
of images from these data provides a dynamic view of the jet at an angular resolution
∼0.1 milliarcseconds (mas) in the direction of the jet, corresponding to 0.064 pc
for Hubble constant H0 = 70 km s−1 Mpc−1 . We processed the data in the same
manner as that of 3C 279. The apparent speeds of the moving components with
well-determined motions are all 4.0c ± 0.2c. The ejection time T0 is the extrapolated
time of coincidence of a moving knot with the position of the (presumed stationary)
core in the VLBA images. Table 3.4 lists the ejection times and Figure 3·13, 3·14 and
3·15 display the VLBA images. Fig. 3·16 presents the X-ray, optical and radio light
curves. In the top panel of the figure, the arrows represent the times of superluminal
ejections, while the line segments perpendicular to the arrows show the uncertainties
in the values of T0 .
3.3
3C 111
3C 111 is a relatively nearby (z = 0.049) broad line radio galaxy (BLRG). The host
galaxy is resolved in the R band with the Hubble Space Telescope, and although the
morphology of the host is somewhat uncertain, it is likely to be a small elliptical-type
galaxy (Martel et al. 1999). At optical and X-ray frequencies, 3C 111 possesses properties similar to Seyfert galaxies and BHXRBs. It has a prominent iron emission line
at a rest energy of 6.4 keV (e.g. Eracleous, Sambruna & Mushotzsky 2000; Reynolds
et al. 1998). This implies that most of the X-rays are produced in the immediate
environs of the accretion disk: the corona, a hot wind, or the base of the jet. In
40
Fig. 3·13.— VLBA images of 3C 120 at 7 mm obtained from 2002 to 2004. The
contours and color (grayscale) show the total and polarized intensity, respectively.
The images are convolved with an elliptical Gaussian beam of FWHM size 0.36×0.15
mas at PA = −6◦ . The global peak over all maps is 1.52 Jy/Beam. The contour
levels are 0.25, 0.5, 1.0, ..., 64.0, 90.0% of the global peak. Individual moving knots
are marked at selected epochs.
41
Fig. 3·14.— VLBA images of 3C 120 at 7 mm obtained from 2004 to 2006. The
contours and color (grayscale) show the total and polarized intensity, respectively.
The images are convolved with an elliptical Gaussian beam of FWHM size 0.36×0.15
mas at PA = −6◦ . The global peak over all maps is 1.52 Jy/Beam. The contour
levels are 0.25, 0.5, 1.0, ..., 64.0, 90.0% of the global peak. Individual moving knots
are marked at selected epochs.
42
Fig. 3·15.— VLBI images of 3C 120 at 7 mm obtained from 2006 to 2007. The
contours and color (grayscale) show the total and polarized intensity, respectively.
The images are convolved with an elliptical Gaussian beam of size 0.36×0.15 mas at
PA = −6◦ . The global peak over all maps is 1.52 Jy/Beam. The contour levels are
0.25, 0.5, 1.0, ..., 64.0, 90.0% of the global peak. Individual moving knots are marked
at selected epochs.
43
9
X-ray (2.4-10 keV)
Flux (10-11 erg cm-2 s-1)
8
7
6
5
4
3
2
Flux Density (mJy)
R Band
V Band
8
6
4
Flux Density (Jy)
6
37 GHz
15 GHz
4
2
0
2003
2004
2005
Year
2006
2007
Fig. 3·16.— Variation of X-ray flux, optical flux density and radio flux density of 3C
120 from 2002 to 2008. In the top panel, the arrows show the times of superluminal
ejections and the line segments perpendicular to the arrows indicate the uncertainties
in the times.
44
Table 3.4 Time, area and width of the X-ray Dips and 37 GHz Flares, and Times of
Superluminal Ejections of 3C 120.
X-ray
T (st)1 T (min)2
6
2002.15
2002.19 2002.30
2002.75 2002.76
2003.02 2003.12
2003.32 2003.58
2003.66 2003.82
2003.95 2003.98
2004.12 2004.17
2004.21 2004.37
T0
657
12
29
172
184
44
20
364
2002.23 ± 0.03
120. 2002.65 ± 0.04
5.
22.5 2003.35 ± 0.15
52.5 2003.67 ± 0.02
40. 2003.81 ± 0.03
15. 2003.98 ± 0.03
15. 2004.16 ± 0.05
65. 2004.37 ± 0.03
03A
03B
03C
03D
04A
04B
2004.62
2005.09
2005.19
2004.66
2005.12
2005.39
30 12.5 2004.82 ± 0.05
33 17.5 2005.14 ± 0.03
351 65. 2005.34 ± 0.02
04C
05A
05B
2005.94
2006.38
2006.96
2006.04
2006.44
2007.09
287 70. 2006.00 ± 0.03
382 72.5 2006.72 ± 0.05
193 62.5 2007.05 ± 0.02
06A
06B
07A
A3
W4
6
6
6
1
Start time of X-ray dips
Time of minimum of X-ray dips
3
Area; Units: 10−6 erg cm−2
4
Width; Units: days
5
Time of maximum of 37 GHz flares
6
Insufficient data
2
Knot ID
02A
02B
37 GHz
T (pk)5 A3
2002.39 195
2002.58 404
W4
95
75
2003.35 17
2003.72 441
2003.92 24
17
85
20
2004.38
2004.49
2005.05
2005.23
2005.36
2005.57
2005.80
2006.43
2006.88
2007.43
2007.87
126 52
60 25
61 27
21 15
10 10
92 57
127 57
126 105
598 62
132 72
122 60
45
the radio, 3C 111 has blazar-like behavior. It is a Fanaroff-Riley class II (Fanaroff &
Riley 1974) radio galaxy with a prominent radio jet that displays strong variability in
flux and jet structure. On parsec scales, the jet is one sided and superluminal knots
are ejected 1-2 times per year with typical speeds of 3 − 5c (Jorstad et al. 2005). The
jet lies at an angle ∼ 18◦ to our line of sight (Jorstad et al. 2005), significantly wider
than is the case for typical blazars.
Fig. 3·17.— 1.5 GHz VLA image of 3C 111 showing the kpc-scale jet (from Figure 1
of Linfield & Perley (1984)).
Table 3.5 summarizes the intervals of monitoring at different frequencies for each
of the three wave bands in our data set. We term the entire light curve “monitor
data”; shorter segments of more intense monitoring are described below.
X-ray Monitoring
The X-ray light curves are based on observations of 3C 111 with the Rossi X-ray
Timing Explorer (RXTE) from 2004 March to 2009 March. We observed 3C 111 with
the RXTE PCA instrument with typical exposure times of 1-2 ks. For each exposure,
46
Table 3.5 Parameters of the Light Curves of 3C 111.
Data set
Start
End
T(days)
Longlook 2009 February 16 2009 February 17
1.2
X-ray
Medium
2006 November
2007 January
56.0
Monitor
2004 March
2009 March
1843.0
Optical
Monitor
2004 November
2009 March
1588.0
37 GHz Monitor
2005 January
2008 December
1458.0
230 GHz Monitor
2004 January
2009 March
1878.0
∆T (days)
0.01
0.25
15.0
-
we used routines from the X-ray data analysis software FTOOLS and the program
XSPEC to calculate and subtract an X-ray background model from the data and to fit
the X-ray spectrum from 2.4 to 10 keV as a power law with low-energy photoelectric
absorption by intervening gas in our Galaxy. For the latter, we used a hydrogen
column density of 9.6 × 1021 atoms cm−2 (Sambruna, Eracleous, & Mushotzky 1999).
The sampling of the X-ray flux varied. Normally, observations were made 2-3 times
per week except during 8-week intervals each year when the radio galaxy is too close
to the Sun’s celestial position to observe safely. In order to sample shorter-term
variations, between 2006 November and 2007 January we obtained, on average, four
measurements per day for almost two months. We refer to these observations as the
“medium” data. XMM-Newton observed 3C 111 quasi-continuously for about 130 ks
on 2009 February 16 and 17. The data were processed with the latest software (SAS
version 8.0.0). A light curve was extracted in the 2.4-10 keV energy band, similar to
that of our RXTE data, and was background-subtracted and binned to 100 s time
intervals. This light curve was used as the “longlook” data. Figure 3·18 presents
these three data sets.
Flux (10-11 erg cm-2 s-1)
8
Flux (10-11 erg cm-2 s-1)
47
6
Monitor
7
6
5
4
3
2
1
2005
2006
2007
2009
Medium
5
4
3
2
2006.9
2006.94
2006.98
2007.02
Longlook
9.3
counts sec-1
2008
8.9
8.5
8.1
7.7
7.3
2009.138
2009.139
2009.140
YEAR
Fig. 3·18.— X-ray light curves of 3C 111 with different sampling rates.
48
8
Flux (10-11 erg cm-2 s-1)
X-ray (2.4-10 keV)
7
6
5
4
3
2
1
Flux Density (0.1 mJy)
6
Optical (R Band)
5
4
3
Flux Density (Jy)
37 GHz
230 GHz
9
7
5
3
1
2005
2006
2007
Year
2008
2009
Fig. 3·19.— Variation of X-ray flux, optical flux density and radio flux density of 3C
111 from 2004 to 2009. In the top panel, the arrows indicate the times of superluminal
ejections and the line segments perpendicular to the arrows represent the uncertainties
in the times.
49
Fig. 3·20.— VLBI image of 3C 111 at 7 mm obtained at one epoch in 2009 April.
The contours and grayscale show the total and polarized intensity, respectively. The
bright feature at the right of the image is the VLBA core and that on its left is a
bright knot moving away from the core.
50
Table 3.6 Times of X-ray Dips and Superluminal Ejections in 3C 111.
Time (X-ray minimum)
2004.19
2005.02
2005.57
2006.47
2006.88
2007.32
2008.51
T0
2004.50±
2005.23±
2005.75±
2006.56±
2006.95±
2007.80±
2008.83±
0.03
0.03
0.03
0.03
0.03
0.03
0.03
Optical Monitoring
We also monitored 3C 111 in the optical R band over a portion of the time span of
the X-ray observations. The majority of the measurements in R band are from the
2 m Liverpool Telescope (LT) at La Palma, Canary Islands, Spain, supplemented by
observations at the 1.8 m Perkins Telescope of Lowell Observatory, Flagstaff, Arizona.
Radio Monitoring
We have compiled a 37 GHz light curve with data from the 13.7 m telescope at
Metsähovi Radio Observatory, Finland. The flux density scale is set by observations
of DR 21. Sources 3C 84 and 3C 274 are used as secondary calibrators. A detailed
description on the data reduction and analysis is given in Teräsranta et al. (1998).
VLBA Monitoring
Starting in 2001 May, we observed 3C 111 with the Very Long Baseline Array (VLBA)
at 43 GHz at roughly monthly intervals, with some gaps of 2-4 months. The sequence
of images from these data provides a dynamic view of the jet at an angular resolution
∼0.1 milliarcseconds (mas) in the direction of the jet, corresponding to 0.094 pc for
an adopted Hubble constant of H0 = 70 km s−1 Mpc−1 . We processed the data in
51
the same manner as those of 3C 279 and 3C 120 described in the previous sections.
The apparent speeds of the moving components with well-determined motions are
3−5c. Table 3.6 lists the ejection times determined by the above procedure. Fig. 3·19
presents the X-ray, optical and radio light curves. In the top panel of the figure,
the arrows represent the times of superluminal ejections, while the line segments
perpendicular to the arrows show the uncertainties in the values of T0 .
52
Chapter 4
Statistical Techniques Developed and
Used in this Study
4.1
Power Spectral Density (PSD)
Power spectral density (PSD) analysis is a unique and reliable approach to characterize time variability. The PSD corresponds to the power in the variability of emission
as a function of timescale. For example, Figure 3·10 shows the X-ray variability of the
radio galaxy 3C 120. It is evident that there is significant variability on timescales
of years, weeks and even fractions of a day. Lawrence et al. (1987) and McHardy &
Czerny (1987) have found that the X-ray PSDs of many Seyfert galaxies are simple
power laws, with slopes between −1 and −2, corresponding to “red noise”. Red noise
is defined as uncorrelated fluctuations where power density decreases with increasing
frequency. In case of astronomical time series this translates to having larger amplitude variations in longer than in shorter timescales. Over the past 10 years, further
studies have indicated that the X-ray PSDs of Seyfert galaxies can be fit by piece-wise
power laws with one or more breaks (Belloni & Hasinger 1990; Nowak et al. 1999;
Uttley et al. 2002; McHardy et al. 2004; Markowitz et al. 2003; Pounds et al. 2001;
Edelson & Nandra 1999). This property of Seyferts is similar to that of Galactic black
hole X-ray binaries (BHXRBs) (Belloni & Hasinger 1990; Nowak et al. 1999).
A given observed power spectrum is a stochastic realization of the underlying
power spectrum. Hence, to calculate the actual underlying power spectrum, any
53
observed power spectrum should be averaged, and to estimate the uncertainties, the
spread in the value of the power at a given frequency should be used. Since the power
at a given frequency deviates significantly from the mean (Timmer & Kon̈ig 1995),
many observed power spectra need to be averaged to identify the underlying power
spectrum accurately. For example, to calculate accurately the power on a timescale of
one year, we need light curves of many (∼100) years. This approach is not suitable for
our purpose given the considerably shorter time span of available data. In addition,
the raw PSD calculated from a light curve is distorted due to uneven sampling. The
raw PSD combines two aspects of the data set: (1) the intrinsic variation of the object
and (2) power generated by the sampling pattern of the observing schedule. Before
conclusions can be drawn about the intrinsic variation of the object by examining its
PSD, the distorting effects must be removed. For this purpose, Uttley et al. (2002)
developed the Power Spectrum Response Method (PSRESP), which is a Monte-Carlo
type approach to determine the intrinsic PSD of a light curve from the raw PSD and
the sampling pattern. I have developed an algorithm similar to PSRESP and use it to
determine both whether the PSDs of the light curves of objects studied in this thesis
can be described as a simple or broken power law, as well as the slope of the power
law(s) along with uncertainties. PSRESP also provides a quantitative measure of the
goodness of fit of the proposed models to the data.
I follow (Uttley et al. 2002) to calculate the PSD of a discretely sampled light
curve f (ti ) of length N points using the formula
|FN (ν)|2 =
" N
X
i=1
f (ti ) cos(2πνti )
#2
+
" N
X
i=1
f (ti ) sin(2πνti )
#2
.
(4.1)
This is the square of the modulus of the discrete Fourier transform of the (mean subtracted) light curve, calculated for evenly spaced frequencies (inverse time) between
νmin and νmax , i.e., νmin , 2νmin, ..., νmax . Here, νmin =1/T (T is the total duration of
54
the light curve, tN − t1 ) and νmax =N/2T equals the Nyquist frequency νNyq . I use
the following normalization to calculate the final PSD:
P (ν) =
2T
|FN (ν)|2 ,
µ2 N 2
(4.2)
where µ is the average flux density over the light curve.
I bin the data in time intervals ∆T ranging from 0.5 to 25 days, as listed in Table 4.1, averaging all data points within each bin to calculate the flux. For short gaps
in the time coverage, I fill empty bins through linear interpolation of the adjacent
bins in order to avoid gaps that would distort the PSD. I account for the effects of
longer gaps, such as sun-avoidance intervals and the absence of X-ray data in 2000,
by inserting in each of the simulated light curves the same long gaps as occur in the
actual data. This involves the following steps:
Table 4.1 Parameters of the light curves of 3C 279 for calculation of PSD.
X-ray
Optical
Radio
data set T (days)
Longlook
55.0
Medium
301.0
Monitor
4150.0
Longlook
86.0
Medium
185.0
Monitor
4225.0
Medium
189.0
Monitor
3984.0
∆T (days)
0.5
5.0
25.0
1.0
5.0
25.0
4.0
25.0
log(fmin ) log(fmax )
-6.67
-4.93
-7.40
-5.93
-8.55
-6.63
-6.86
-5.23
-7.17
-5.92
-8.55
-6.63
-7.18
-5.83
-8.53
-6.63
Npoints
111
127
1213
94
77
995
59
609
1. Calculation of the PSD of the observed light curve (PSDobs ) with formulas (4.1)
and (4.2).
2. Simulation of M artificial light curves of red noise nature with a trial shape (simple
power law, broken power law, bending power law, etc.) and slope. I use M = 100.
3. Resampling of the simulated light curves with the observed sampling function.
55
4. Calculation of the PSD of each of the resampled simulated light curves (PSDsim,i ,
i=1, M). The resampling with the observed sampling function (which is irregular)
adds the same distortions to the simulated PSDs that are present in the real PSD
(PSDobs ).
5. Calculation of two functions similar to χ2 :
χ2obs
=
νX
max
ν=νmin
and
(P SDobs − PSDsim )2
(∆P SDsim )2
(4.3)
ν(max
χ2dist,i
=
X (P SDsim,i − PSDsim )2
,
2
(∆P
SD
)
sim
ν=ν
(4.4)
min
where PSDsim is the average of (PSDsim,i ) and ∆PSDsim is the standard deviation of
(PSDsim,i ), with i=1, M.
6. Comparison of χ2obs with the χ2dist distribution. Let m be the number of χ2dist,i for
which χ2obs is smaller than χ2dist,i . Then (Fsucc = m/M is the success fraction of that
trial shape and slope, a measure of its success at representing the shape and slope of
the intrinsic PSD.
7. Repetition of the entire procedure (steps 2 to 6) for a set of trial shapes and slopes
of the initial simulated PSD to determine the shape and slope that gives the highest
success fraction. I scan a range of trial slopes from −1.0 to −2.5 in steps of 0.1 for
the simple power-law fit.
I perform a few additional steps to overcome the distorting effects of finite length
and discontinuous sampling of the light curves. These steps are implicitly included
in the light curve simulation (step 2). The light curve of an astronomical source
is essentially infinitely long, but I have sampled a 5-10-year long interval of it and
am calculating the PSD based on that interval. As a result, power from longer
(than observed) timescales “leaks” into the shorter timescales and hence distorts the
56
observed PSD. This effect, called “red noise leak” (RNL), can be accounted for in
PSRESP. I overcome this by simulating light curves that are more than 100 times
longer than the observed light curve. As a consequence, the resampled simulated light
curves are a small subset of the originally simulated ones, and similar RNL distortions
are included in PSDsim,i that are present in PSDobs .
On the other hand, if a light curve is not continuously sampled, power from frequencies higher than the Nyquist frequency (νNyq ) is shifted or “aliased” to frequencies
below νNyq . The observed PSD in that case will be distorted by the aliased power,
which is added to the observed light curve from timescales as small as the exposure
time (Texp ) of the observation (about 1000 seconds for the X-ray light curve). Ideally,
one should account for this by simulating light curves with a time-resolution as small
as 1000 seconds so that the same amount of aliasing occurs in the simulated data.
This involves excessive computing time for decade-long light curves. To avoid this,
I follow (Uttley et al. 2002) by simulating light curves with a resolution 10Texp . To
calculate the aliasing power from timescales from Texp to 10Texp , I use an analytic
approximation of the level of power added to all frequencies by the aliasing, given by
PC =
1
νNyq − νmin
−1
(2TZ
exp )
P (ν)dν.
(4.5)
νNyq
I use PSRESP to account for aliasing at frequencies lower than (10Texp )−1 .
I also add Poisson noise to the simulated light curves :
Pnoise =
PN
i=1 (σ(i))
2
N(νNyq − νmin )
,
(4.6)
where σ(i) are observational uncertainties.
The goal of adding the noise and resampling with the observed sampling function
is to simulate a data set that has the same properties, including the imperfections, as
57
the observed one. This provides a physically meaningful comparison of the observed
PSD with the distribution of the simulated PSDs.
4.1.1
Results: 3C 279
The observed PSDs of X-ray, optical, and radio light curves of the blazar 3C 279
and their best-fit models are shown in Figure 4·1. The uncertainties on the slope
represent the HWHM of the Fsucc vs. slope curve (Figure 4·2). The PSDs at all wave
bands show red noise behavior, i.e., there is higher amplitude variability on longer
than on shorter timescales. The X-ray PSD is best fit with a simple power law of
slope −2.3±0.3, for which the success fraction (Fsucc ) is 45%. The slope of the optical
PSD is −1.7 ± 0.3 with Fsucc = 62%, and for the radio PSD it is −2.3 ± 0.5 with
Fsucc = 96%. The rejection confidence, equal to one minus Fsucc , is much less than
90% in all three cases (55%, 38%, and 4% in the X-ray, optical, and radio wavebands,
respectively). This implies that a simple power-law model provides an acceptable fit
to the PSD at all three wavebands.
I also fit a broken power-law model to the X-ray PSD, setting the low-frequency
slope at −1.0 and allowing the break frequency and the slope above the break to vary
over a wide range of parameters (10−9 to 10−6 Hz and −1.0 to −2.5, respectively)
while calculating the success fractions ((McHardy et al. 2006)). Although this gives
lower success fractions than the simple power-law model for the whole parameter
space, a break at a frequency . 10−8 Hz with a high frequency slope as steep as −2.4
cannot be rejected at the 95% confidence level.
4.1.2
Results: 3C 120
At first I fit a simple power-law model to the X-ray PSD of 3C 120, but found that
the value of Fsucc was unacceptably low (0.16). This implies that a simple power-law
is not the best model for this PSD. Then I fit a bending power-law model (broken
58
X-ray: Slope = -2.3
log PSD (rms2 Hz-1)
8
6
4
2
0
Optical: Slope = -1.7
log PSD (rms2 Hz-1)
8
6
4
2
0
Radio: Slope = -2.3
log PSD (rms2 Hz-1)
8
6
4
2
0
-8.5
-8
-7.5
-7
-6.5
log [Frequency (Hz)]
-6
-5.5
-5
Fig. 4·1.— Result of application of the PSRESP method to the light curves of 3C
279. PSDs of the observed data at high, medium and low frequency range are given
by the solid, dashed and dotted jagged lines, respectively, while the underlying powerlaw model is given by the dotted straight line. Points with error bars (open squares,
solid circles and asterisks for high, medium and low frequency ranges, respectively)
correspond to the mean value of the PSD simulated from the underlying power-law
model (see text). The errorbars are the standard deviations of the distribution of
simulated PSDs. The broadband PSD in all three wavelengths can be described by a
simple power law.
59
0.5
Success Fraction
X-ray
0.4
0.3
0.2
0.1
0
-1
-1.2
-1.4
-1.6
-1.8
-2
-2.2
-2.4
0.7
Success Fraction
0.6
Optical
0.5
0.4
0.3
0.2
0.1
0
-1
-1.2
-1.4
-1.6
-1.8
-2
-2.2
-1.4
-1.6
-1.8
-2
-2.2
-2.4
1
Success Fraction
Radio
0.8
0.6
0.4
0.2
0
-1
-1.2
-2.4
Power-law Slope
Fig. 4·2.— Success fraction vs. slope for all three PSDs of 3C 279. The success
fractions indicate the goodness of fit obtained from the PSRESP method.
60
power law with a smooth break) to the X-ray PSD,
P (ν) = Aν −αL [1 + (
ν (αL −αH ) −1
)
] .
νB
(4.7)
Here, A is a normalization constant, νB is the break frequency, and αH and αL are the
slopes of the power-laws above and below the break frequency, respectively (McHardy
et al. 2004). During the fitting, I varied νB from 10−9 to 10−5 Hz in steps of 100.05 ,
αH from −1.5 to −3.0 in steps of 0.1, and αL from −1.0 to −1.5 in steps of 0.1.
These ranges include the values of α found in the light curves of Galactic black hole
X-ray binaries (BHXRBs), for which αL ≈ −1 and αH is between −2 and −3 (e.g.
Remillard, & McClintock 2006). This procedure yields a much higher success fraction
than the simple power-law model. Based on the model with the highest success
+0.3
fraction, I obtain a best fit with the parameters αL = −1.3+0.2
−0.1 , αH = −2.5−0.5 , and
log10 (νB ) = −5.05+0.2
−0.6 Hz. The success fraction for this fit is high, 0.9. Figure 4·3
presents this best-fit model and the corresponding PSD. As seen in the figure, the
high frequency part of the PSD is dominated by Poisson noise. This is because the
fluxes of the longlook light curve (from which this part of the PSD is generated) have
larger uncertainties than for the other light curves owing to shorter exposure time for
the former. The figure shows that when the estimated Poisson noise is added to the
best-fit model PSD, it matches the observed PSD quite well.
4.1.3
Results: 3C 111
At first I fit a simple power-law model to the X-ray PSD, but found that the value
of Fsucc was unacceptably low (0.10). This implies that a simple power-law is not
the best model for this PSD. Then we fit a bending power-law model to the Xray PSD similar to the analysis of the PSD of 3C 120. This procedure yields a
much higher success fraction than the simple power-law model. Based on the model
61
log [Power X Frequency] (rms2)
-1
-2
-3
-4
-5
-6
-8
-7
-6
-5
log Frequency (Hz)
-4
-3
Fig. 4·3.— Result of application of the PSRESP method to the X-ray light curve of
3C 120. The PSD of the observed data at high, medium and low frequencies is given
by the solid, dashed and dotted jagged lines, respectively, while the underlying powerlaw model is given by the thicker solid bent line. Points with error bars (open squares,
solid circles and asterisks for high, medium and low frequency range, respectively)
correspond to the mean value of the PSD simulated from the underlying powerlaw model (see text). The errorbars are the standard deviation of the distribution
of simulated PSDs. The broadband power spectral density is best described by a
bending power law with low frequency slope −1.3, high frequency slope −2.5 and
break frequency 10−5.05 Hz.
62
with the highest success fraction (0.85), we obtain a best fit with the parameters
+0.2
+0.3
αL = −1.0+0.1
−0.1 , αH = −2.8−0.6 , and log10 (νB ) = −6.05−0.3 Hz. Figure 4·4 presents this
best-fit model and the corresponding PSD.
0
log [Power X Frequency] (rms2)
-1
-2
-3
-4
-5
-6
-7
-8
-7
-6
-5
log Frequency (Hz)
-4
-3
Fig. 4·4.— Result of application of the PSRESP method to the X-ray light curve of
3C 111. The PSD of the observed data at high, medium and low frequencies is given
by the solid, dashed and dotted jagged lines, respectively, while the underlying powerlaw model is given by the thicker solid bent line. Points with error bars (open squares,
solid circles and asterisks for high, medium and low frequency range, respectively)
correspond to the mean value of the PSD simulated from the underlying powerlaw model (see text). The errorbars are the standard deviations of the distribution
of simulated PSDs. The broadband power spectral density is best described by a
bending power law with low frequency slope −1.0, high frequency slope −2.8 and
break frequency 10−6.05 Hz.
4.2
Cross-correlation Function
Cross-correlation function is used to compare the flux variations at multiple wave
bands and to determine the inter-wave band time delay. Comparison of flux variations at different wavelengths is important for distinguishing between possible models
63
of variability. The cross-frequency time lag relates to the relative locations of the emission regions at the different wavebands, which in turn depend on the physics of the
jet and the radiation mechanism(s). The traditional cross-correlation function requires evenly sampled data. Due to observational constraints, the data that I use are
not evenly sampled. For this reason, I employ the discrete cross-correlation function
(Edelson & Krolik 1988, DCCF) method to find the correlation between variations
at pairs of wavebands.
4.2.1
Significance of Correlation
A reliable estimate of the time lag requires sufficiently long light curves, but in our
case these are not regularly sampled. This can cause the correlation coefficients to be
artificially low. In addition, time lags between light curves that vary (intrinsically)
over the years will reduce the level of correlation over the full length of the light
curves. In light of these complications, I use simulated light curves based on the
previously determined PSD to estimate the significance of the correlations derived
from the data. For this, I perform the following steps :
1. Simulation of M (I use M=100) artificial light curves generated with a Monte-Carlo
algorithm based on the shape and slope of the PSD as determined using PSRESP for
both wavebands (total of 2M light curves).
2. Resampling of the artificial light curves with the observed sampling function.
3. Correlation of random pairs of simulated light curves (one at each waveband).
4. Identification of the peak in each of the M random correlations.
5. Comparison of the peak values from step 4 with the peak value of the real correlation between the observed light curves. For example, if 10 out of 100 random
peak values are greater than the maximum of the real correlation, I conclude that
there is a 10% chance of finding the observed correlation by chance. Therefore, if this
percentage is low, then the observed correlation is significant even if the correlation
64
coefficient is substantially lower than unity.
4.2.2
Uncertainties in Cross-correlation Coefficients and Time Delay
I use the “Flux randomization (FR) and random subset selection (RSS)” method
(Peterson et al. 1998) to reliably calculate the the uncertainties in the cross-correlation
time delay. This method includes two steps in a single Monte-Carlo simulation. One
step is to add noise to the flux values, where the noise is Gaussian-distributed random
numbers with mean equal to zero and standard deviation equal to the average of
observed uncertainties. This is called flux randomization (FR). The other step is to
randomly select M epochs from a total of M epochs without regard to whether or not
the epoch has been previously selected. This method is called “bootstrapping.” As a
result, some (∼37%) epochs are not used and some epochs are repeated in each try.
This is called random subset selection (RSS). I make N pairs of light curves using this
method (including both FR and RSS). Then I calculate N DCCFs and construct a
distribution of time delays of peak co-efficients from the N DCCFs. This distribution
may not be Gaussian. The median is selected as the value of the parameter (crosscorrelation time delay or the coefficient). The positive uncertainty (δτ+ ) is defined
such that 15.87% of the realizations in the distribution are above τmedian +δτ+ and the
negative uncertainty (δτ− ) is defined such that 15.87% of the realizations are below
τmedian − δτ− . As a result, 68.27% of the realizations will be within τmedian + δτ+ and
τmedian − δτ− , which corresponds to 1 σ error for a Gaussian distribution.
4.2.3
Results: 3C 279
X-ray, Optical, Radio Correlation
As determined by the DCCF (Figure 4·5), the X-ray variations are correlated with
those at both optical and radio wavelengths in 3C 279. The peak X-ray vs. optical
DCCF is 0.66, which corresponds to a 98% significance level. The peak X-ray vs.
65
radio DCCF is relatively modest (0.42), with a significance level of 79%. The radiooptical DCCF has a similar peak value (0.45) at a 62% significance level. The crosscorrelation also indicates that the optical variations lead the X-ray by 20 ± 15 and
+35
the radio by 260+30
−60 days, while X-rays lead the radio by 240−40 days.
Correlation of X-ray Flux and Position Angle of the Inner Jet in 3C 279
I find a significant correlation (maximum DCCF=0.6) between the PA of the jet and
the X-ray flux (see Figure 4·6). The changes in the position angle lead those in the
X-ray flux by 80 ± 150 days. The large uncertainty in the time delay results from the
broad, nearly flat peak in the DCCF. This implies that the jet direction modulates
rather gradual changes in the X-ray flux instead of causing specific flares. This is as
expected if the main consequence of a swing in jet direction is an increase or decrease
in the Doppler beaming factor on a timescale of one or more years.
4.2.4
Results: 3C 120
X-ray/Radio Correlation
The 37 GHz light curve of 3C 120 has an average sampling frequency of about once per
week. I bin the X-ray and the 37 GHz light curves in 7-day intervals before performing
the cross-correlation, so that the light curves being compared have similar sampling
frequency. As determined by the DCCF (top panel of Figure 4·7), the X-ray flux
variations are anti-correlated with those at 37 GHz in 3C 120. The highest amplitude
of the X-ray versus 37 GHz DCCF is at a value of −0.68 ± 0.11, which corresponds to
a 90% significance level. In the case of 3C 120, I correlate simulated X-ray light curves
with the observed optical/radio light curves to calculate the significance of correlation.
The time lag of the peak indicates that the X-ray lead the radio variations by 120±30
days. This procedure gives quantitative support to the trend that is apparent by
inspection of the light curve, i.e., X-ray dips are followed by appearances of new
66
0.8
Xray-Optical
0.6
DCCF
0.4
0.2
0
-0.2
-0.4
-0.6
0.5
Xray-Radio
0.4
DCCF
0.3
0.2
0.1
0
-0.1
-0.2
0.8
Optical-Radio
0.6
DCCF
0.4
0.2
0
-0.2
-0.4
-600
-400
-200
0
200
400
600
Time Delay (Days)
Fig. 4·5.— Discrete cross-correlation function (DCCF) of the optical, X-ray, and
radio monitor data of 3C 279. The time delay is defined as positive if the variations
at the higher frequency waveband lag those at the lower frequency.
67
0.8
0.6
DCCF
0.4
0.2
0
-0.2
-0.4
-600
-400
-200
0
200
Time Delay (days)
400
600
Fig. 4·6.— Cross-correlation function of the X-ray light curve and the position angle
of the jet of 3C 279. Changes in the position angle lead those in the X-ray flux by
80 ± 150 days.
superluminal knots and hence enhancements in the 37 GHz flux. The bottom panel
of Figure 4·7 shows the X-ray/37 GHz DCCF but without the data after 2006 April,
in order to exclude the two deepest X-ray dips and the highest amplitude flare at 37
GHz toward the end of our monitoring program. The X-ray/37 GHz anti-correlation
remains, although the minimum of the DCCF, −0.4, has lower magnitude with a
significance level of 72%. The X-ray variations lead the radio by 80 ± 30 days. Thus,
the X-ray/37 GHz anti-correlation is a robust result rather than the consequence of a
singular event. The longer time delay of the major event in late 2006 was caused by
the longer time between the start of the radio outburst and the peak relative to other
radio flares, especially the one at 2003.7. This is naturally explained as a consequence
of higher optical depth of stronger radio outbursts.
68
Correlation Coefficient
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
Correlation Coefficient
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-300
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·7.— Discrete cross-correlation function (DCCF) of the X-ray and radio monitor
data of 3C 120. The time delay is defined as positive if the X-ray variations lag those
at radio frequency. Top panel shows the correlation function for the entire data
set. The X-ray and radio variations are anti-correlated with the X-ray leading by
∼120 days. The bottom panel shows the same excluding the data during the major
flare at 37 GHz in 2006-07 and the corresponding deep dip at X-ray energies. The
anti-correlation remains although the amplitude is lower.
69
X-ray/Optical Correlation
I bin the X-ray and the combined optical light curves of 3C 120 in 2-day intervals
before performing the cross-correlation, so that the light curves being compared have
similar sampling frequency. As determined by the DCCF (Figure 4·8), I find that
the X-ray variations are very strongly correlated with those at optical wavelengths in
3C 120. The peak X-ray versus optical DCCF is 0.80 ± 0.07, which corresponds to a
99% significance level. The position of the peak of the correlation function indicates
the relative time delay between the variations at the two wavelengths. In this case,
the peak is very wide, so that the value of the relative time delay cannot be easily
estimated from the DCCF plot. I used the FR-RSS technique proposed by Peterson
et al. (1998) to calculate the mean value and the uncertainty of the cross-correlation
time lag. This method indicates that the X-ray variations lead the optical by 0.5 ± 4
days. The highly significant correlation and short time delay between the X-ray and
optical variations indicates that emission at these wave bands is at least partially
co-spatial.
Between 2006 November and 2007 January, the X-ray light curve was sampled
4 times per day and the combined optical light curve has a sampling rate of twice
per day, on average. I bin these light curves in 0.5 day intervals. I cross-correlate
the binned light curves in order to compare the correlation function with that of the
longterm light curves. The correlation function, shown in Figure 4·9, has a similarly
significant correlation coefficient and time delay. The similar values of correlation coefficient and time delay using very well-sampled light curves illustrates the robustness
of the correlation result.
70
1
Correlation Coefficient
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-300
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·8.— Discrete cross-correlation function (DCCF) of the optical and X-ray monitor data of 3C 120 for the entire 5 yr interval. The time delay is defined as positive
if the variations at the higher frequency waveband lag those at the lower frequency.
X-ray variations are strongly correlated with those at optical wavelengths with the
X-ray variations leading the optical by 0.5 ± 4 days.
Correlation Coefficient
1
0.5
0
-0.5
-1
-1.5
-40
-20
0
20
40
Time Delay (Days)
Fig. 4·9.— Discrete cross-correlation function (DCCF) of the optical and X-ray data
of 3C 120 between 2006 November and 2007 January, binned to an interval of 0.5 day.
The data in this interval are more intensely sampled than the rest. The DCCF shows
that the two variations are strongly correlated and almost simultaneous as shown by
Fig. 4·8 for the entire interval.
71
4.2.5
Results: 3C 111
X-ray/Radio Correlation
We bin the X-ray and 37 GHz light curves in 7-day intervals before performing the
cross-correlation, so that the light curves being compared have similar sampling frequency. As determined by the DCCF (top panel of Figure 4·10), the X-ray flux
variations are correlated with those at 37 GHz in 3C 111. The peak X-ray versus 37
GHz DCCF is 0.80, which corresponds to a 95% significance level. The time lag of
the peak indicates that the X-ray lead the radio variations by 40 ± 5 days.
We also calculate the X-ray/230 GHz DCCF between 2007 April and 2008 August.
As determined by the DCCF (Figure 4·11), the X-ray flux variations are strongly
correlated with those at 230 GHz. The maximum coefficient value is 0.86. The time
lag of the peak indicates that the 230 GHz lead the X-ray variations by 5 ± 7 days. I
discuss the physical interpretation of the X-ray/radio correlation in 3C 111 in Chapter
6.
X-ray/Optical Correlation
We bin the X-ray and optical light curves in 7-day intervals before performing the
cross-correlation, so that the light curves being compared have similar sampling frequency. As determined by the DCCF (Figure 4·12), we find that the X-ray variations
of 3C 111 are very strongly correlated with those at optical wavelengths. The peak
X-ray versus optical DCCF is 0.87, which corresponds to a 99% significance level.
The position of the peak of the correlation function indicates the relative time delay
between the variations at the two wavelengths. The FR-RSS technique indicates that
the X-ray variations lead those in the optical by 17 ± 5 days. The highly significant
correlation between the X-ray and optical variations implies that emission at these
wave bands is causally connected.
Correlation Coefficient
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
Correlation Coefficient
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
Correlation Coefficient
72
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
Mar 04 to Mar 09
Mar 04 to Apr 07
-300
May 07 to Mar 09
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·10.— Discrete cross-correlation function (DCCF) of the X-ray and radio monitor data of 3C 111. The time delay is defined as positive if the X-ray variations lag
those at radio frequency. Top panel shows the correlation function for the entire data
set, the middle and the bottom panel show the same for the intervals 2004 March to
2007 April and 2007 May to 2009 March, respectively.
73
Correlation Coefficient
1
0.5
0
-0.5
-150
-100
-50
0
50
100
150
Time Delay (Days)
Fig. 4·11.— Discrete cross-correlation function (DCCF) of the X-ray and 230 GHz
monitor data of 3C 111 between 2007 April and 2008 August. 230 GHz variations
lead those in the X-rays by 5 ± 7 days.
4.3
Time Window
I have developed a program that calculates the cross-correlation function of two
longterm light curves with a controllable moving time window. This allows me to
study the changes in the correlation function and the cross-frequency time delay over
the years.
4.3.1
Results: 3C 279
The X-ray and the optical light curves of 3C 279 are correlated at a very high significance level. However, the uncertainty in the X-ray-optical time delay is comparable
to the delay itself. To characterize the variation of the X-ray/optical time lag over the
years, I divide both light curves into overlapping two-year intervals, and repeat the
DCCF analysis on each segment. The result indicates that the correlation function
74
Correlation Coefficient
1
0.5
0
-0.5
-1
-300
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·12.— Discrete cross-correlation function (DCCF) of the optical and X-ray
monitor data of 3C 111 for the entire 5 yr interval. The time delay is defined as
positive if the variations at the higher frequency waveband lag those at the lower
frequency. The X-ray variations are very strongly correlated with those at optical
wavelengths with the former leading by ∼17 days.
varies significantly with time (Fig. 4·13) over the 11 years of observation. Of special
note are the following trends:
1. During the first four years of our program (96-97, 97-98, 98-99) the X-ray variations lead the optical (negative time lag).
2. There is a short interval of weak correlation in 1999-2000.
3. In 2000-01, the time delay shifts such that the optical leads the X-ray variations
(positive time lag). This continues into the next interval (2001-02).
4. In 2002-03, there is another short interval of weak correlation (not shown in the
figure).
5. In the next interval (2003-04), the delay shifts again to almost zero.
6. Over the next 3 years the correlation is relatively weak and the peak is very broad,
centered at a slightly negative value.
This change of time lag over the years is the main reason why the peak value of the
75
overall DCCF is significantly lower than unity. I discuss the physical cause of the
shifts in cross-frequency time delay in Chapter 6.1.2.
4.3.2
Results: 3C 120
To characterize the variation of the X-ray/optical time lag in 3C 120 over the years,
I divide both light curves into two intervals, 2004 July to 2005 May and 2005 June to
2007 May, and repeat the DCCF analysis on each segment. The result (Figure 4·14)
indicates that in the first segment, the X-ray variations lead those in the optical by
∼25 days while in the second segment the correlation function is similar to what
I obtained for the entire time interval, with similar time delay (Figure 4·8). This
variation of the time lag over the years may be the cause of the observed wide peak
in the correlation function.
4.3.3
Results: 3C 111
To characterize the variation of the X-ray/37 GHz time lag over the years, we divide
both light curves into two intervals, 2004 March to 2007 April and 2007 May to 2009
March, and repeat the DCCF analysis on each segment. The result indicates that in
the first segment (middle panel of Figure 4·10), the X-ray and radio variations are anticorrelated, with X-ray leading by ∼120 days. In the second segment (bottom panel
of Figure 4·10), the correlation function is similar to that obtained for the entire time
interval, with peak coefficient of 0.95, which corresponds to a 99% significance level.
The similarity of the correlation function at the top and bottom panels indicate that
the correlation peak seen in the middle panel is a “reflection” of the anti-correlation
minimum and is not physically meaningful. The X-ray/37 GHz correlation result
and its variation over 5 years imply that decreases in X-ray production were linked to
increases in the 37 GHz flux between 2004 March and 2007 April, but after that the Xray and 37 GHz variations are strongly correlated. I discuss the physical interpretation
DCCF
76
1
0.8
0.6
0.4
0.2
0
-0.2
1996-97
1997-98
1
1998-99
1999-00
DCCF
0.8
0.6
0.4
0.2
0
-0.2
1
2000-01
2001-02
DCCF
0.8
0.6
0.4
0.2
0
DCCF
-0.2
1
0.8
0.6
0.4
0.2
0
-0.2
2003-04
2004.0-2007.5
-60 -40 -20 0 20 40 60
Time Delay (days)
-60 -40 -20 0 20 40 60
Time Delay (days)
Fig. 4·13.— Variation of X-ray/optical time lag of 3C 279 across overlapping 2-yr
intervals from the beginning of the first year to the end of the second, except for the
bottom right panel, for which the interval is indicated more precisely. Notice the big
change between 1998-99 and 2000-2001, when the time delay went from X-ray leading
optical to the opposite sense. There is a major change between 2001-02 and 2003-04
as well, when the time delay went from optical leading X-ray to the opposite sense. In
the last 4 years (bottom right panel) the correlation became weaker but maintained
the negative time delay.
77
1
July 04 to May 05
Correlation Coefficient
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
June 05 to May 07
Correlation Coefficient
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-150
-100
-50
0
50
100
150
Time Delay (Days)
Fig. 4·14.— Variation of the X-ray/optical correlation function of 3C 120 across two
intervals. The X-ray variations lead those in the optical by 25 days during the first
interval and the two variations are almost simultaneous during the second interval.
78
of the X-ray/radio correlation in 3C 111 and its variation over time in Chapter 6.
4.4
Comparison of DCCF and ICCF
Interpolated cross-correlation function (ICCF) is another method to calculate the
cross-correlation of unevenly sampled discrete data (Gaskell & Peterson 1987). In
this method one or both of the light curves are interpolated before calculating their
cross-correlation function. Hence interpolation between two consecutive data points
to fill in a gap in the light curve assumes no variability at the timescale of the gap.
In blazar light curves, short timescale variability is often important. For this reason,
I do not use ICCF in the analysis presented in this work. Fig 4·15 to 4·20 show the
ICCF as well as DCCF of all the pairs of light curves of 3C 120 which were shown
in sections 4.2.4 and 4.3.2. It can be seen that the ICCF and DCCF produce very
similar correlation functions. The ICCF is much smoother in case where the lower
frequency light curve is interpolated. The smoothness is a result of smoothing out the
shorter (than interpolation length) timescale variability, which may not be accurate
in case of blazar light curves.
4.5
Light Curve Decomposition: Characterizing individual
flares
Comparison of the properties of contemporaneous flares at different wavebands is a
telling diagnostic. For example, if the X-rays are produced by the external Compton
(EC) process, it is predicted that the X-ray flares will decay slowly. This is because
the electrons that up-scatter external IR or optical photons to X-rays have relatively
low energies, and therefore have long radiative cooling times. In some objects, flares
or dips in one wavelength may be related to other properties of the object such as
ejections of new superluminal knots, significant changes in the polarization proper-
79
1
ICCF (Op int)
ICCF (X int)
DCCF
Correlation Coefficient
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-300
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·15.— Cross-correlation function of the optical and X-ray monitor data of 3C
120 for the entire 5 yr interval. The time delay is defined as positive if the variations
at the higher frequency waveband lag those at the lower frequency. In this and the
next five plots, the dotted curve shows the DCCF, the dashed curve shows the ICCF
where the X-ray light curve is interpolated and the solid curve shows the ICCF where
the lower frequency (optical or radio) light curve is interpolated. ICCF and DCCF
produce very similar correlation functions.
0.8
ICCF (Op int)
ICCF (X int)
DCCF
Correlation Coefficient
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-150
-100
-50
0
50
100
150
Time Delay (Days)
Fig. 4·16.— X-ray/optical correlation function of 3C 120 in the interval June 2004
to May 2005. The X-ray variations lead those in the optical by 25 days during this
interval. ICCF and DCCF produce very similar correlation functions. Curves are as
described in fig 4·15.
80
0.9
ICCF (Op int)
ICCF (X int)
DCCF
Correlation Coefficient
0.8
0.7
0.6
0.5
0.4
0.3
0.2
-150
-100
-50
0
50
100
150
Time Delay (Days)
Fig. 4·17.— X-ray/optical correlation function of 3C 120 in the interval June 2005 to
May 2007. Two variations are almost simultaneous during this interval. ICCF and
DCCF produce very similar correlation functions. Curves are as described in fig 4·15.
0.8
Correlation Coefficient
0.6
ICCF (Op int)
ICCF (X int)
DCCF
0.4
0.2
0
-0.2
-0.4
-0.6
-30
-20
-10
0
10
20
30
Time Delay (Days)
Fig. 4·18.— Cross-correlation function of the optical and X-ray data of 3C 120 between 2006 November and 2007 January, binned to an interval of 0.5 day. The light
curves in this interval is much better sampled than for the entire interval. Two variations are almost simultaneous during this interval. ICCF and DCCF produce very
similar correlation functions. Curves are as described in fig 4·15.
81
0.6
Correlation Coefficient
0.4
ICCF (Rad int)
ICCF (X int)
DCCF
0.2
0
-0.2
-0.4
-0.6
-0.8
-300
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·19.— Cross-correlation function of the X-ray and radio monitor data of 3C
120. The time delay is defined as positive if the X-ray variations lag those at radio
frequency. This shows the correlation function for the entire data set. ICCF and
DCCF produce very similar correlation functions. Curves are as described in fig 4·15.
0.4
Correlation Coefficient
0.3
ICCF (Rad int)
ICCF (X int)
DCCF
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-300
-200
-100
0
100
200
300
Time Delay (Days)
Fig. 4·20.— Cross-correlation function of the X-ray and radio monitor data of 3C
120. The time delay is defined as positive if the X-ray variations lag those at radio
frequency. This shows the correlation function for the entire data set excluding the
data during the major flare at 37 GHz in 2006-07 and the corresponding deep dip at
X-ray energies. ICCF and DCCF produce very similar correlation functions. Curves
are as described in fig 4·15.
82
ties, etc. Characterization of individual flares is required to investigate the existence
of such connections. To achieve this, I decompose the light curves into individual
(sometimes overlapping) flares each with exponential rise and decay following the
procedure of Valtaoja et al. (1999). I adopt four free parameters for each flare: the
rise and decay timescales, and the height and epoch of the peak. I proceed by first
fitting the highest peak in the smoothed light curve to an exponential rise and fall,
and then subtracting the flare thus fit from the light curve. I do the same to the
“reduced” light curve, i.e., I fit the next highest peak. This reduces confusion created
by a flare already rising before the decay of the previous flare is complete. I fit the
entire light curve in this manner with a number of individual (sometimes overlapping)
flares, leaving a residual flux much lower than the original flux at all epochs. The
goal of this analysis is to decompose a light curve into a sum of individual flares and
then to compare the properties, e.g., times of peaks, widths (defined as the mean of
the rise and decay times), and total energy output of major long-term flares present
in the lightcurves. I calculate the area under the curve for each flare to represent the
total energy output of the outburst. The flare decomposition technique can also give
us a sense of the average number of outbursts of a given amplitude taking place in
an object and how that correlates with the properties of that object, e.g., black hole
mass, polarization, accretion rate, etc.
4.5.1
Results: 3C 279
Before the decomposition, I smooth the X-ray and optical light curves of 3C 279
using a Gaussian function with a 10-day FWHM smoothing time. I have determined
that the PSD of the X-ray and optical light curves are simple power laws of slopes
−2.3 ± 0.3. and −1.7 ± 0.3. This means that the power of variability on 10 to 100-day
timescales ∼ 20 and ∼ 5 times more than that on 1 to 10-day timescales for X-ray
and optical wavebands, respectively. Because of this, I endeavor to understand the
83
physical processes causing the more powerful longer timescale flares rather than the
relatively weak flares on small timescales. I adopt four free parameters for each flare:
the rise and decay timescales, and the height and epoch of the peak.
Figure 4·21 compares the smoothed light curves with the summed flux (sum of
contributions from all the model flares at all epochs). I identify 13 X-ray/optical
flare pairs in which the flux at both wavebands peaks at the same time within ±50
days. Since both light curves are longer than 4200 days and there are only about
20 significant flares during this time, it is highly probable that each of these Xray/optical flare pairs corresponds to the same physical event. There are some X-ray
and optical flares with no significant counterpart at the other waveband. I note that
this does not imply complete absence of flaring activity at the other wavelength,
rather that the corresponding increase of flux was not large enough to be detected in
our decomposition of the smoothed light curve.
I calculate the area under the curve for each flare to represent the total energy
output of the outburst. In doing so, I multiply the R-band flux density by the
central frequency (4.7 × 1014 Hz) to estimate the integrated optical flux. For each
of the flares, I determine the time of the peak, width (defined as the mean of the
rise and decay times), and area under the curve from the best fit model. Table 4.2
lists the parameters of each flare pair, along with the ratio ζXO of X-ray to optical
energy output. The time delays of the flare pairs can be divided into three different
classes: X-ray significantly leading the optical peak (XO, 6 out of 13), optical leading
the X-ray (OX, 3 out of 13), and nearly coincident (by < 10 days, the smoothing
length) X-ray and optical maxima (C, 4 out of 13). The number of events of each
delay classification is consistent with the correlation analysis (Figure 4·13). XO flares
dominate during the first and last segments of our program, but OX flares occur in
the middle. In both the DCCF and flare analysis, there are some cases just before
84
5
8
X-ray light curve
Sum of the flares
4.5
Flux (10-11erg cm-2 s-1)
4
3.5
12
4
3
2
2.5
13
1
6
3
7
11
2
9
5
10
1.5
1
0.5
0
35
Optical light curve
Sum of the flares
8
Flux Density (mJy)
30
25
13
20
7
15
2
3 4
6
10
1
12
9
5
10
11
5
0
1996
1998
2000
2002
2004
2006
2008
YEAR
Fig. 4·21.— Smoothed X-ray and optical light curves of 3C 279. Curves correspond
to summed flux after modeling the light curve as a superposition of many individual
flares. Thick horizontal strips in the X-ray light curve in 2000 correspond to epochs
when no data are available. Flare pairs listed in Table 4.2 are marked with the
respective ID numbers.
85
and after the transition in 2001 when variations in the two wavebands are almost
coincident (C flares). The value of ζXO ≈ 1 in 5 out of 13 cases; in one flare pair
ζXO = 1.4. In all the other cases it is less than unity by a factor of a few. In all the
C flares ζXO ≈ 1, while in the 3 OX cases the ratio 1. In the C pairs, the width
of the X-ray flare profile ∼ 2 times that of the optical, but in the other events the
X-ray and optical widths are comparable. I discuss the physical interpretation of this
analysis in Chapter 6.1.3.
0.8
0.6
DCCF
0.4
0.2
0
-0.2
-0.4
-0.6
-500
-400
-300
-200
-100
0
100
200
300
400
Time Delay (days)
Fig. 4·22.— Cross-correlation of the X-ray and 43 GHz core light curves of 3C 279.
Changes in the X-ray flux lead those in the radio core by 130+70
−45 days.
Flare-Ejection Correlation
The core region on VLBI images becomes brighter as a new superluminal knot passes
through it (Savolainen et al. 2002). Hence, maxima in the 43 GHz light curve of the
core indicate the times of ejection of knots. I find that the core (Figure 3·8) and
X-ray light curves are well correlated (correlation coefficient of 0.6), with changes in
86
the X-ray flux leading those in the radio core by 130+70
−45 days (see Figure 4·22). The
broad peak in the cross-correlation function suggests that the flare-ejection time delay
varies over a rather broad range. This result is consistent with the finding of Lindfors
et al. (2006) that high-energy flares generally occur during the rising portion of the
37 GHz light curve of 3C 279.
4.5.2
Results: 3C 120
X-ray Dips and Radio Flares
In order to determine the physical link between the accretion disk and jet in 3C 120, I
check whether the amplitudes of the X-ray dips and associated radio flares are related.
To test this, I calculate the equivalent width of each X-ray dip and the area under
the curve of each 37 GHz flare to measure the total energy involved in the events.
I approximate that the radio light curve is a superposition of a constant baseline of
1.5 Jy and long-term flares. I then follow the method described at the start of this
section (4.4) to decompose the baseline-subtracted light curve into individual flares.
Before the decomposition, I smooth the light curve using a Gaussian function with a
10-day FWHM smoothing time.
The X-ray light curve has a long-term trend, i.e., the baseline is not constant.
I define the baseline X-ray flux as a cubic-spline fit of the annual mean plus one
standard deviation. Although this is an arbitrary definition, this baseline reproduces
reasonably well the mean flux level in between obvious dips and flares. There is a
long-term trend in the spectral index variations as well. The X-ray spectral index αx ,
defined by fx ∝ ν αx , where fx is the X-ray flux density and ν is the frequency, varied
between −0.5 and −1.1, with an average value of −0.83 and a standard deviation of
0.10 over the 5.2 yr of observation. In addition to the short term fluctuations, there is
a long term trend of increasing values of αx during this interval. I calculate a baseline
in the same manner as for the X-ray flux variations to highlight the change in spectral
Table 4.2. Total energy output (area) and widths of flare pairs of 3C 279.
ID
Time1
119 (1996.10)
717 (1997.74)
920 (1998.30)
1050 (1998.65)
1263 (1999.24)
1509 (1999.91)
2045 (2001.38)
2151 (2001.67)
2419 (2002.40)
3185 (2004.50)
3416 (2005.13)
3792 (2006.16)
4035 (2006.83)
33.2
371.8
172.8
338.7
160.7
699.8
103.7
453.6
193.5
191.8
217.7
525.3
324.2
2
Width3
6.0
90.0
50.0
70.0
77.5
202.5
60.0
62.5
80.0
92.5
70.0
120.0
105.0
Time1
Optical
∆T
2
3
Area Width (days)
134 (1996.14)
76.3
744 (1997.81) 929.5
944 (1998.36) 278.2
1099 (1998.79) 502.8
1266 (1999.24) 168.9
1517 (1999.93) 715.4
2029 (2001.33) 568.3
2126 (2001.60) 1188.3
2422 (2002.41) 222.6
3191 (2004.52) 218.6
3444 (2005.21) 198.7
3814 (2006.22) 375.6
4008 (2006.76) 1068.4
1
Modified Julian Date (decimal year)
2
Units: 10−6 erg cm−2
3
Units: days
4
Ratio of X-ray to optical energy output integrated over flare
12.0
97.5
35.0
57.5
42.5
90.0
65.0
57.5
40.0
55.0
50.0
67.5
75.0
-15
-27
-24
-49
-3
-8
16
25
-3
-6
-28
-22
27
TDC
ζXO
XO
XO
XO
XO
C
C
OX
OX
C
C
XO
XO
OX
0.44
0.40
0.62
0.67
0.95
0.98
0.18
0.38
0.87
0.88
1.09
1.40
0.30
4
87
1
2
3
4
5
6
7
8
9
10
11
12
13
X-ray
Area
88
index during the dips (see Figure 4·23). I proceed by subtracting the baseline and
then modeling the dips as inverted exponential flares. Figure 4·24 shows the model
fits to both the X-ray and 37 GHz light curves. Table 3.4 lists the parameters of the
X-ray dips and the corresponding 37 GHz flares along with the times of superluminal
ejections. Using the results of this analysis, I plot the equivalent width of X-ray dips
versus the energy output of the corresponding 37 GHz flares in Figure 4·25. Since the
correlation functions with and without the data in 2007 (during the large amplitude
37 GHz flare) show that the X-ray dips lead the 37 GHz flares by 120 ± 30 and
80 ± 30 days, respectively, and I have identified 15 significant dips during the 5.2 yr
of monitoring, I assume that a radio flare that peaks between 20 and 180 days after
an X-ray minimum is physically related to it. The 37 GHz flare at 2003.72 has a
wide decaying wing and there are two X-ray dips (at 2003.58 and 2003.82) that may
be related to this flare as well as another smaller 37 GHz flare (at 2003.92) on top
of that wing. Similarly, there are two X-ray dips at 2005.12 and 2005.39, and there
are four corresponding 37 GHz flares very close to each other in time at 2005.23,
2005.36, 2005.57, 2005.80. In the above cases, I plot the total energy output of the
group of 37 GHz flares against the total equivalent width of the corresponding group
of X-ray dips. The energy output of the flares and the dips are corrected by adding
the residuals shown in Figure 4·24 so that the imperfections in the model-fit do not
affect the results derived from the fit. The plot reveals a positive correlation between
the flare and dip strengths. The level of change in the accretion disk and/or corona
is therefore closely related to the amount of excess energy injected into the jet.
It can be seen from Table 3.4 that 14 out of 15 significant X-ray dips are followed by
a superluminal ejection. This strongly supports the proposition (Marscher et al. 2002)
that in 3C 120, a decrease in the X-ray production is linked with increased speed in
the jet flow, causing a shock front to subsequently move downstream. Generally, there
89
9
Baseline
X-ray Flux (10-11 erg cm-1 s-1)
8
7
6
5
4
3
2
1
1.4
Baseline
1.3
1.2
Spectral Index
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
2002
2003
2004
2005
Year
2006
2007
Fig. 4·23.— Variation of X-ray flux and the X-ray spectral index of 3C 120 during
2002-2007. Curves are the cubic spline interpolation of the yearly mean of the data
plus one standard deviation. In case of X-rays, variations (both positive and negative)
are relative to the baseline.
90
Baseline subtracted X-ray light curve
Residual flux
Sum of Flares
Flux (10-11erg cm-2 s-1)
6
5
4
3
2
1
0
37 GHz light curve
Residual flux
Sum of Flares plus baseline
7
Flux Density (Jy)
6
5
4
3
2
1
0
2002
2003
2004
2005
2006
2007
2008
Year
Fig. 4·24.— X-ray and 37 GHz light curves of 3C 120. Curves correspond to summed
flux after modeling the light curve as a superposition of many individual X-ray dips
or radio flares and a baseline as shown in Figure 4·23.
91
Energy Output of 37 GHz Flares (10-6 erg cm-2)
700
600
500
400
300
200
100
0
0
100
200
300
400
500
600
700
800
Equivalent Widths of X-ray Dips (10-6 erg cm-2)
Fig. 4·25.— Total energy output of the 37 GHz flares versus equivalent width of the
corresponding X-ray dips of 3C 120.
is a close correspondence of superluminal ejections with 37 GHz flares, but sometimes
flux declines of old knots farther out in the jet offset much of the flux increase from
the appearance of a new knot. In such cases, the corresponding increase of flux was
not large enough to be detected in our decomposition of the smoothed light curve.
This causes the minimum in the X-ray DCCF to be less significant than it would be if
old knots were to completely fade before new ones appear. Despite this complication,
the X-ray/37 GHz cross-correlation verifies with an objective statistical method that
radio events in the jet are indeed associated with X-ray dips. The mean time delay
between the start of the X-ray dips and the time of “ejection” of the corresponding
superluminal knot in 3C 120 is 0.18 ± 0.14 yr. The apparent speeds of the moving
components with well-determined motions are all similar, 4.0c ± 0.2c. Therefore, a
knot moves a distance of 0.22 pc in 0.18 yr, projected on the plane of the sky. Since
the angle of the jet axis of 3C 120 to the line of sight ∼20◦ , the actual distance
traveled by the knot ∼ 0.5 pc. Hence, we derive a distance ∼ 0.5 pc from the corona
92
Flux (10-11 erg cm-2 s-1)
7
6
5
4
3
2
1
2005
2006
2007
2008
2009
Year
Fig. 4·26.— X-ray light curve of 3C 111. The curve corresponds to the same data,
smoothed with a Gaussian function with a 10-day FWHM smoothing time. The
arrows indicate the times of superluminal ejections and the line segments perpendicular to the arrows represent the uncertainties in the times. All of the ejections are
preceded by a significant dip in the X-ray flux.
93
(where the X-rays are produced) to the VLBA 43 GHz core region. This confirms
that the core is offset from the position of the BH. This is one of the few cases where
we are able to probe the connection between the central engine and core using the
time variable emission at a combination of wave bands.
4.5.3
Results: 3C 111
I smooth the X-ray light curve using a Gaussian function with a 10-day FWHM
smoothing time to identify the major long-term trends in the light curve. Figure
4·26 shows the smoothed X-ray light curve and the times of superluminal ejections
with arrows. It can be seen that all of the ejections are preceded by a significant
dip in the X-ray flux. We calculate the center of each dip by determining the local
minimum of the X-ray flux. The mean time delay between the minimum of the X-ray
dips and the time of “ejection” of the corresponding superluminal knot is 0.24 ± 0.14
yr. The apparent speeds of the moving components with well-determined motions
are all similar, 4.1c ± 0.2c. Therefore, a knot moves a distance of 0.30 pc in 0.24 yr,
projected on the plane of the sky. Since the angle of the jet axis of 3C 111 to the line
of sight ∼18◦ , the actual distance traveled by the knot ∼ 1.0 pc. Hence, we derive a
distance ∼ 1.0 pc from the corona (where the X-rays are produced) to the VLBA 43
GHz core region. This is one of the few cases, similar to 3C 120, where we are able
to specify the distance between the central engine and core in an AGN.
94
Chapter 5
Theoretical Modeling
5.1
Emission from Relativistic Jets
In blazars, non-thermal radiation produced by the jet is strongly amplified by relativistic beaming and dominates the spectral energy distribution (SED). The subparsec-scale jet is not spatially resolved even with the Very Long Baseline Array
(VLBA) and hence the location of the optical to γ-ray emission must be inferred from
less direct methods than pure imaging. The X-ray and γ-ray emission is produced by
inverse Compton scattering of the synchrotron photons from the jet itself and/or seed
photons from outside the jet (Mause et al. 1996; Romanova & Lovelace 1997; Coppi &
Aharonian 1999; Blażejowski et al. 2000; Sikora et al. 2001; Chiang & Böttcher 2002;
Arbeiter et al. 2005). Therefore, numerical modeling of the emission mechanisms in
the relativistic jet is necessary to use observational data to identify the location and
mechanism of ongoing emission processes. The data analysis mentioned in the previous chapters gives us characteristic timescales of variability, cross-frequency time
delays, properties of the long-term flares in the light curves and their relation to the
flares in other wavebands. To connect these results with the physical variables in
the jet, e.g., the magnetic field, number density and energy distribution of electrons
and bulk Lorentz factors, I have carried out numerical calculation of the nonthermal
emission from the jet.
95
5.1.1
Single Zone Model
I have developed a computer code that calculates the synchrotron and synchrotron
self-Compton (SSC) radiation from a source with a power-law distribution of electrons having a range of Lorentz factors from γmin to γmax . The synchrotron emission
coefficient in the rest frame of the plasma is given by
jνS (ν)
=
γZmax
γmin
Z+∞
N0 γ dγ x
K 5 (ξ) dξ,
−s
(5.1)
3
x
where the power-law electron energy distribution is given by N(γ) = N0 γ −s . The
critical frequency, near which most of the synchrotron luminosity occurs, is given by
νc = k1 γ 2 , while the synchrotron energy loss rate is given by dγ/dt = −k2 γ 2 . Both k1
and k2 are functions of B and are given by k1 = 4.2 × 106 B and k2 = 1.3 × 10−9 B 2 ,
where B is in Gauss. Here, K 5 is the modified Bessel function of the second kind of
3
and x = ν/νc . These definitions are similar to those in Chapter 2. Figure
Synchrotron Emission Co-efficient (arbitrary units)
order
5
3
100
1
0.01
1e-04
1e-06
1e-08
1e-10
10000
1e+08
1e+12
1e+16
Frequency (Hz)
Fig. 5·1.— Synchrotron spectrum in case of a single-zone model.
1e+20
96
5·1 shows the synchrotron spectrum (log Fν versus log ν) from a uniform source with
s = 2.5, γmax = 3 × 105, γmin = 50, and B = 1 Gauss. Fν ∝ ν 1/3 for frequencies below
the critical frequency of the lowest energy electrons, which is ∼ 5×109 Hz in this case.
Beyond that Fν ∝ ν −(s−1)/2) , which in this case is Fν ∝ ν −0.75 . The spectrum cuts off
exponentially at the critical frequency of the highest energy electrons (∼ 1 × 1017 Hz
in this case).
On the other hand, the inverse-Compton (SSC) emission coefficient is given by
jνC
=
Z Z
ν
γ
νf S
j (νi )Rσ(i , f , γ)N(γ) dγdνi,
νi ν
(5.2)
where the emission/scattering region is spherical with radius R. The Compton cross
section σ is a function of electron energy γ as well as the incident (νi ) and scattered
(νf ) frequencies of the photons:
σ(νi , νf , γ) =
1
x
3
σT
[8 + 2x − x2 + 4x ln( )],
2
32 νi γ
4
(5.3)
where x ≡ νf /(νi γ 2 ) and σT is the Thompson cross-section. Figure 5·2 shows the
synchrotron self-Compton spectrum from the same distribution of electrons as in Fig.
5·1.
The location of the emission region should also have an effect on the multiwaveband nature of the flares. The magnetic field B and electron energy density
parameter N0 both decrease with distance r from the base of the jet: B ∼ r −b and
N0 ∼ r −n ; I adopt a conical geometry, n = 2 (assuming continuous reconversion of
flow energy into internal energy) and b = 1 (assuming conservation of magnetic flux,
field transverse to jet axis). The cross-sectional radius R of the jet expands with r
(R ∝ r). I have performed a theoretical calculation of the energy output of flares
that includes the dependence on the location of the emission region. I introduce
time variability of the radiation with an exponential rise and decay in B and/or N0
97
IC Emission Co-efficient (arbitrary units)
1e-04
1e-06
1e-08
1e-10
1e-12
1e-14
1e-16
1e-18
1e-20
1e+12
1e+16
1e+20
1e+24
1e+28
1e+32
Frequency (Hz)
Fig. 5·2.— Synchrotron self-Compton spectrum in case of a single-zone model.
with time. In addition, I increase γmax with time in some computations in order
to simulate gradual acceleration of the electrons proposed by Böttcher et al. (2007).
Figure 5·3 shows segments of the actual X-ray and optical light curves along with
light curves produced from the above model. This shows that the model light curves
are qualitatively similar to the observed ones. I discuss this further in Chapter 6 in
the context of quantitative comparison of the X-ray and optical flares in the blazar
3C 279.
5.1.2
Multi-Zone Model
In the “single-zone” model, it is assumed that the radiating electrons in the emission
region form a single energy distribution that applies across the entire volume. As a
result, variability produced by the decay time of the high energy electrons cannot be
reproduced properly in these models if they are shorter than the light crossing time
of the zone. To make the models more realistic with gradients in electron energies, we
Flux (10-11 ergs cm-2 sec-1)
98
6.5
6
Real
Model
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
700 720 740 760 780 800 0 10 20 30 40 50 60 70 80 90 100
Flux (10-11 ergs cm-2 sec-1)
3.5
Real
Model
3
2.5
2
1.5
1
1200 1220 1240 1260 1280 1300 0 10 20 30 40 50 60 70 80 90 100
Time (MJD)
Time (MJD)
Fig. 5·3.— Simulated light curves from the time variable single zone model along
with selected segments of real light curves of 3C 279 (optical/synchrotron: solid line,
X-ray/SSC: dashed line) over ∼ 100 day intervals similar to the length of model light
curves. Optical flux density is multiplied by R band central frequency (4.7 × 1014 Hz)
to obtain the flux.
99
need to include multiple zones, each with an electron energy distribution of its own.
Electrons in each zone evolve with time according to the energy that they radiate.
Different zones may also have separate magnetic fields and electron number densities
depending on their positions. I model the emission spectrum from a relativistic jet
using a multi-zone model in the following manner.
I consider an elongated box having 64×2 ×2 cells, limited by computation time. I
assume that initially the electrons are in a quiescent state and the radiation they emit
is negligible. A shock front moves through this box from one end to the other and
electrons at the shock front are energized by the passage of the shock to a power-law
distribution within a range γmin to γmax . After this excitation, the electrons start losing energy through synchrotron and inverse-Compton (IC) processes. I assume that
the source (the elongated box in this case) is optically thin to synchrotron radiation at
the frequency of interest. The synchrotron emission coefficient, in this case, is given by
jν (ν) =
γZmax
N0 γ −s (1 − γk2 t)s−2
γmin
Z+∞
dγ x
K 5 (ξ) dξ.
3
(5.4)
x
Here the electron energy distribution evolves with time, i.e., N = N(γ, t) as does
the maximum electron energy in a zone (γmax = γmax (t)). As time passes, more and
more electrons are energized by the shock front and the emission increases. But the
highest energy electrons lose their energy faster than the lower energy electrons, and
so the spectrum cuts off at increasingly lower energies as the time since energization
increases. After the shock front reaches the end of the box, no new electrons are
energized. Therefore, the emission reaches a maximum, after which the cut-off energy
continuously decreases.
For each time step, I calculate the synchrotron radiation incident on a cell from
all the other cells, weighted by the inverse of their respective distance squared. For
SSC radiation, this is the total photon field available for scattering within that cell.
Synchrotron Emission Co-efficient (arbitrary units)
100
10000
100
1
0.01
1e-04
1e-06
1e-08
1e-10
10000
1e+08
1e+12
1e+16
1e+20
Frequency (Hz)
Fig. 5·4.— Time variability of the synchrotron spectrum. The solid curve shows
the synchrotron spectrum emitted by the elongated box (see text) when the shock
is passing through the source. The dashed curve shows the same when the shock
reaches the end of the box, i.e., when the emission is at the highest level. The dotted
curve shows the spectrum sometime after the shock has already passed through the
object. The high-energy cut-off has moved to lower energy, since the highest energy
electrons have already undergone significant cooling.
101
IC Emission Co-efficient (arbitrary units)
0.01
1e-04
1e-06
1e-08
1e-10
1e-12
1e-14
1e-16
1e-18
1e-20
1e+12
1e+16
1e+20
1e+24
1e+28
1e+32
Frequency (Hz)
Fig. 5·5.— Time variability of the SSC spectrum. The solid curve shows the SSC
spectrum emitted by the elongated box (see text) when the shock is passing through
the source. The dashed curve shows the same when the shock reaches the end of
the box, i.e., when all the electrons have been energized and hence the emission is
at the highest level. The dotted curve shows the spectrum sometime after the shock
has already passed through the object. The high-energy cut-off has moved to lower
energy, since the highest energy electrons have already undergone significant cooling.
102
Then the SSC emission can be calculated from that photon field and the electron
density and energy in that cell. The SSC emission coefficient is given by
jνC
=
Z Z
ν
γ
νf
jν (νi )Rσ(νi , νf , γ)N(γ, t) dγdνi,
νi
(5.5)
where the electron energy distribution evolves with time as in 5.4. Figures 5·4 and 5·5
display the time variable synchrotron and SSC spectrum from the multi-zone source
described above.
Fraction of Total Emission
0.25
Synch Radio
Synch Op
SSC X-ray (2 keV)
SSC gamma-ray (1GeV)
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
60
70
Zone Number
Fig. 5·6.— Fraction of total emission at different energies versus the zone number
starting at the downstream end.
Figure 5·6 shows the fractional intensity versus zone number (4 cells at the same
r) for multiple wavelengths when the shock front has just passed the box. It is evident from the figure that optical emission produced by synchrotron radiation and
γ-ray emission produced by the SSC process are generated by the highest energy electrons, which reside very close to the shock front. The intensity at these wavelengths
approaches zero after about the 10th zone. On the other hand, synchrotron radio
103
Synch Radio
Synch Op
SSC X-ray (2 keV)
SSC gamma-ray (1GeV)
Cumulative Fraction
1.2
1
0.8
0.6
0.4
0.2
0
10
20
30
40
50
60
Zone Number
Fig. 5·7.— Cumulative fraction of total emission at different energies versus the zone
number.
and SSC X-ray emission is generated by relatively lower energy electrons, which are
present throughout the 64 zones of the box. Hence, all zones contribute significantly
(and almost equally) to the emission at these wave bands.
Figure 5·7 displays the cumulative fraction of the emission versus zone number.
This shows that essentially all of the emission generated by the highest energy electrons occur within the first 10 zones behind the shock front, while emission from the
lower energy electrons increases continuously toward the upstream end of the box.
Emission at different frequencies generated by different mechanisms is distributed
over various spatial extents behind the shock front. This is called “frequency stratification,” whose consequences regarding the relative time delay between flares at
multiple wavebands are discussed in chapter 6.
104
5.2
Emission from the Disk-Corona System
The bulk of the optical-UV continuum from non-blazar AGNs is thought to emanate
from the accretion disk (Malkan 1983). Since the central black holes in AGNs are
massive (106 − 109 M ) and the accretion disk temperature has an inverse relation
with the mass of the BH (T ∼M −1/4 ), even the innermost regions of AGN accretion
disks are not hot enough to produce X-rays. This feature of AGN accretion disks is
different from that of the Galactic X-ray binaries where the innermost regions of the
accretion disk are hot enough to produce X-rays due to their much smaller mass of
∼10 M . The picture of the emission from the non-blazar AGNs that has emerged in
the last decade or so consists of an accretion disk that emits as a multi-color blackbody
supplemented by a distribution of hot electrons above the disk (or centered at the
inner parts of the disk), which inverse-Compton scatter the disk photons to X-rays
(Kazanas & Nayakshin 2001). This region of hot electrons is named the “corona”.
Since the spatial scale of the accretion disk of AGNs is not resolved by telescopes at
any wavelengths, one useful approach to understand the structure of the disk-corona
system and the relevant emission mechanism is to model this region and compare the
time variability properties predicted by the model with those of observations.
I have performed a theoretical calculation to produce multi-wavelength light curves
from a disk-corona system. I assume that (1) the temperature of the disk changes
with its radius according to T∼ r −3/4 (Shakura & Sunyaev 1973), (2) each annulus
radiates as a perfect black-body, (3) the X-rays are produced in a spherical region
(corona) close to the center of the disk by up-scattering of the disk photons that
reach the corona, and (4) lower energy radiation (UV-optical) is produced both by
black-body radiation in the disk and re-heating of the disk by the X-rays from the
corona. I treat the X-ray production in the corona as a reflection that increases the
energy of the radiation. Figure 5·8 shows the variation of the total UV and optical
105
1
0.9
Bνr (arbitrary units)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
0
200
400
600
Radius (rg)
800
1000
1
0.9
Bνr (arbitrary units)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Fig. 5·8.— Total intensity of radiation coming from different annuli of an accretion
disk versus the annular radii. The top and bottom panels show UV (100 nm) and
optical (650 nm) wavelengths, respectively.
106
intensity emitted by an annulus at radius r of thickness ∆r ∝ r, i.e., Bν r versus
r. This shows that the annulus that produces the largest amount of UV radiation
(“region U”) lies ∼5 rg from the center and for optical emission (“region O”) it is at
∼75 rg . This distance is much smaller than what would be expected if most of the
optical radiation were to come from radii near where the Planck curve Bν peaks at R
band. Although these radii lie ∼4 light-days (1000 rg ) from the center (see Figures
5·9 and 5·10), regions closer to the center are at higher temperature and therefore
emit at a higher blackbody intensity at all wavelengths. Although Bν keeps increasing
with decreasing radii, Bν r peaks at a radius ∼75 rg at R band.
1
Intensity (arbitrary units)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
100
200
300
400
500
600
700
800
900
Wavelength (nm)
Fig. 5·9.— The emission spectrum radiated by the annulus at a radius of 50 rg . The
Wien peak is in the UV part of the spectrum.
I have created a computer code to simulate this disk-corona system and then
introduce a disturbance in the temperature of the accretion disk that propagates
from the center toward the outside or vice versa. The temperature at a given annulus
varies with time according to a Gaussian profile. This causes a flare in the emission of
the entire system at all wavelengths, although the flare starts and peaks at different
107
1
Intensity (arbitrary units)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
100
200
300
400
500
600
700
800
900
Wavelength (nm)
Fig. 5·10.— The emission spectrum radiated by the annulus at a radius of 1000 rg .
The Wien peak is in the optical R band.
times at different wavelengths (see Figure 5·11). I produce these light curves at X-ray,
UV, and optical bands, including delays from internal light travel time. The top panel
of Figure 5·12 shows the X-ray and optical light curves from the above calculation
when the disturbance propagates toward smaller radii. As a result, the emission from
the outer disk flares before that close to the BH. Therefore, the optical variation leads
that in the X-rays. In this simulation, the disturbance propagates at a speed 0.1c and
the time delay between the peaks of the X-ray and optical light curves ∼4 days.
In Figure 5·12, the two panels show results for different levels of feedback (the
fraction of the X-rays produced in the corona that reflect toward and re-heat the
disk). The top panel has feedback fraction equal to zero, i.e., none of the X-rays
re-heat the disk.It can be seen from the figure that, as feedback is introduced, the
resulting time delay becomes shorter and less precise. Figure 5·13 shows the light
curves when the disturbance is propagating outwards from the BH. In this case, as
expected, the X-ray variations lead those in the optical (by a similar amount as
108
1.02
10 rg
1000 rg
1500 rg
1
Temperature (normalized)
0.98
0.96
0.94
0.92
0.9
0.88
0.86
0.84
0.82
0
5
10
15
20
25
30
Time (Days)
35
40
45
50
Fig. 5·11.— The temperatures flares at different radii caused by the propagation of
a disturbance away from the BH. The flare starts and ends at larger radii at later
times.
in Figure 5·12) for the same propagation speed. The panels show, as above, that
including feedback makes the time delay shorter. Hence, feedback from the corona
may also contribute to the range of time delays that we see in the data.
109
1
X-Ray
Optical
0.95
Flux (arbitrary units)
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
1
X-Ray
Optical
0.95
Flux (arbitrary units)
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0
10
20
30
40
50
Time (Days)
Fig. 5·12.— Simulated X-ray (2 keV) and optical (650 nm) light curves from an
accretion disk-corona system using our theoretical calculation. The disturbance is
propagating inwards towards the BH. The top panel corresponds to zero feedback
and the bottom panel shows the same after including feedback.
110
1
X-Ray
Optical
0.95
Flux (arbitrary units)
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
1
X-Ray
Optical
0.95
Flux (arbitrary units)
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0
10
20
30
40
50
Time (Days)
Fig. 5·13.— Simulated X-ray (2 keV) and optical (650 nm) light curves from an
accretion disk-corona system using our theoretical calculation. The disturbance is
propagating outwards away from the BH. The top panel corresponds to zero feedback
and the bottom panel shows the same after including feedback.
111
Chapter 6
Discussion of Results
6.1
6.1.1
3C 279
Red Noise Behavior and Absence of a Break in the PSD
The PSDs of 3C 279 at all three wavebands are best fit with a simple power law
which corresponds to red noise. The red noise nature—greater amplitudes on larger
timescales—of the flux variations at all three wavebands revealed by the PSD analysis
is also evident from visual inspection of the light curves of 3C 279 (Figures 3·2, 3·3,
and 3·4).
The PSD break frequency in BHXRBs and Seyferts scales with the mass of the
black hole (Uttley et al. 2002; McHardy et al. 2004, 2006; Markowitz et al. 2003;
Edelson & Nandra 1999). Using the best-fit values and uncertainties in the relation
between break timescale, black-hole mass, and accretion rate obtained by McHardy
et al. (2006), I estimate the expected value of the break frequency in the X-ray PSD
of 3C 279 to be 10−7.6±0.7 Hz, which is just within our derived lower limit of 10−8.5
Hz. Here I use a black-hole mass of 3 × 108 M (Woo & Urry 2002; Liu, Jiang & Gu
2006) for 3C 279 and a bolometric luminosity of the big blue bump of 4 × 1045 ergs/s
(Hartman et al. 1996). The PSDs can be described as power laws with no significant
break although if I follow McHardy et al. (2006) and set the low-frequency slope of
the X-ray PSD at −1.0 and allow the high-frequency slope to be as steep as −2.4, a
break at a frequency . 10−8 Hz cannot be rejected at the 95% confidence level. An
even longer light curve is needed to place more stringent limits on the presence of a
112
break at the expected frequency.
6.1.2
Correlation between Light Curves at Different Wavebands
The cross-frequency time delays uncovered by our DCCF analysis relate to the relative
locations of the emission regions at the different wavebands, which in turn depend on
the physics of the jet and the high-energy radiation mechanism(s). If the X-rays are
synchrotron self-Compton (SSC) in nature, their variations may lag the optical flux
changes owing to the travel time of the seed photons before they are up-scattered.
As discussed in Sokolov et al. (2004), this is an important effect provided that the
angle (θobs ) between the jet axis and the line of sight in the observer’s frame is
sufficiently small, . 1.2◦ ± 0.2◦ , in the case of 3C 279, where I have adopted the
bulk Lorentz factor (Γ = 15.5 ± 2.5) obtained by Jorstad et al. (2005). According to
Sokolov et al. (2004), if the emission region is thicker (thickness ∼radius), the allowed
angle increases to 2◦ ± 0.4◦ . X-rays produced by inverse Compton scattering of seed
photons from outside the jet (external Compton, or EC, process) may lag the low
frequency emission for any value of θobs between 0◦ and 90◦ . However, in this case
I expect to see a positive X-ray spectral index over a significant portion of a flare if
θobs is small, and the flares should be asymmetric, with much slower decay than rise
(Sokolov & Marscher 2005). This is because the electrons that up-scatter external
photons (radiation from a dusty torus, broad emission-line clouds, or accretion disk)
to X-rays have relatively low energies, and therefore have long radiative cooling times.
Expansion cooling quenches such flares quite slowly, since the EC flux depends on
the total number of radiating electrons (rather than on the number density), which
is relatively weakly dependent on the size of the emitting region.
Time delays may also be produced by frequency stratification in the jet. This
occurs when the electrons are energized along a surface (e.g., a shock front) and then
move away at a speed close to c as they lose energy via synchrotron and IC processes
113
(Marscher & Gear 1985). This causes the optical emission to be radiated from the
region immediately behind the surface, with the IR emission arising from a somewhat
thicker region and the radio from an even more extended volume. This was shown
quantitatively in the theoretical calculation related to multi-zone emission model of
AGN jets (Figure 5·6 and 5·7). An optical to radio synchrotron flare then begins
simultaneously (if opacity effects are negligible), but the higher-frequency peaks occur earlier. On the other hand, SSC (and EC) X-rays are produced by electrons
having a range of energies that are mostly lower than those required to produce optical synchrotron emission (McHardy et al. 1999). Hence, X-rays are produced in
a larger region than is the case for the optical emission, so that optical flares are
quenched faster and peak earlier. The flatter PSD of 3C 279 in the optical waveband
is consistent with this picture.
In each of the above cases, the optical variations lead those at X-ray energies.
But in the majority of the observed flares in 3C 279, the reverse is true. This may
be explained by another scenario, mentioned by Böttcher et al. (2007), in which the
acceleration timescale of the highest-energy electrons is significantly longer than that
of the lower-energy electrons, and also longer than the travel time of the seed photons
and/or time lags due to frequency stratification. In this case, X-ray flares can start
earlier than the corresponding optical events.
I thus have a working hypothesis that XO (X-ray leading) flares are governed
by gradual particle acceleration. OX events can result from either (1) light-travel
delays, since the value of θobs determined by Jorstad et al. (2005) (2.1◦ ± 1.1◦ ) is
close to the required range and could have been smaller in 2001-03 when OX flares
were prevalent, or (2) frequency stratification. One way to test this further would be
to add light curves at γ-ray energies, as will be possible with the Fermi Gamma-ray
Space Telescope. If the X and γ rays are produced by the same mechanism and the X-
114
ray/optical time lag is due to light travel time, I expect the γ-ray/optical time lag to
be similar. If, on the other hand, the latter delay is caused by frequency stratification,
then it will be shorter, since IC γ rays and optical synchrotron radiation are produced
by electrons of similarly high energies.
If the synchrotron flare and the resultant SSC flare are produced by a temporary
increase in the Doppler factor of the jet (due to a change in the direction, Lorentz
factor, or both), then the variations in flux should be simultaneous at all optically
thin wavebands. It is possible for the C flare pairs (where the X-ray and optical flares
are almost coincident, time delay <10 days) to be produced in this way. Alternatively,
the C events could occur in locations where the size or geometry are such that the
time delays from light travel and frequency stratification are very short compared to
the durations of the flares.
As is discussed in Chapter 4, the X-ray/optical time delay varies significantly over
the observed period (see Table 4.2 and Fig. 4·13). As discussed above, XO flares can
be explained by gradual acceleration of electrons. The switch in the time delay from
XO to OX at the onset of the highest amplitude multi-waveband outburst, which
occurred in 2001 (MJD 2000 to 2200), might then have resulted from a change in the
jet that shortened the acceleration time significantly. This could have caused the time
delay from light travel time of the SSC seed photons and/or the effects of gradients in
maximum electron energy to become a more significant factor than the acceleration
time in limiting the speed at which flares developed during the outburst period.
However, the flux from the 43 GHz core also reached its maximum value in early
2002, and the apparent speed of the jet decreased from ∼ 17c in 2000 to ∼ 4 − 7c
in 2001-2003. This coincided with the onset of a swing toward a more southerly
direction of the trajectories of new superluminal radio knots. We can hypothesize
that the change in direction also reduced the angle between the jet and the line
115
of sight, so that the Doppler factor δ of the jet increased significantly, causing the
elevated flux levels and setting up the conditions for major flares to occur at all
wavebands. The pronounced variations in flux during the 2001-2002 outburst cannot
be explained solely by fluctuations in δ, however, since the time delay switched to OX
rather than C. Instead, a longer-term switch to a smaller viewing angle would have
allowed the SSC light-travel delay to become important, causing the switch from XO
to OX flares.
6.1.3
Quantitative Comparison of X-ray and Optical Flares
The relative amplitude of synchrotron and IC flares depends on which physical parameters of the jet control the flares. The synchrotron flux is determined by the
magnetic field B, the total number of emitting electrons N S , and the Doppler factor
of the flow δ. The IC emission depends on the density of seed photons, number of
electrons available for scattering N IC , and δ. An increase solely in N S would enhance
the synchrotron and EC flux by the same factor, while the corresponding SSC flare
would have a higher relative amplitude owing to the increase in both the density of
seed photons and number of scattering electrons. If the synchrotron flare were due
solely to an increase in B, the SSC flare would have a relative amplitude similar to
that of the synchrotron flare, since B affects the SSC output mainly by increasing the
density of seed photons. In this case, there would be no EC flare at all. Finally, if
the synchrotron flare were caused solely by an increase in δ, the synchrotron and SSC
flux would rise by a similar factor, while the EC flare would be more pronounced,
since the density and energy of the incoming photons in the plasma frame would both
increase by a factor δ. Table 6.1 summarizes these considerations.
I have carried out a numerical simulation of synchrotron and SSC flares produced
in the jet, which was described in chapter 5.1. In this simulation, the jet is modeled as
a single-zone source, the magnetic field (B) and the electron number density parame-
116
Table 6.1 Theoretical expectation about the comparison of SSC and EC flares following a synchrotron flare.
Parameter
δ
N
B
SSC/Synch
≈1
>1
≈1
EC/Synch
>1
≈1
<1
ter (N0 ) are functions of the distance of the emission region from the BH and the time
variability is produced by exponential variations in B and N0 . In Figure 6·1, the top
left panel shows the synchrotron and SSC flares at a given distance r from the base
of the jet, where r is a constant times a factor afac . The right panel shows the same
at a farther distance (afac = 5). The flares are created by an exponential rise and
decay in the B field, while the value of γmax is held constant. The total time of the
flares is fixed at 107 seconds (120 days). According to Figure 6·1, at larger distances
(right panel) the SSC flare has a lower amplitude than the synchrotron flare, even
though at smaller values of r (left panel) they are comparable. The bottom panels of
Figure 6·1 are similar except here the value of γmax increases with time (as inferred
from the forward time delay that occurs in some events). The same effect is apparent
as in the top panels. In Figure 6·2, the top and bottom panels show similar results,
but in these cases the flares are created by an exponential rise and fall in the value of
N0 . Again, the results are similar. The energy output of both synchrotron and SSC
flares decreases with increasing r, but more rapidly in the latter. As a result, the
ratio of SSC to synchrotron energy output ζXO decreases with r. The case ζXO 1
is therefore a natural consequence of gradients in B and N0 .
From Table 4.2, it can be seen that in half of the flare pairs ζXO 1. In one pair
ζXO > 1 and in all other pairs ζXO ≈ 1. The theoretical calculation suggests that
the pairs where the ratio is less than 1 are produced at a larger distance from the
117
1.2
γmax=const, afac=1
γmax=const, afac=5
γmax=γmax(t), afac=1
γmax=γmax(t), afac=5
jν (arbitrary units)
1
0.8
0.6
0.4
0.2
0
1.2
jν (arbitrary units)
1
0.8
0.6
0.4
0.2
0
20
40
60
80
Time (days)
100
20
40
60
Time (days)
80
100
Fig. 6·1.— Model synchrotron (solid curve) and SSC (dashed curve) flares. Here
all flares are created by an exponential rise and decay in the magnetic field B (B,
N0 , and R are functions of distance along the jet). In the bottom panels, γmax is
increased linearly with time, causing the SSC flux to peak ahead of the synchrotron
flux. Flare amplitudes have been scaled such that they can be seen on the same plot.
Normalization in the two upper panels is the same and that in the two lower panels
is the same.
118
1.2
γmax=const, afac=1
γmax=const, afac=5
γmax=γmax(t), afac=1
γmax=γmax(t), afac=2
jν (arbitrary units)
1
0.8
0.6
0.4
0.2
0
1.2
jν (arbitrary units)
1
0.8
0.6
0.4
0.2
0
20
40
60
80
Time (days)
100
20
40
60
Time (days)
80
100
Fig. 6·2.— Model synchrotron (solid curve) and SSC (dashed curve) flares. Here all
flares are created by an exponential rise and decay in the electron number density
parameter N0 (B, N0 , and R are functions of distance along the jet). In the bottom
panels, γmax is increased linearly with time, causing the SSC flux to peak ahead of
the synchrotron flux. Flare amplitudes have been scaled such that they can be seen
on the same plot. Normalization in the two upper panels is the same and that in the
two lower panels is the same.
119
base of the jet than those where the ratio & 1. The size of the emission region should
be related to the cross-frequency time delay, since for all three explanations of the
lag a larger physical size of the emission region should lead to a longer delay. I can
then predict that the X-ray/optical time delay of the latter flares should be smaller
than for the pairs with ratio < 1. Indeed, inspection of Table 4.2 shows that for most
of the pairs, shorter time delays correspond to larger ζXO , as expected. The smaller
relative width of the optical C flares supports the conclusion that these occur closer
to the base of the jet than the other flare pairs.
6.2
6.2.1
3C 120
PSD
Using the best-fit values and uncertainties in the relation between break timescale, BH
mass, and accretion rate obtained by McHardy et al. (2006), I estimate the expected
value of the break frequency in the X-ray PSD of 3C 120 to be 10−5.0±0.7 Hz. Hence,
our derived break frequency of 10−5.1 Hz lies within the expected range. Here I adopt
a BH mass of 5.5 × 107 M from emission-line reverberation mapping (Peterson et
al. 2004) and a bolometric luminosity of the big blue bump of 2.2 × 1045 ergs s−1
(Woo & Urry 2002). The break frequency of 10−5.1±0.7 Hz corresponds to a timescale
of 1.3 days. This result demonstrates that the X-ray emission from this radio galaxy
contains a characteristic timescale similar to that seen in X-ray binaries. This is
consistent with the hypothesis that the accretion processes by black holes of a large
range of masses (10M − 108 M ) are similar.
6.2.2
Disk-Jet Connection
The physical cause of the connection between events in the central engine and the jet
of BHXRBs and AGNs is currently a matter of considerable speculation. If the jet is
120
magnetically launched from the accretion disk (Blandford & Payne 1982), then there
must be a link between the magnetic state at the base of the jet and the accretion
state in the inner disk. One scenario, proposed for BHXRBs by Livio, Pringle, & King
(2003) and King et al. (2004), involves a change in the magnetic field configuration in
the inner disk from a turbulent condition in the high-soft state (when the X-ray flux
is relatively higher and softer) to mainly poloidal in the low-hard X-ray state. The
turbulence is needed for viscous heating, which in the BHXRB case leads directly to
bright X-ray emission with a soft spectrum. In an AGN it causes strong ultraviolet
emission, which is Compton scattered in the corona to a hard X-ray spectrum. If the
field switches from chaotic to mainly poloidal, which Livio, Pringle, & King (2003)
suggest can occur by random episodes of near-alignment of the field in the relatively
small number of turbulent cells in the inner disk, then the radiation in the inner
disk will be quenched at the same time as energy flow into the jet is promoted. The
transition back to the turbulent, radiative inner disk of the high-soft state would
need to involve a surge of energy injected into the jet in order to send a shock wave
(Miller-Jones et al. 2005) down the jet. Perhaps global magnetic reconnection could
cause this, but no detailed MHD model has been published to date.
Alternatively, it is possible that the “corona,” where the X-ray emission seen in
AGN supposedly arises from Compton up-scattering of softer accretion-disk photons,
might be the base of the jet (Markoff, Nowak, & Wilms 2005). If this is the case, then
the X-ray flux will be related to the number of electrons residing there and available
for scattering to create X-rays. The mass loading of the jet should also affect the
asymptotic Lorentz factor of the flow downstream if the jet is magnetically driven
(e.g. Vlahakis & Königl 2004). The same decrease in electron number that causes a
drop in scattered X-ray emission near the disk would lead to a time-delayed increase
in the speed of the jet downstream. The flatter-spectrum nonthermal X-ray emission
121
from the downstream jet would then play a larger relative role in the X-ray emission,
causing the observed hardening of the spectrum during the dips. The increase in flow
speed of the jet could form a shock wave, seen as a superluminal radio knot. It is
difficult to speculate why the mass loading should change, since we do not understand
the processes by which material from the disk and/or ergosphere are injected into the
base of the jet. However, observations of the microquasar GRS 1915+105 suggest that
outflow of matter from the disk alternates from mainly a wind to the jet (Neilsen &
Lee 2009). In an AGN with a magnetically driven jet, it may be the case that a
lower rate of mass injection into the jet actually enhances the jet emission owing to
an increase in the flow speed driving a shock wave down the jet, as described above.
6.2.3
Source of Optical Emission
The strong correlation between the X-ray and optical variations in 3C 120 implies
that the emission at both wave bands arises from the same general region. Since the
X-rays originate in the corona, the optical emission is probably thermal emission from
the accretion disk (Malkan 1983). We can reject the alternative hypothesis that the
main component of optical emission is synchrotron radiation from the jet. In that
case, the emission should be significantly polarized, contrary to observations showing
the optical linear polarization to be < 0.3% (Jorstad et al. 2007). Furthermore, the
anti-correlation of the X-ray and 37 GHz emission (the latter of which is produced
in the jet) implies that any optical synchrotron emission from the jet should also
anti-correlate with the X-ray flux, contrary to the strong observed correlation.
The X-rays are predominantly produced by inverse Compton (IC) scattering of the
thermal optical/UV seed photons from the accretion disk by hot, but non-relativistic,
electrons in the corona. In addition, the optical/UV emission and the X-rays are
tied together by another mechanism: some of the optical/UV radiation is produced
by heating of the accretion disk by X-rays produced in the above process (“feed-
122
back” mechanism). Feedback may smear the time delay by producing a fraction of
the optical/UV photons with different temporal properties from that of the direct
emission.
There is a weak correlation between the X-ray spectral index and the X-ray flux,
indicating that the spectrum becomes harder during a decrease in the X-ray production. This kind of “pivoting” has been seen before (Ogle et al. 2005; Maraschi et al.
1991). The X-rays may be produced mainly by up-scattering of UV photons and not
optical photons, consistent with the correlation found by Ogle et al. (2005) between
the X-ray and UV variations in 3C 120. This could occur if the flux of optical photons reaching the corona is much smaller than that of UV photons. Such a scenario is
likely if the corona is small such that the region where the UV photons are generated
is much closer to the corona than the region where the majority of the optical photons are produced. Any disturbance propagating outwards in the accretion disk will
cause a change in the UV flux (and a resultant nearly immediate change in the X-ray
emission) followed by a similar change in the optical flux. The sign of the time delay
will switch if the disturbance propagates inwards. The observed mean time delay
between X-ray and optical variations may be due to such propagation time delays. If
we adopt typical parameters such as ∼ 0.1 for accretion efficiency, L/Led ∼ 0.3 (Ogle
et al. 2005), and Lbol ∼ 2× 1045 ergs/sec (Woo & Urry 2002) and neglect General
Relativistic effects, the region in the accretion disk where the emission peaks in the
extreme UV/soft X-ray range (λ = 10 nm) should be very close to the innermost
stable orbit (∼ 5 rg , where rg is the gravitational radius of the black hole). The
region where the emission peaks in the optical (λ = 600 nm) lies at ∼ 1000rg (using
Equation 2.10 and 2.11). For 3C 120, with a BH mass of ∼ 5×107 M , 1000 rg is
equivalent to ∼4 light days. I consider a model that includes both time delays and
coupling of emission from the corona and disk.
123
In 3C 120, the X-ray/optical time delay is centered on 0.5 day with an uncertainty
of ±4 days (Figure 4·8), hence the direction of the time delay cannot be specified with
certainty. Because of this, we also perform the correlation for a 2-month-long portion
of the data set where the X-ray and optical sampling is much better than for the rest
of the data. That correlation function also shows a relatively broad peak centered
on zero, with a similar uncertainty in the time delay (Figure 4·9). This may be due
to a dichotomy in the speed of propagation of the disturbances and their directions,
respectively, i.e., the uncertainty corresponds to an actual range of time delays. This
also constrains the size of the corona. For example, if the corona were spread such
that the “region O” and “region U” were at the same distance from the corona, then
these regions will contribute equally to the flux of seed photons that are up-scattered
to X-rays. In that case, the X-ray flares would be much broader than observed and
no optical/X-ray time delay would be present. This is contrary to the observation of
relatively sharp X-ray flares and X-ray/optical time delays up to 4 days. In addition,
although overall we find a short mean time delay (0.5 day), in some of the individual
flares the time delay is longer (∼25 days; see top panel of Figure 4·14). Also, if optical
and UV photons were up-scattered to soft and hard X-rays, respectively, a significant
“soft-hard” time delay would be expected. We have cross-correlated the hard (4-10
keV) and soft (0.2-4 keV) longlook X-ray light curves, finding an excellent correlation
with nearly zero time lag (Figure 6·3). From the above discussion, we conclude that
the corona is situated close to the center of the accretion disk, and its size is such that
the flux of photons reaching the corona from “region O” is negligible with respect to
that from “region U”. Based on the solid angle of a spherical surface, the coronal
radius should be less than 40rg for the flux from “region O” to be less than 10% of
that from “region U”.
In another possible scenario, the X-ray variability is caused by intrinsic changes in
124
the hot electrons in the corona and the UV-optical changes are due to feedback, i.e.,
there is no intrinsic variability in the accretion disk. In this case, the X-ray/optical
time delay will solely be due to light travel time from the corona to the accretion disk.
This will produce time lags of a small fraction of a day (Kazanas & Nayakshin 2001),
which is too small to observe with the sampling of the data used in this work. The
observed essentially zero time lag between the long-term X-ray and optical light curves
(0.5 ± 4 days) and smaller variability amplitude in the short-term optical light curve
than that in the X-rays are consistent with the above scenario. In fact the steepening
of the X-ray spectrum and decrease in the mean X-ray flux level after 2006.0 (see
Fig. 4·23) suggest a long-term steepening of the energy distribution of electrons in
the corona. But the longer X-ray/optical time delay over a significant portion of the
data set (Figure 4·14) and comparable X-ray/optical B-band variability amplitude in
the long-term light curves (Doroshenko et al. 2009) with B-band variations sometimes
leading, indicate that propagation of disturbances in the accretion disk must produce
at least part of the X-ray/optical variability in this radio galaxy. Figure 6·4 shows a
Correlation Coefficient
0.5
0.4
0.3
0.2
0.1
0
-0.1
-40000 -30000 -20000 -10000
0
10000 20000 30000 40000
Time Delay (Seconds)
Fig. 6·3.— Discrete cross-correlation function (DCCF) of the soft and hard longlook
X-ray data of 3C 120.
125
sketch of the accretion disk-corona system as derived in this paper. The black filled
circle is the position of the BH, the temperature of the accretion disk is shown by
gray scale with lighter color meaning higher temperature, and the larger circular area
filled with dots is the corona. “region U” and “region O” are shown as thick solid
lines on the accretion disk. The radius of the corona and the distance of the relevant
emission regions from the BH are shown in units of rg .
Fig. 6·4.— Sketch of the accretion disk-corona system as derived in this work.
From the above model and the correlation results, I conclude that most, if not all,
of the optical emission in 3C 120 is produced in the accretion disk. The X-rays are
produced by scattering of (mostly) UV radiation in the corona. Optical/UV emission
due to re-heating of the disk by the X-rays is also a possible ongoing mechanism that
126
X-ray (10-11 erg cm-2 sec-1)/Optical (mJy) Flux
9
Optical
X-ray
8
7
6
5
4
3950
4000
4050
4100
4150
4200
MJD
Fig. 6·5.— Points represent the X-ray and optical light curves between MJD 3950
and 4200 (2006 October and 2007 April) when the time sampling was dense during
a minimum in the light curves. The curves represent the same data smoothed with
a Gaussian function with a 3 day FWHM smoothing time. The smoothed curves
identify the significant trends in the light curves while ignoring the small timescale
fluctuations.
may cause the spread of the time delay. The presence of sharp X-ray flares and the
X-ray/optical time delay of weeks in some individual flares indicate that the corona
must lie sufficiently close to the BH that the flux of seed photons reaching the corona
is dominated by UV light.
The light curve during the dip at X-ray and optical wave bands between 2006
October and 2007 April, displayed in Figure 6·5, is very well-sampled. It is evident
that the optical flux starts to decrease after ∼MJD 4025, 40 days earlier than the
decrease starts in the X-rays. The minimum in optical occurs ∼40 days earlier than
that in the X-rays as well. This indicates that the decrease was caused by a disturbance propagating from the outer radii of the accretion disk toward the BH. If this
disturbance is a thermal fluctuation propagating inward, then it should have an effec-
127
tive speed . 0.01c to cause a time delay of ∼40 days. This is one order of magnitude
higher than the sound speed for a gas pressure dominated disk of temperature ≤ 105
K. Therefore, the above disturbance cannot be transmitted by sound waves (Krolik et
al. 1991) unless the relevant regions of the disk are dominated by radiation pressure,
which cannot be ruled out in 3C 120 given its high accretion rate, nearly the Eddington value (0.3 LE ). On the other hand, this scenario is consistent with the model
proposed by King et al. (2004), in which large scale alignment of poloidal magnetic
field in the inner accretion disk from random fluctuations causes the decrease in the
X-ray flux. Such alignment occurs at a timescale 2R/H k(R3 /GM)1/2 , where R/H is
the radius to thickness ratio of the disk, k is a constant ∼10 (Tout & Pringle 1992;
Stone et al. 1996), and (R3 /GM)1/2 is the disk dynamical timescale at radius R. This
alignment timescale, for a 10M BH, is few seconds, which translates to ∼50 days for
a ∼ 5 × 107 M BH in 3C 120. Model light curves of King et al. (2004) also contain
short timescale, small amplitude fluctuations on top of the big flares and dips caused
by small-scale alignment of the poloidal magnetic field, similar to that observed in
the light curves of 3C 120 presented in this thesis.
6.3
6.3.1
3C 111
PSD Break-BH Mass Relation
Using the best-fit values and uncertainties in the relation between break timescale, BH
mass, and accretion rate obtained by McHardy et al. (2006), a bolometric luminosity
3 ×1044 ergs s−1 (Marchesini et al. 2004, with the more accurate extinction correction
from Ungerer et al. 1985), and the PSD break timescale 13+12
−7 days determined above,
I calculate the BH mass of 3C 111 to be (7.0 ± 3.5) × 107 M . This gives a ratio of
luminosity to Eddington luminosity of 0.09. The expected FWHM of the Hβ broad
emission line for this value of the BH mass is ∼3400 km/sec (using λLλ = 2.9 × 1043
128
erg/sec from Sargent (1977) in Equation 2 of Vestergaard & Petereson (2006)). Other
parameters used in the equation are also taken from Vestergaard & Petereson (2006).
This is about 30% less than the FWHM of the Hα broad emission line in 3C 111,
4800 km/s (Eracleous & Halpern 2003). The above-mentioned equation is used to
determine the BH mass of a system from its Hβ emission line width but the relevant
measurement is not available. Instead, we approximate that it is the same as the
FWHM of the Hα emission line. Our calculation of the BH mass using the X-ray
PSD break timescale implies that this approximation is valid within an uncertainty
of 30% in the case of 3C 111.
6.3.2
X-ray/Optical Correlation
Similar analysis as for 3C 120 implies that in 3C 111 the X-rays are produced by
scattering of (mostly) UV radiation in the corona. The corona must lie sufficiently
close to the BH that the flux of seed photons reaching the corona is dominated by
UV light. Unlike 3C 120, the X-ray variations clearly lead those in the optical by
17 ± 5 days which implies that most of the variations are caused by disturbances
propagating outward from the center of the accretion disk.
6.3.3
Variation of X-ray/Radio Correlation
The X-ray/37 GHz correlation result and its variation over 5 years imply that decreases in X-ray production are linked to increases in the 37 GHz flux between 2004
March and 2007 April, but after that the X-ray and 37 GHz variations are strongly
correlated. This suggests that, in 3C 111, X-rays are produced both in the accretion disk-corona region and in the jet. When the X-ray variations are predominantly
produced in the jet, they correlate with the 37 GHz variations (also produced in
the jet), but when the X-ray variations are produced mainly in the accretion diskcorona region, they anti-correlate with the 37 GHz variations. The X-ray/37 GHz
129
anti-correlation gives quantitative support to the trend that is apparent by inspection
of the light curve, i.e., X-ray dips are followed by the appearance of new superluminal
knots and hence enhancement in the 37 GHz flux. After 2007 April, appearances of
two new knots follow dips in the X-ray light curve, but a bright flare occurs at both
X-ray and 37 GHz wave bands between 2007 June and December. The correlation
during the second segment is dominated by these flares, resulting in a correlation
rather than an anti-correlation.
The X-ray and 230 GHz variations are strongly correlated and almost simultaneous
during the large flare between 2007 June and 2008 June. Temporal association of
the similarly bright X-ray, 230 GHz and 37 GHz flares implies that the X-ray flare
also originated in the jet along with those at 230 GHz and 37 GHz. The 230 GHz
emission is due to synchrotron radiation. The strong correlation between the X-ray
and 230 GHz variations suggests that the X-rays are produced by the synchrotron
self-Compton (SSC) process. If the X-rays are SSC in nature, their variations may
lag the radio flux changes owing to the travel time of the seed photons before they
are up-scattered. But in this case, the time delay is very small. Such a small time
lag results from the relatively large angle, ∼ 18◦ , between the jet axis and the line of
sight. As discussed in Sokolov et al. (2004), the time delay should be very short if
the angle between the jet axis and the line of sight in the observer’s frame is larger
than ∼ 4◦ in the case of 3C 111, for the bulk Lorentz factor (Γ = 4.1 ± 1.3) obtained
by Jorstad et al. (2005).
The 37 GHz flare started at the same time as in 230 GHz, but it reached maximum
level at a later time than both the 230 GHz and the X-ray flare. This is due to
the larger optical depth effect at longer wavelengths. The similar amplitudes of
the 37 and 230 GHz flares provide support for the shock in jet model (Marscher &
Gear 1985), which predicts that, in synchrotron flares produced in the jet, the peak
130
amplitude should stay constant as emission from different distances behind the shock
front reaches maximum at different times.
131
Chapter 7
Conclusions
Although considerable progress has been made in our understanding of the nature
of active galactic nuclei over the last two decades, fundamental questions about the
formation of AGN jets, particle acceleration, and broadband radiation mechanisms
are still unanswered. Theoretical ideas about the launching and collimation of the
jet are incomplete, while the high-energy emission mechanisms are not well-tested by
observations. However, we can use time variability—one of the defining properties
of AGNs—to probe the location and physical processes related to the emission at
resolutions even finer than provided by very long baseline interferometry (VLBI).
This dissertation presents extensive multi-frequency monitoring data of the blazar
3C 279 (over 10 years long) and the radio galaxies 3C 120 and 3C 111 (∼5 years),
including well-sampled light curves at X-ray energies (2-10 keV), optical wavelengths
(R and V bands), and radio frequencies (14.5 GHz and 37 GHz) as well as monthly
images obtained with the Very Long Baseline Array (VLBA) at 43 GHz that follow
changes in the emission structure of the jet on parsec scales. I have developed and
applied a set of statistical tools to characterize the time variability of AGNs, including the power spectral density (PSD) and its uncertainties, using an adaptation of
a method developed by Uttley et al. (2002), and discrete cross-correlation function
method (DCCF; Edelson & Krolik 1988) to infer the relationship of the emission
across different wavebands. I have determined the significance of the correlations
using simulated light curves based on the previously calculated PSDs. I study the
132
changes in the correlation function and the cross-frequency time delay over the years,
which are important for distinguishing among possible models. I compare the properties of contemporaneous flares at different frequencies by decomposing each light
curve into a number of individual (sometimes overlapping) flares.
In the above objects, the radio emission comes from the jet while the X-ray and
optical emission come from the jet and/or the accretion disk-corona region. I have
developed and employed numerical models of the time variable emission spectrum of
AGN jets and accretion disk-corona system. Comparing the results of the models
and the application of the above-mentioned statistical procedures on the real data,
I have drawn conclusions about the location of the emission regions of these objects
and identify the ongoing emission mechanisms and implications regarding the physics
of jets.
The main conclusions drawn for each of the three objects studied are summarized
below.
7.1
3C 279
(1) The X-ray, optical, and radio PSDs of 3C 279 are of red noise nature, i.e., there
is higher amplitude variability at longer timescales than at shorter timescales. The
PSDs can be described as power laws with no significant break, although a break in
the X-ray PSD at a variational frequency . 10−8 Hz cannot be excluded at the 95%
confidence level.
(2) X-ray variations correlate with those at optical and radio wavebands, as expected
if nearly all of the X-rays are produced in the jet. The X-ray flux correlates with the
projected jet direction, as expected if Doppler beaming modulates the mean X-ray
flux level.
(3) X-ray flares are associated with superluminal knots, with the times of the latter
133
indicated by increases in the flux of the core region in the 43 GHz VLBA images.
The correlation has a broad peak at a time lag of 130+70
−45 days, with X-ray variations
leading.
(4) Analysis of the X-ray and optical light curves and their interconnection indicates
that the X-ray flares are produced by SSC scattering and the optical flares by the
synchrotron process. Cases of X-ray leading the optical peaks can be explained by an
increase in the time required to accelerate electrons to the high energies needed for
optical synchrotron emission. Time lags in the opposite sense can result from either
light-travel delays of the SSC seed photons or gradients in maximum electron energy
behind the shock fronts.
(5) The switch to optical-leading flares during the major multi-frequency outburst
of 2001 coincided with a decrease in the apparent speeds of knots from 16-17c to
4-7c and a swing toward the south of the projected direction of the jet near the core.
This behavior, as well as the high amplitude of the outburst, can be explained if the
redirection of the jet (only a 1◦ -2◦ change is needed) caused it to point closer to the
line of sight than was the case before and after the 2001-02 outburst.
(6) Contemporaneous X-ray and optical flares with similar radiative energy output
originate closer to the base of the jet, where the cross-section of the jet is smaller,
than do flares in which the optical energy output dominates. This is supported by
the longer time delay in the latter case. This effect is caused by the lower electron
density and magnetic field and larger cross-section of the jet as the distance from the
base increases.
7.2
3C 120
(1) The X-ray PSD of 3C 120 is best fit by a bending power-law model where there is
a smooth change in the slope above and below a break frequency. The best-fit value
134
of break frequency for 3C 120 is 10−5.05 Hz, which agrees very well with the relation
between break timescale, BH mass and accretion rate obtained by McHardy et al.
(2006) spanning a range of BH mass from 10 M to 109 M . This indicates that the
accretion process in 3C 120 is similar to that of the BHXRBs.
(2) The X-ray and 37 GHz variations are anti-correlated, with the X-ray leading the
radio by ∼120 days. The anti-correlation remains even if the large X-ray dips and
radio flares after 2006 are excluded.
(3) Almost all X-ray dips are followed by the ejection of a new knot in the VLBA
images. This and the anti-correlation mentioned in (2) imply that decrease in the
X-ray production is linked with increased speed in the jet flow, causing a shock front
to form and move downstream. This property of 3C 120 is also similar to the Galactic
black hole systems where transitions to high-soft X-ray states are associated with the
emergence of very bright features that proceed to propagate down the radio jet.
(4) We derive a distance ∼0.5 pc from the corona (where the X-rays are produced)
to the VLBA 43 GHz core region using the average time delay between the start of
the X-ray dips and the time of “ejection” of the corresponding superluminal knots.
(5) The X-ray and optical variations in 3C 120 are very strongly correlated. This
correlation, absence of significant optical polarization and anti-correlation of X-ray
and 37 GHz variations (the latter of which are produced in the jet), together imply
that the optical emission is blackbody radiation from the accretion disk.
(6) The X-rays are produced by scattering of (mostly) UV radiation in the corona.
Comparison of simulated light curves from a disk-corona system and the observed
variation imply that the corona must lie sufficiently close to the BH that the flux of
seed photons reaching the corona is dominated by UV light.
135
7.3
3C 111
(1) The X-ray PSD of 3C 111 is best fit by a bending power-law model similar to
that in 3C 120. The best-fit value of break frequency for 3C 111 is 10−6.05 Hz,
corresponding to a timescale of ∼13 days. We then calculate the black hole mass to
be ∼ 7 × 107 M from the relation between break timescale, BH mass and accretion
rate given by McHardy et al. (2006).
(2) The X-ray flux variations are anti-correlated with those at 37 GHz in 3C 111,
with X-ray leading by ∼120 days during the first 3 years of monitoring. In contrast,
over the last 2 years, the X-ray and radio variations are strongly correlated, with
the X-ray leading by ∼40 days. This suggests that X-rays are produced both in the
accretion disk-corona region and in the jet in 3C 111. When the X-ray variations
are predominantly produced in the jet, they correlate with the 37 GHz variations
(also produced in the jet), but when the X-ray variations are produced mainly in the
accretion disk-corona region, they anti-correlate with the 37 GHz variations.
(3) The X-ray and 230 GHz variations are strongly correlated and almost simultaneous
during the large flare between 2007 June and 2008 June. Temporal association of
the similarly bright X-ray, 230 GHz and 37 GHz flares implies that the X-ray flare
also originated in the jet along with that at 230 GHz and 37 GHz. The 230 GHz
emission is due to synchrotron radiation. The strong correlation between the X-ray
and 230 GHz variations indicate that the X-rays are produced by the synchrotron
self-Compton process. The small time lag is expected owing to the relatively large
angle ∼ 18◦ between the jet axis and the line of sight. As discussed in Sokolov et
al. (2004), the time delay between the variations in synchrotron and SSC emission
is negligible if the angle between the jet axis and the line of sight in the observer’s
frame is not sufficiently small (. 4.0◦ , in the case of 3C 111).
(4) All the superluminal ejections identified in the sequence of VLBA images are
136
preceded by a significant dip in the X-ray flux. The mean time delay between the
minimum of the X-ray dips and the time of ejection of the corresponding superluminal
knot is 0.24 ± 0.14 yr. Using this time delay, we derive a distance ∼1.0 pc from the
corona (where the X-rays are produced) to the VLBA 43 GHz core region, similar to
3C 120.
(5) The X-ray and optical variations in 3C 111 are very strongly correlated, which
indicates that these emission regions are co-spatial. During the related X-ray/230
GHz/37 GHz flares between 2007 June and 2008 June, optical emission also underwent
a large outburst and was significantly polarized, which implies that in that period
most of the optical emission is synchrotron radiation from the jet. At other times,
significant polarization in the optical is absent. These results indicate that in 3C 111
the optical emission is generated both as blackbody radiation in the accretion disk
as well as synchrotron radiation in the jet. The latter dominated the total emission
during the large multi-wavelength outburst during the second half of the monitoring.
(6) Similar analysis as for 3C 120 implies that in 3C 111 the X-rays are produced by
scattering of (mostly) UV radiation in the corona. The corona must lie sufficiently
close to the BH that the flux of seed photons reaching the corona is dominated by
UV light, and most of the variations are caused by disturbances propagating outward
from the center of the accretion disk.
7.4
Implications for the General Population of Radio-Loud
AGNs
Larger variability amplitude on longer (few months) than shorter (few days) timescales
in all three of these radio-loud AGNs implies that the major variability mechanism(s)
occur on timescales of few months. Propagation of a shock wave as the cause of the
large amplitude variability and presence of turbulent structure of the magnetic field
137
and electron density in the jet and accretion disk as the cause of the smaller amplitude variability are consistent with the timescales of variations inferred from the data
presented in this thesis.
In radio-loud AGNs with very powerful jets pointing along our line of sight, such
as 3C 279 (average bulk Lorentz factor of the moving knots ∼ 15, angle between line
of sight and jet axis ∼ 1◦ −2◦ ), emission from the jet outshines that from the accretion
disk across all wavebands. As a result, the observed X-ray, optical and radio emission
originates almost entirely in the jet. The location and emission mechanism of the high
and low energy radiation are inter-related. Optical and lower frequency emission is
produced by synchrotron radiation and X-rays are generated through SSC scattering.
The time delay between variations in high and low frequency emission depends on
the relative importance of acceleration timescale of the emitting electrons, effect of
the angle between the jet axis and line of sight on the value of the time delay, travel
time of the synchrotron photons before they are inverse-Compton scattered by the
high energy electrons and the size of the emission region. Therefore, measurement
of the time delay by itself is not always sufficient to fully understand the spatial
and temporal relation of the emission at multiple wavebands. Inter-waveband time
delays and comparison of contemporaneous flares at multiple wavebands indicate that
multiple regions in the jet upstream and downstream of the VLBA core can produce
the emission at both high and low energies. These data also imply that in many of the
major multi-wavelength outbursts, the acceleration of electrons occur on timescales
of several days, which is consistent with the natural timescale of acceleration of high
energy particles in diffusive shocks.
In radio-loud AGNs with less powerful jets pointing at an angle to our line of
sight, such as 3C 120 and 3C 111 (average bulk Lorentz factor of the moving knots
∼ 4, angle between line of sight and jet axis ∼ 20◦ ), most of the observed X-ray
138
and optical emission is from the accretion disk, while the observed radio emission is
generated in the jet. In these objects, the optical emission is blackbody radiation from
the accretion disk and the X-rays are produced by the inverse-Compton scattering
of thermal optical-UV photons from the disk by a distribution of hot electrons —
the corona — situated near the disk. The variable X-ray and optical emission can
be used to constrain the extent of the corona within about 50 gravitational radii
from the black hole. The X-ray and optical variability can be caused by magnetic
disturbances propagating on the disk-dynamo timescale of tens of days. The X-ray
emission from these radio galaxies contains characteristic timescales proportional to
their respective BH masses similar to that seen in Galactic BH X-ray binaries and
Seyfert galaxies. This result implies that there is a universality in the accretion
processes of BHs in the mass range 10M to 108 M . These objects also show a clear
connection between the radiative state of the accretion disk and events in the jet. This
connection is expected according to all theories of jet launching and collimation, but
has not been demonstrated previously to extend to radio-loud AGNs. The disk-jet
connection and existence of a characteristic timescale in the X-ray emission in these
AGNs also provide strong support to the paradigm that AGNs and Galactic BHXRBs
are fundamentally similar, with characteristic time and size scales proportional to the
mass of the central BH which implies that we can develop and test models of AGNs
based partly on observations of BHXRBs.
Further progress in our understanding of the physical structures and processes
in compact relativistic jets can be made by increasing the number of wave bands
subject to intense monitoring. Expansion of such monitoring to a wide range of γ-ray
energies (20 MeV to 300 GeV) is now possible through the Fermi Gamma-ray Space
Telescope (Thompson 2004). Fermi is expected to detect ∼1000 γ-ray blazars and
produce daily light curves for some of these. The Fermi bright source list from only
139
the first three months of observation contains 205 highly significant γ-ray sources
(Abdo et al. 2009), more than half of which are AGNs. A multitude of telescopes
around the world have started to provide simultaneous multi-wavelength monitoring
of many of the blazars that Fermi will detect. The light curves from some of these
lower frequency observing campaigns are being made accessible to public soon after
observation. By combining these data at lower frequencies, as well as VLBI imaging,
with the Fermi data, more stringent tests on models for the nonthermal emission and
jet physics in AGNs will be possible.
List of Journal Abbreviations
ARA&A
Annual Review of Astronomy and Astrophysics
AJ
Astronomical Journal
A&A
Astronomy and Astrophysics
A&AS
Astronomy and Astrophysics Supplement
ApJ
Astrophysical Journal
ApJL
Astrophysical Journal Letters
ApJS
Astrophysical Journal Supplement
MNRAS
Monthly Notices of the Royal Astronomical Society
140
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Curriculum Vitae
Ritaban Chatterjee
Address: Department of Astronomy, Boston University, 725 Commonwealth Avenue,
Boston, MA 02215
Phone: (617) 353-7430
email: [email protected]
webpage: http://people.bu.edu/ritaban
Nationality : Indian
Date of birth : September 21st, 1980.
Education
1. Boston University, Boston, Massachusetts: Ph.D. in Astronomy, 2003-present. Expected graduation : July 2009. Thesis : Multi-Wavelength Time Variability of Active
Galactic Nuclei. Advisor : Prof. Alan P. Marscher.
2. Indian Institute of Technology, Kanpur: M.Sc. in Physics, 2003. Theory project :
Constraints on Torsion Gravity from Collider Data. Experimental project : Fabrication and Characterization of Polymer LEDs.
3. Presidency College, University of Calcutta: B.Sc. in Physics (Major) with Mathematics and Chemistry in 2001.
Professional Experience
1. Graduate Research Assistant, Department of Astronomy, Boston University, 2005Present.
2. Graduate Teaching Fellow, Astronomy 102 (Stars and Galaxies), Department of
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Astronomy, Boston University, 2003-2005.
3. Junior member, American Astronomical Society, 2006-Present.
4. Co-Investigator in the VLBA program BM256: Probing Blazars through Multiwaveband Variability of Flux, Polarization, and Structure, which completed observations in September, 2008.
Awards and Fellowships
1. 1 year, $69,000 grant from Fermi Cycle 2 Guest Investigator Program for the proposal “Investigating the location and mechanism of emission in the jets of gamma-ray
blazars using time variability.”
2. Council of Scientific and Industrial Research (CSIR) fellowship through the National Eligibility Test (NET) conducted by University Grants Commission (UGC),
Government of India, 2003.
3. HRI summer research fellowship, Harish Chandra Research Institute, Allahabad,
2002. Project : Optical Image Processing and Photometry of Active Galactic Nuclei.
4. Institute Merit-cum-Means Scholarship, Indian Institute of Technology, Kanpur,
India, 2001.
5. National scholarships for secondary (1996) and Higher secondary (1998) examinations, Government of India.
Talks, Poster Presentations, and Summer Schools
1. “Multi-Wavelength Time Variability of Active Galactic Nuclei,” dissertation talk
at American Astronomical Society Meeting 213, January 4-8, 2009, Long Beach, CA,
USA.
2. “X-ray dips and Superluminal Ejections in the Radio Galaxy 3C 120”, talk at
“Radio Galaxies in the Chandra Era”, July 8-11, 2008, Cambridge, MA (hosted by
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Chandra X-ray Center).
3. “Time Variability of Active Galactic Nuclei: Why, How and some recent results
of the Blazar 3C 279”, invited talk at Indian Institute of Astrophysics, Bangalore,
India, June 12, 2008.
4. “Time Variability of Active Galactic Nuclei: Why, How and some recent results
of the Blazar 3C 279”, invited talk at National Centre for Radio Astrophysics, Pune,
India, June 11, 2008.
5. “Time Variability of Active Galactic Nuclei”, invited talk at Saha Institute of
Nuclear Physics, Calcutta, India, June 4, 2007.
6. “Correlated Multi-Frequency Variability in the Blazars 3C 279 and PKS 1510-089”,
poster presentation, American Astronomical Society Meeting 209, January 5-10, 2007,
Seattle, WA, USA.
7. Participant at the “Astro-statistics Summer School”, Pennsylvania State University, June 6th-10th 2006.
8. “Evidence Supporting the Accretion Disk - Jet Connection in the Radio Galaxy
3C 120”, poster presentation, Annual New England Regional Quasar/AGN Meeting
Tuesday, May 30, 2006, MIT.
Refereed Publications
1. Correlated Multi-Waveband Variability in the Blazar 3C 279 from 1996 to 2007,
Chatterjee et al. 2008, ApJ, 689, 79
2. Disk-jet Connection in the Radio Galaxy 3C 120, Chatterjee et al. 2009, submitted
to ApJ.
3. Longterm Multi-Waveband Variability in the Radio Galaxy 3C 111, in preparation.
4. Synchrotron and Inverse Compton Models for Time Variable Nonthermal Emission
in Blazars, Chatterjee and Marscher, in preparation.
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Computer Skills
1. 6 years of experience in FORTRAN 77.
2. Other programming language used : C, perl, IDL.
3. Operating systems : Linux, Windows.