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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, PhDProfessor of Astronomy

Second Reader

Kenneth Brecher, PhDProfessor 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 re-

search, 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 per-

sonal 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 Michi-

gan), 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 Univer-

sity, Russia), Anne Lahteenmaki, Merja Tornikoski, and Talvikki Hovatta (Metsahovi

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 appar-

ent 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 pro-

fessional 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 Ku-

mar 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 time-

lessness 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 dis-

couraged 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 X-

viii

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 52

4.1 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

4.2 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

4.3 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

5 Theoretical Modeling 94

5.1 Emission from Relativistic Jets . . . . . . . . . . . . . . . . . . . . . 94

5.1.1 Single Zone Model . . . . . . . . . . . . . . . . . . . . . . . . 95

5.1.2 Multi-Zone Model . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.2 Emission from the Disk-Corona System . . . . . . . . . . . . . . . . . 104

xi

6 Discussion of Results 111

6.1 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

6.2 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.2.1 PSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.2.2 Disk-Jet Connection . . . . . . . . . . . . . . . . . . . . . . . 119

6.2.3 Source of Optical Emission . . . . . . . . . . . . . . . . . . . . 121

6.3 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. 21

3.2 Ejection times, apparent speeds, and position angle of superluminal

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

xv

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 107

xvi

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 lon-

glook 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; Bland-

ford & 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 (syn-

chrotron 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; B lazejowski et al.

2000; Sikora et al. 2001; Chiang & Bottcher 2002; Arbeiter et al. 2005; B lazejowski

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), presum-

ably 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 kpcscale 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 jetof the quasar 3C 279. Contours and color (grayscale) denote total and polarizedintensity, respectively. The VLBA, with its sub-milliarcsecond (mas) resolution, canprobe 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 multi-

waveband 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 com-

parison 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 con-

nection 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 rel-

ativistic 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 as-

sociated 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 un-

derlying 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 men-

tioned in the previous section gives us characteristic timescales of variability, cross-

frequency 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

C6

C5

C4

C3

C2

C1

2"

0827+243

D C1C2

3"

1222+216

Fig. 2·1.— kilo-parsec scale jet of AGNs. The grayscale and contours denote theX-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.

C

3"

1317+520

C3C2

C1

2"

2209+080

Fig. 2·2.— kilo-parsec scale jet of AGNs. The grayscale and contours denote theX-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 atseven epochs in 2002. The contours and color (grayscale) show the total and polarizedintensity, respectively. Individual moving knots are marked at selected epochs. In thisobject knots move at an apparent speed of ∼ 4c. The core is the bright, stationaryfeature on the left of each image.

12

(mostly electrons) have a power-law energy distribution given by

N(γ) = N0γ−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 =

∫

E

N(E)dE (2.2)

and

nE =

∫

E

EN(E)dE, (2.3)

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. Konigl (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 ob-

served 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 − β2)−1/2. (2.6)

The observed flux density of the plasma from a moving knot

Fν ∝ δ3+α, (2.7)

where α is the spectral index. In the above expression, one factor of δ2 occurs be-

cause 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 δα 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 theunits 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 ac-

cretion 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 =2hν3/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 Boltz-

mann’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 ∝ ν1/3exp(−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:

λmaxT = 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

the central BH (MBH) as T ∝ M−1/4BH . The temperature of the accretion disk is given

by (Krolik 1999)

T = 6.8 × 105η−1/4(L/LE)1/2L−1/446 R

1/4R (r/rg)

−3/4K, (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 = k1γ2, while the synchrotron energy loss rate is given by dγ/dt = −k2γ

2. Both k1

and k2 are functions of B and are given by k1 = 2.8 × 106B and k2 = 1.3 × 10−9B2,

where B is in Gauss. The spectrum of emission from a single electron is given by,

P (ν) = c1F (x), (2.12)

where c1 is a constant and

F (x) = x

+∞∫

x

K 53(ξ) dξ, (2.13)

17

where x = ν/νc and K 53

is the modified Bessel function of the second kind of order

53. The synchrotron emission coefficient is given by

jν(ν) =

γmax∫

γmin

N0γ−sF (x)dγ. (2.14)

This can also be written as

jν(ν) ∝ N0B(s+1)/2ν−(s−1)/2, (2.15)

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 ∝ γ2Uph, where Uph is

the energy density of the seed photon field. The frequency of the scattered photon

(νf ) is approximately given by

νf ∼ γ2νi, (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

jICν ∝

γmax∫

γmin

νmax∫

νmin

N0γ−sγ2Uphdγdν (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 ac-

celerated 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 be-

lieved 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 over-

take 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 Understand-

ing 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 forma-

tion 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 VER-

ITAS 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 nonther-

mal 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 promi-

nent blazars owing to its high optical polarization and variability of flux across the

electromagnetic spectrum. Very long baseline interferometry (VLBI) reveals a one-

sided 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 Radiodata set Start End Start End Start End

Longlook Dec 96 Jan 97 Mar 05 Jun 05Medium Nov 03 Sep 04 Jan 04 Jul 04 Mar 05 Sep 05Monitor 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 ex-

posure, 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 ab-

sorption 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 radiolobe extending to the northwest. The inset is a zoomed-in view of the nucleus. TheHST FOC V-band image (color/gray scale) is shown with a MERLIN+VLA 5 GHzimage overlaid. The 15 GHz fluxes are plotted logarithmically in steps of factor 2beginning 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 ∝ ναx , 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

0

1

2

3

4

5

6

1996 1998 2000 2002 2004 2006 2008

Flu

x (1

0-11 e

rg c

m-2

s-1

) Monitor

0 0.2 0.4 0.6 0.8

1 1.2 1.4 1.6 1.8

2

2003.8 2004 2004.2 2004.4 2004.6

Flu

x (1

0-11 e

rg c

m-2

s-1

) Medium

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1996.94 1996.98 1997.02 1997.06 1997.1

Flu

x (1

0-11 e

rg c

m-2

s-1

)

YEAR

Longlook

Fig. 3·2.— X-ray (2-10 keV) data of 3C 279 on different time-scales. In the upperpanel, the arrows show the times of superluminal ejections and the line segmentsperpendicular 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

0

5

10

15

20

25

30

35

1996 1998 2000 2002 2004 2006 2008

Flu

x D

ensi

ty (

mJy

)

Monitor

0

2

4

6

8

10

2004 2004.1 2004.2 2004.3 2004.4 2004.5 2004.6

Flu

x D

ensi

ty (

mJy

)

Medium

0

2

4

6

8

10

2005.2 2005.24 2005.28 2005.32 2005.36 2005.4 2005.44 2005.48

Flu

x D

ensi

ty (

mJy

)

YEAR

Longlook

Fig. 3·3.— Optical (R-band) data of 3C 279 on different time-scales.

27

10

15

20

25

30

35

1996 1998 2000 2002 2004 2006 2008

Flu

x D

ensi

ty (

Jy)

Monitor

14

15

16

17

18

2005.2 2005.3 2005.4 2005.5 2005.6 2005.7 2005.8

Flu

x D

ensi

ty (

Jy)

YEAR

Medium

Fig. 3·4.— Radio (14.5 GHz) data of 3C 279 on different time-scales.

28

below) of new superluminal knots.

Fig. 3·5.— Angular separation from the core vs. epoch of all knots brighter than 100mJy within 2.0 mas of the core of 3C 279. The solid lines indicate the motion of eachknot listed in Table 3.2. A knot is identified through continuity of the trajectory fromone epoch to the next. The diameter of each symbol is proportional to the logarithmof 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.

29

0

1

2

3

4

5

6

Flu

x (1

0-11 e

rg c

m-2

s-1

)

X-ray, Monitor

0

5

10

15

20

25

30

35

Flu

x D

ensi

ty (

mJy

) Optical, Monitor

10

15

20

25

30

35

Flu

x D

ensi

ty (

Jy) 14.5 GHz, Monitor

-180-170-160-150-140-130-120-110-100-90-80

1996 1998 2000 2002 2004 2006 2008

Pos

ition

Ang

le (

Deg

ree)

YEAR

Fig. 3·6.— Variation of X-ray flux, optical flux, radio flux and position angle of thejet from 1996 to 2008. The circled data points in the bottom panel are the epochsshown in Fig. 3·7.

30

Fig. 3·7.— VLBA images of the pc-scale jet of 3C 279 at one epoch during each yearof 11-year monitoring. The images are convolved with the beam of the size 0.38 ×0.14mas 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

2

4

6

8

10

12

14

16

1996 1998 2000 2002 2004 2006 2008

Cor

e F

lux

Den

sity

(Jy

bea

m-1

)

YEAR

Fig. 3·8.— Light curve of the VLBA core region of 3C 279 at 43 GHz. The jaggedline 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 determineaccurately, but typically 10-20%.

Fig. 3·9.— 5 GHz VLA image of 3C 120 showing the kpc-scale jet (from Figure 4 ofWalker et al. (1987)).

33

Table 3.2 Ejection times, apparent speeds, and position angle of superluminal knotsin 3C 279.

Knot T0 T0 (MJD1) βapp θ (deg)2

C8 1996.09± 0.10 115± 36 5.4± 0.7 −130± 3C9 1996.89± 0.12 407± 44 12.9± 0.3 −131± 5C10 1997.24± 0.16 536± 58 9.9± 0.5 −132± 6C11 1997.59± 0.11 662± 40 10.1± 1.2 −135± 4C12 1998.56± 0.09 1016± 33 16.9± 0.4 −129± 3C13 1998.98± 0.07 1174± 26 16.4± 0.5 −130± 4C14 1999.50± 0.09 1360± 33 18.2± 0.7 −135± 6C15 1999.85± 0.05 1487± 18 17.2± 2.3 −131± 7C16 2000.27± 0.05 1642± 18 16.9± 3.5 −140± 8C17 2000.96± 0.12 1895± 44 6.2± 0.5 −133± 12C18 2001.40± 0.16 2054± 58 4.4± 0.7 −150± 8C19 2002.97± 0.12 2648± 44 6.6± 0.6 −133± 7C20 2003.39± 0.10 2781± 44 6.0± 0.5 −155± 10C21 2004.75± 0.05 3280± 18 16.7± 0.3 −147± 7C22 2005.18± 0.06 3434± 22 12.4± 1.2 −102±17C23 2006.41± 0.15 3888± 55 16.5± 2.3 −114± 5

1MJD = Julian date minus 24500002Average position angle of knot within 1 mas of the core.

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 X-

ray 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.

Data set Start End T(days) ∆T (days)Longlook 2002 December 13 2002 December 14 1.5 0.01

X-ray Medium 2006 November 2007 January 60.0 0.25Monitor 2002 March 2007 May 1910.0 15.0

Optical Monitor 2004 August 2008 January 1250.0 -Radio Monitor 2002 March 2008 January 2167.0 -

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 background-

subtracted 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.

36

1

2

3

4

5

6

7

8

9

2003 2004 2005 2006 2007

Flu

x (1

0-11 e

rg c

m-2

s-1

)Monitor

2

3

4

2006.9 2006.94 2006.98 2007.02

Flu

x (1

0-11 e

rg c

m-2

s-1

)

Medium

0.3

0.5

0.7

0.9

2002.9592002.9582002.9572002.956

coun

ts s

ec-1

YEAR

Longlook

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

Metsahovi 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 Terasranta 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

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

R-B

and

Flu

x (m

Jy)

V-Band Flux (mJy)

Fig. 3·11.— Filled circles show the 38 data points for 3C 120 that we measured within0.5 day of each other in V and R band, along with the respective uncertainties. Thedashed line represents the best fit straight line through these points, which is usedfor the V band to R band flux conversion.

5

6

7

8

9

10

11

2003 2004 2005 2006 2007 2008

Flu

x D

ensi

ty (

mJy

)

Year

Fig. 3·12.— Light curve of 3C 120 constructed by combining the V and R band lightcurves.

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 prop-

erties 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. Thecontours and color (grayscale) show the total and polarized intensity, respectively.The images are convolved with an elliptical Gaussian beam of FWHM size 0.36×0.15mas at PA = −6. The global peak over all maps is 1.52 Jy/Beam. The contourlevels are 0.25, 0.5, 1.0, ..., 64.0, 90.0% of the global peak. Individual moving knotsare marked at selected epochs.

41

Fig. 3·14.— VLBA images of 3C 120 at 7 mm obtained from 2004 to 2006. Thecontours and color (grayscale) show the total and polarized intensity, respectively.The images are convolved with an elliptical Gaussian beam of FWHM size 0.36×0.15mas at PA = −6. The global peak over all maps is 1.52 Jy/Beam. The contourlevels are 0.25, 0.5, 1.0, ..., 64.0, 90.0% of the global peak. Individual moving knotsare marked at selected epochs.

42

Fig. 3·15.— VLBI images of 3C 120 at 7 mm obtained from 2006 to 2007. Thecontours 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 atPA = −6. The global peak over all maps is 1.52 Jy/Beam. The contour levels are0.25, 0.5, 1.0, ..., 64.0, 90.0% of the global peak. Individual moving knots are markedat selected epochs.

43

2

3

4

5

6

7

8

9

Flu

x (1

0-11 e

rg c

m-2

s-1

)X-ray (2.4-10 keV)

4

6

8

Flu

x D

ensi

ty (

mJy

)

R BandV Band

0

2

4

6

2003 2004 2005 2006 2007

Flu

x D

ensi

ty (

Jy)

Year

37 GHz15 GHz

Fig. 3·16.— Variation of X-ray flux, optical flux density and radio flux density of 3C120 from 2002 to 2008. In the top panel, the arrows show the times of superluminalejections and the line segments perpendicular to the arrows indicate the uncertaintiesin the times.

44

Table 3.4 Time, area and width of the X-ray Dips and 37 GHz Flares, and Times ofSuperluminal Ejections of 3C 120.

X-ray T0 Knot ID 37 GHzT (st)1 T (min)2 A3 W4 T (pk)5 A3 W4

6 2002.15 6 6 2002.23 ± 0.03 02A 2002.39 195 952002.19 2002.30 657 120. 2002.65 ± 0.04 02B 2002.58 404 752002.75 2002.76 12 5.2003.02 2003.12 29 22.5 2003.35 ± 0.15 03A 2003.35 17 172003.32 2003.58 172 52.5 2003.67 ± 0.02 03B 2003.72 441 852003.66 2003.82 184 40. 2003.81 ± 0.03 03C 2003.92 24 202003.95 2003.98 44 15. 2003.98 ± 0.03 03D2004.12 2004.17 20 15. 2004.16 ± 0.05 04A2004.21 2004.37 364 65. 2004.37 ± 0.03 04B 2004.38 126 52

2004.49 60 252004.62 2004.66 30 12.5 2004.82 ± 0.05 04C 2005.05 61 272005.09 2005.12 33 17.5 2005.14 ± 0.03 05A 2005.23 21 152005.19 2005.39 351 65. 2005.34 ± 0.02 05B 2005.36 10 10

2005.57 92 572005.80 127 57

2005.94 2006.04 287 70. 2006.00 ± 0.03 06A 2006.43 126 1052006.38 2006.44 382 72.5 2006.72 ± 0.05 06B 2006.88 598 622006.96 2007.09 193 62.5 2007.05 ± 0.02 07A 2007.43 132 72

6 2007.87 122 60

1Start time of X-ray dips2Time of minimum of X-ray dips3Area; Units: 10−6 erg cm−2

4Width; Units: days5Time of maximum of 37 GHz flares6Insufficient data

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 1of 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) ∆T (days)Longlook 2009 February 16 2009 February 17 1.2 0.01

X-ray Medium 2006 November 2007 January 56.0 0.25Monitor 2004 March 2009 March 1843.0 15.0

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 -

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.

47

1

2

3

4

5

6

7

8

2005 2006 2007 2008 2009

Flu

x (1

0-11 e

rg c

m-2

s-1

)Monitor

2

3

4

5

6

2006.9 2006.94 2006.98 2007.02

Flu

x (1

0-11 e

rg c

m-2

s-1

)

Medium

7.3

7.7

8.1

8.5

8.9

9.3

2009.1402009.1392009.138

coun

ts s

ec-1

YEAR

Longlook

Fig. 3·18.— X-ray light curves of 3C 111 with different sampling rates.

48

1

2

3

4

5

6

7

8

Flu

x (1

0-11 e

rg c

m-2

s-1

)X-ray (2.4-10 keV)

3

4

5

6

Flu

x D

ensi

ty (

0.1

mJy

) Optical (R Band)

1

3

5

7

9

2005 2006 2007 2008 2009

Flu

x D

ensi

ty (

Jy)

Year

37 GHz230 GHz

Fig. 3·19.— Variation of X-ray flux, optical flux density and radio flux density of 3C111 from 2004 to 2009. In the top panel, the arrows indicate the times of superluminalejections and the line segments perpendicular to the arrows represent the uncertaintiesin 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. Thebright feature at the right of the image is the VLBA core and that on its left is abright 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) T0

2004.19 2004.50± 0.032005.02 2005.23± 0.032005.57 2005.75± 0.032006.47 2006.56± 0.032006.88 2006.95± 0.032007.32 2007.80± 0.032008.51 2008.83± 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

Metsahovi 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 Terasranta 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 character-

ize 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 ampli-

tude 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 & Konig 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∑

i=1

f(ti) cos(2πνti)

]2

+

[

N∑

i=1

f(ti) sin(2πνti)

]2

. (4.1)

This is the square of the modulus of the discrete Fourier transform of the (mean sub-

tracted) 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

µ2N2|FN(ν)|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 Ta-

ble 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.

data set T (days) ∆T (days) log(fmin) log(fmax) Npoints

Longlook 55.0 0.5 -6.67 -4.93 111X-ray Medium 301.0 5.0 -7.40 -5.93 127

Monitor 4150.0 25.0 -8.55 -6.63 1213Longlook 86.0 1.0 -6.86 -5.23 94

Optical Medium 185.0 5.0 -7.17 -5.92 77Monitor 4225.0 25.0 -8.55 -6.63 995

Radio Medium 189.0 4.0 -7.18 -5.83 59Monitor 3984.0 25.0 -8.53 -6.63 609

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 =

νmax∑

ν=νmin

(PSDobs − PSDsim)2

(∆PSDsim)2(4.3)

and

χ2dist,i =

ν(max∑

ν=νmin

(PSDsim,i − PSDsim)2

(∆PSDsim)2, (4.4)

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 χ2

dist distribution. Let m be the number of χ2dist,i for

which χ2obs is smaller than χ2

dist,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 fre-

quencies 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

(2Texp)−1∫

νNyq

P (ν)dν. (4.5)

I use PSRESP to account for aliasing at frequencies lower than (10Texp)−1.

I also add Poisson noise to the simulated light curves :

Pnoise =

∑Ni=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

0

2

4

6

8

log

PS

D (

rms2 H

z-1)

X-ray: Slope = -2.3

0

2

4

6

8

log

PS

D (

rms2 H

z-1)

Optical: Slope = -1.7

0

2

4

6

8

-8.5 -8 -7.5 -7 -6.5 -6 -5.5 -5

log

PS

D (

rms2 H

z-1)

log [Frequency (Hz)]

Radio: Slope = -2.3

Fig. 4·1.— Result of application of the PSRESP method to the light curves of 3C279. PSDs of the observed data at high, medium and low frequency range are givenby the solid, dashed and dotted jagged lines, respectively, while the underlying power-law 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-lawmodel (see text). The errorbars are the standard deviations of the distribution ofsimulated PSDs. The broadband PSD in all three wavelengths can be described by asimple power law.

59

0

0.1

0.2

0.3

0.4

0.5

-2.4-2.2-2-1.8-1.6-1.4-1.2-1

Suc

cess

Fra

ctio

nX-ray

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-2.4-2.2-2-1.8-1.6-1.4-1.2-1

Suc

cess

Fra

ctio

n

Optical

0

0.2

0.4

0.6

0.8

1

-2.4-2.2-2-1.8-1.6-1.4-1.2-1

Suc

cess

Fra

ctio

n

Power-law Slope

Radio

Fig. 4·2.— Success fraction vs. slope for all three PSDs of 3C 279. The successfractions 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

νB)(αL−αH)]−1. (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

fraction, I obtain a best fit with the parameters αL = −1.3+0.2−0.1, αH = −2.5+0.3

−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 X-

ray 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

-6

-5

-4

-3

-2

-1

-8 -7 -6 -5 -4 -3

log

[Pow

er X

Fre

quen

cy] (

rms2 )

log Frequency (Hz)

Fig. 4·3.— Result of application of the PSRESP method to the X-ray light curve of3C 120. The PSD of the observed data at high, medium and low frequencies is givenby the solid, dashed and dotted jagged lines, respectively, while the underlying power-law 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 power-law model (see text). The errorbars are the standard deviation of the distributionof simulated PSDs. The broadband power spectral density is best described by abending power law with low frequency slope −1.3, high frequency slope −2.5 andbreak frequency 10−5.05 Hz.

62

with the highest success fraction (0.85), we obtain a best fit with the parameters

αL = −1.0+0.1−0.1, αH = −2.8+0.2

−0.6, and log10(νB) = −6.05+0.3−0.3 Hz. Figure 4·4 presents this

best-fit model and the corresponding PSD.

-7

-6

-5

-4

-3

-2

-1

0

-8 -7 -6 -5 -4 -3

log

[Pow

er X

Fre

quen

cy] (

rms2 )

log Frequency (Hz)

Fig. 4·4.— Result of application of the PSRESP method to the X-ray light curve of3C 111. The PSD of the observed data at high, medium and low frequencies is givenby the solid, dashed and dotted jagged lines, respectively, while the underlying power-law 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 power-law model (see text). The errorbars are the standard deviations of the distributionof simulated PSDs. The broadband power spectral density is best described by abending power law with low frequency slope −1.0, high frequency slope −2.8 andbreak 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 varia-

tions 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 emis-

sion 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 re-

quires 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 cor-

relation 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 (cross-

correlation 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 radio-

optical DCCF has a similar peak value (0.45) at a 62% significance level. The cross-

correlation also indicates that the optical variations lead the X-ray by 20 ± 15 and

the radio by 260+30−60 days, while X-rays lead the radio by 240+35

−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

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8D

CC

F

Xray-Optical

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

DC

CF

Xray-Radio

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-600 -400 -200 0 200 400 600

DC

CF

Time Delay (Days)

Optical-Radio

Fig. 4·5.— Discrete cross-correlation function (DCCF) of the optical, X-ray, andradio monitor data of 3C 279. The time delay is defined as positive if the variationsat the higher frequency waveband lag those at the lower frequency.

67

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-600 -400 -200 0 200 400 600

DC

CF

Time Delay (days)

Fig. 4·6.— Cross-correlation function of the X-ray light curve and the position angleof the jet of 3C 279. Changes in the position angle lead those in the X-ray flux by80 ± 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

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Cor

rela

tion

Coe

ffici

ent

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

-300 -200 -100 0 100 200 300

Cor

rela

tion

Coe

ffici

ent

Time Delay (Days)

Fig. 4·7.— Discrete cross-correlation function (DCCF) of the X-ray and radio monitordata of 3C 120. The time delay is defined as positive if the X-ray variations lag thoseat radio frequency. Top panel shows the correlation function for the entire dataset. 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 majorflare at 37 GHz in 2006-07 and the corresponding deep dip at X-ray energies. Theanti-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 co-

efficient and time delay using very well-sampled light curves illustrates the robustness

of the correlation result.

70

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Fig. 4·8.— Discrete cross-correlation function (DCCF) of the optical and X-ray mon-itor data of 3C 120 for the entire 5 yr interval. The time delay is defined as positiveif 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 theX-ray variations leading the optical by 0.5 ± 4 days.

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rela

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ffici

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Fig. 4·9.— Discrete cross-correlation function (DCCF) of the optical and X-ray dataof 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 showsthat the two variations are strongly correlated and almost simultaneous as shown byFig. 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 fre-

quency. 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 fre-

quency. 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.

72

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May 07 to Mar 09

Fig. 4·10.— Discrete cross-correlation function (DCCF) of the X-ray and radio mon-itor data of 3C 111. The time delay is defined as positive if the X-ray variations lagthose at radio frequency. Top panel shows the correlation function for the entire dataset, the middle and the bottom panel show the same for the intervals 2004 March to2007 April and 2007 May to 2009 March, respectively.

73

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Fig. 4·11.— Discrete cross-correlation function (DCCF) of the X-ray and 230 GHzmonitor data of 3C 111 between 2007 April and 2008 August. 230 GHz variationslead 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 signif-

icance 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

-1

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tion

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ent

Time Delay (Days)

Fig. 4·12.— Discrete cross-correlation function (DCCF) of the optical and X-raymonitor data of 3C 111 for the entire 5 yr interval. The time delay is defined aspositive if the variations at the higher frequency waveband lag those at the lowerfrequency. The X-ray variations are very strongly correlated with those at opticalwavelengths 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 varia-

tions 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 anti-

correlated, 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 X-

ray and 37 GHz variations are strongly correlated. I discuss the physical interpretation

76

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1996-97 1997-98

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2003-04

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Time Delay (days)

2004.0-2007.5

Fig. 4·13.— Variation of X-ray/optical time lag of 3C 279 across overlapping 2-yrintervals from the beginning of the first year to the end of the second, except for thebottom right panel, for which the interval is indicated more precisely. Notice the bigchange between 1998-99 and 2000-2001, when the time delay went from X-ray leadingoptical to the opposite sense. There is a major change between 2001-02 and 2003-04as well, when the time delay went from optical leading X-ray to the opposite sense. Inthe last 4 years (bottom right panel) the correlation became weaker but maintainedthe negative time delay.

77

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June 05 to May 07

Fig. 4·14.— Variation of the X-ray/optical correlation function of 3C 120 across twointervals. The X-ray variations lead those in the optical by 25 days during the firstinterval 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

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ICCF (Op int)ICCF (X int)

DCCF

Fig. 4·15.— Cross-correlation function of the optical and X-ray monitor data of 3C120 for the entire 5 yr interval. The time delay is defined as positive if the variationsat the higher frequency waveband lag those at the lower frequency. In this and thenext five plots, the dotted curve shows the DCCF, the dashed curve shows the ICCFwhere the X-ray light curve is interpolated and the solid curve shows the ICCF wherethe lower frequency (optical or radio) light curve is interpolated. ICCF and DCCFproduce very similar correlation functions.

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ICCF (Op int)ICCF (X int)

DCCF

Fig. 4·16.— X-ray/optical correlation function of 3C 120 in the interval June 2004to May 2005. The X-ray variations lead those in the optical by 25 days during thisinterval. ICCF and DCCF produce very similar correlation functions. Curves are asdescribed in fig 4·15.

80

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ICCF (Op int)ICCF (X int)

DCCF

Fig. 4·17.— X-ray/optical correlation function of 3C 120 in the interval June 2005 toMay 2007. Two variations are almost simultaneous during this interval. ICCF andDCCF produce very similar correlation functions. Curves are as described in fig 4·15.

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ICCF (Op int)ICCF (X int)

DCCF

Fig. 4·18.— Cross-correlation function of the optical and X-ray data of 3C 120 be-tween 2006 November and 2007 January, binned to an interval of 0.5 day. The lightcurves in this interval is much better sampled than for the entire interval. Two vari-ations are almost simultaneous during this interval. ICCF and DCCF produce verysimilar correlation functions. Curves are as described in fig 4·15.

81

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ICCF (Rad int)ICCF (X int)

DCCF

Fig. 4·19.— Cross-correlation function of the X-ray and radio monitor data of 3C120. The time delay is defined as positive if the X-ray variations lag those at radiofrequency. This shows the correlation function for the entire data set. ICCF andDCCF produce very similar correlation functions. Curves are as described in fig 4·15.

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DCCF

Fig. 4·20.— Cross-correlation function of the X-ray and radio monitor data of 3C120. The time delay is defined as positive if the X-ray variations lag those at radiofrequency. This shows the correlation function for the entire data set excluding thedata during the major flare at 37 GHz in 2006-07 and the corresponding deep dip atX-ray energies. ICCF and DCCF produce very similar correlation functions. Curvesare 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 X-

ray/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

0

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Fig. 4·21.— Smoothed X-ray and optical light curves of 3C 279. Curves correspondto summed flux after modeling the light curve as a superposition of many individualflares. Thick horizontal strips in the X-ray light curve in 2000 correspond to epochswhen no data are available. Flare pairs listed in Table 4.2 are marked with therespective 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.

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CF

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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 ∝ ναx , 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

87

Table 4.2. Total energy output (area) and widths of flare pairs of 3C 279.

ID X-ray Optical ∆T TDC ζXO4

Time1 Area 2 Width3 Time1 Area2 Width3 (days)

1 119 (1996.10) 33.2 6.0 134 (1996.14) 76.3 12.0 -15 XO 0.442 717 (1997.74) 371.8 90.0 744 (1997.81) 929.5 97.5 -27 XO 0.403 920 (1998.30) 172.8 50.0 944 (1998.36) 278.2 35.0 -24 XO 0.624 1050 (1998.65) 338.7 70.0 1099 (1998.79) 502.8 57.5 -49 XO 0.675 1263 (1999.24) 160.7 77.5 1266 (1999.24) 168.9 42.5 -3 C 0.956 1509 (1999.91) 699.8 202.5 1517 (1999.93) 715.4 90.0 -8 C 0.987 2045 (2001.38) 103.7 60.0 2029 (2001.33) 568.3 65.0 16 OX 0.188 2151 (2001.67) 453.6 62.5 2126 (2001.60) 1188.3 57.5 25 OX 0.389 2419 (2002.40) 193.5 80.0 2422 (2002.41) 222.6 40.0 -3 C 0.8710 3185 (2004.50) 191.8 92.5 3191 (2004.52) 218.6 55.0 -6 C 0.8811 3416 (2005.13) 217.7 70.0 3444 (2005.21) 198.7 50.0 -28 XO 1.0912 3792 (2006.16) 525.3 120.0 3814 (2006.22) 375.6 67.5 -22 XO 1.4013 4035 (2006.83) 324.2 105.0 4008 (2006.76) 1068.4 75.0 27 OX 0.30

1Modified Julian Date (decimal year)

2Units: 10−6 erg cm−2

3Units: days

4Ratio of X-ray to optical energy output integrated over flare

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

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Year

Baseline

Fig. 4·23.— Variation of X-ray flux and the X-ray spectral index of 3C 120 during2002-2007. Curves are the cubic spline interpolation of the yearly mean of the dataplus one standard deviation. In case of X-rays, variations (both positive and negative)are relative to the baseline.

90

0

1

2

3

4

5

6F

lux

(10-1

1 erg

cm-2

s-1

)Baseline subtracted X-ray light curve

Residual fluxSum of Flares

0

1

2

3

4

5

6

7

2002 2003 2004 2005 2006 2007 2008

Flu

x D

ensi

ty (

Jy)

Year

37 GHz light curveResidual flux

Sum of Flares plus baseline

Fig. 4·24.— X-ray and 37 GHz light curves of 3C 120. Curves correspond to summedflux after modeling the light curve as a superposition of many individual X-ray dipsor radio flares and a baseline as shown in Figure 4·23.

91

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800

Ene

rgy

Out

put o

f 37

GH

z F

lare

s (1

0-6 e

rg c

m-2

)

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 thecorresponding 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

1

2

3

4

5

6

7

2005 2006 2007 2008 2009

Flu

x (1

0-11 e

rg c

m-2

s-1

)

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. Thearrows indicate the times of superluminal ejections and the line segments perpendic-ular to the arrows represent the uncertainties in the times. All of the ejections arepreceded 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 rel-

ativistic beaming and dominates the spectral energy distribution (SED). The sub-

parsec-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; B lazejowski et al. 2000; Sikora et al. 2001; Chiang & Bottcher 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 pre-

vious 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 elec-

trons having a range of Lorentz factors from γmin to γmax. The synchrotron emission

coefficient in the rest frame of the plasma is given by

jSν (ν) =

γmax∫

γmin

N0γ−sdγ x

+∞∫

x

K 53(ξ) dξ, (5.1)

where the power-law electron energy distribution is given by N(γ) = N0γ−s. The

critical frequency, near which most of the synchrotron luminosity occurs, is given by

νc = k1γ2, while the synchrotron energy loss rate is given by dγ/dt = −k2γ

2. Both k1

and k2 are functions of B and are given by k1 = 4.2 × 106B and k2 = 1.3 × 10−9B2,

where B is in Gauss. Here, K 53

is the modified Bessel function of the second kind of

order 53

and x = ν/νc. These definitions are similar to those in Chapter 2. Figure

1e-10

1e-08

1e-06

1e-04

0.01

1

100

10000 1e+08 1e+12 1e+16 1e+20Syn

chro

tron

Em

issi

on C

o-ef

ficie

nt (

arbi

trar

y un

its)

Frequency (Hz)

Fig. 5·1.— Synchrotron spectrum in case of a single-zone model.

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 ∝ ν1/3 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

jCν =

∫

ν

∫

γ

νf

νi

jSν (νi)Rσ(εi, εf , γ)N(γ) dγdνi, (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) =3

32σT

1

νiγ2[8 + 2x − x2 + 4x ln(

x

4)], (5.3)

where x ≡ νf/(νiγ2) 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 multi-

waveband 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

1e-20

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

1e-04

1e+12 1e+16 1e+20 1e+24 1e+28 1e+32

IC E

mis

sion

Co-

effic

ient

(ar

bitr

ary

units

)

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 Bottcher 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

98

1 1.5

2 2.5

3 3.5

4 4.5

5 5.5

6 6.5

700 720 740 760 780 800

Flu

x (1

0-11 e

rgs

cm-2

sec

-1)

Real

0 10 20 30 40 50 60 70 80 90 100

Model

1

1.5

2

2.5

3

3.5

1200 1220 1240 1260 1280 1300

Flu

x (1

0-11 e

rgs

cm-2

sec

-1)

Time (MJD)

Real

0 10 20 30 40 50 60 70 80 90 100

Time (MJD)

Model

Fig. 5·3.— Simulated light curves from the time variable single zone model alongwith 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 lightcurves. 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 los-

ing 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) =

γmax∫

γmin

N0γ−s(1 − γk2t)

s−2 dγ x

+∞∫

x

K 53(ξ) dξ. (5.4)

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.

100

1e-10

1e-08

1e-06

1e-04

0.01

1

100

10000

10000 1e+08 1e+12 1e+16 1e+20Syn

chro

tron

Em

issi

on C

o-ef

ficie

nt (

arbi

trar

y un

its)

Frequency (Hz)

Fig. 5·4.— Time variability of the synchrotron spectrum. The solid curve showsthe synchrotron spectrum emitted by the elongated box (see text) when the shockis passing through the source. The dashed curve shows the same when the shockreaches the end of the box, i.e., when the emission is at the highest level. The dottedcurve shows the spectrum sometime after the shock has already passed through theobject. The high-energy cut-off has moved to lower energy, since the highest energyelectrons have already undergone significant cooling.

101

1e-20

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

1e-04

0.01

1e+12 1e+16 1e+20 1e+24 1e+28 1e+32

IC E

mis

sion

Co-

effic

ient

(ar

bitr

ary

units

)

Frequency (Hz)

Fig. 5·5.— Time variability of the SSC spectrum. The solid curve shows the SSCspectrum emitted by the elongated box (see text) when the shock is passing throughthe source. The dashed curve shows the same when the shock reaches the end ofthe box, i.e., when all the electrons have been energized and hence the emission isat the highest level. The dotted curve shows the spectrum sometime after the shockhas already passed through the object. The high-energy cut-off has moved to lowerenergy, 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

jCν =

∫

ν

∫

γ

νf

νi

jν(νi)Rσ(νi, νf , γ)N(γ, t) dγdνi, (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.

0

0.05

0.1

0.15

0.2

0.25

0 10 20 30 40 50 60 70

Fra

ctio

n of

Tot

al E

mis

sion

Zone Number

Synch RadioSynch Op

SSC X-ray (2 keV)SSC gamma-ray (1GeV)

Fig. 5·6.— Fraction of total emission at different energies versus the zone numberstarting 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 ev-

ident 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 elec-

trons, 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

0

0.2

0.4

0.6

0.8

1

1.2

10 20 30 40 50 60

Cum

ulat

ive

Fra

ctio

n

Zone Number

Synch RadioSynch Op

SSC X-ray (2 keV)SSC gamma-ray (1GeV)

Fig. 5·7.— Cumulative fraction of total emission at different energies versus the zonenumber.

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 elec-

trons 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 strat-

ification,” 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 − 109M) 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

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

Bνr

(ar

bitr

ary

units

)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Bνr

(ar

bitr

ary

units

)

Radius (rg)

Fig. 5·8.— Total intensity of radiation coming from different annuli of an accretiondisk versus the annular radii. The top and bottom panels show UV (100 nm) andoptical (650 nm) wavelengths, respectively.

106

intensity emitted by an annulus at radius r of thickness ∆r ∝ r, i.e., Bνr 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, Bνr peaks at a radius ∼75 rg at R band.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600 700 800 900

Inte

nsity

(ar

bitr

ary

units

)

Wavelength (nm)

Fig. 5·9.— The emission spectrum radiated by the annulus at a radius of 50 rg. TheWien 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

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600 700 800 900

Inte

nsity

(ar

bitr

ary

units

)

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

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

0 5 10 15 20 25 30 35 40 45 50

Tem

pera

ture

(no

rmal

ized

)

Time (Days)

10 rg1000 rg1500 rg

Fig. 5·11.— The temperatures flares at different radii caused by the propagation ofa disturbance away from the BH. The flare starts and ends at larger radii at latertimes.

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

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Flu

x (a

rbitr

ary

units

)X-Ray

Optical

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 10 20 30 40 50

Flu

x (a

rbitr

ary

units

)

Time (Days)

X-RayOptical

Fig. 5·12.— Simulated X-ray (2 keV) and optical (650 nm) light curves from anaccretion disk-corona system using our theoretical calculation. The disturbance ispropagating inwards towards the BH. The top panel corresponds to zero feedbackand the bottom panel shows the same after including feedback.

110

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Flu

x (a

rbitr

ary

units

)X-Ray

Optical

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 10 20 30 40 50

Flu

x (a

rbitr

ary

units

)

Time (Days)

X-RayOptical

Fig. 5·13.— Simulated X-ray (2 keV) and optical (650 nm) light curves from anaccretion disk-corona system using our theoretical calculation. The disturbance ispropagating outwards away from the BH. The top panel corresponds to zero feedbackand the bottom panel shows the same after including feedback.

111

Chapter 6

Discussion of Results

6.1 3C 279

6.1.1 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 oc-

cur 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 op-

tical 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 Bottcher 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 pa-

rameters of the jet control the flares. The synchrotron flux is determined by the

magnetic field B, the total number of emitting electrons NS, 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 NS 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 follow-ing a synchrotron flare.

Parameter SSC/Synch EC/Synchδ ≈ 1 > 1N > 1 ≈ 1B ≈ 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

0

0.2

0.4

0.6

0.8

1

1.2

j ν (

arbi

trar

y un

its)

γmax=const, afac=1 γmax=const, afac=5

0

0.2

0.4

0.6

0.8

1

1.2

20 40 60 80 100

j ν (

arbi

trar

y un

its)

Time (days)

γmax=γmax(t), afac=1

20 40 60 80 100

Time (days)

γmax=γmax(t), afac=5

Fig. 6·1.— Model synchrotron (solid curve) and SSC (dashed curve) flares. Hereall 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 isincreased linearly with time, causing the SSC flux to peak ahead of the synchrotronflux. 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 panelsis the same.

118

0

0.2

0.4

0.6

0.8

1

1.2

j ν (

arbi

trar

y un

its)

γmax=const, afac=1 γmax=const, afac=5

0

0.2

0.4

0.6

0.8

1

1.2

20 40 60 80 100

j ν (

arbi

trar

y un

its)

Time (days)

γmax=γmax(t), afac=1

20 40 60 80 100

Time (days)

γmax=γmax(t), afac=2

Fig. 6·2.— Model synchrotron (solid curve) and SSC (dashed curve) flares. Here allflares are created by an exponential rise and decay in the electron number densityparameter N0 (B, N0, and R are functions of distance along the jet). In the bottompanels, γmax is increased linearly with time, causing the SSC flux to peak ahead ofthe synchrotron flux. Flare amplitudes have been scaled such that they can be seenon the same plot. Normalization in the two upper panels is the same and that in thetwo 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 3C 120

6.2.1 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 − 108M) 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 & Konigl 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-

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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 produc-

tion. 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 pho-

tons 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 pho-

tons 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.

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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

-0.1

0

0.1

0.2

0.3

0.4

0.5

-40000 -30000 -20000 -10000 0 10000 20000 30000 40000

Cor

rela

tion

Coe

ffici

ent

Time Delay (Seconds)

Fig. 6·3.— Discrete cross-correlation function (DCCF) of the soft and hard longlookX-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

4

5

6

7

8

9

3950 4000 4050 4100 4150 4200

X-r

ay (

10-1

1 erg

cm

-2 s

ec-1

)/O

ptic

al (

mJy

) F

lux

MJD

OpticalX-ray

Fig. 6·5.— Points represent the X-ray and optical light curves between MJD 3950and 4200 (2006 October and 2007 April) when the time sampling was dense duringa minimum in the light curves. The curves represent the same data smoothed witha Gaussian function with a 3 day FWHM smoothing time. The smoothed curvesidentify the significant trends in the light curves while ignoring the small timescalefluctuations.

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 distur-

bance 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 Edding-

ton 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/Hk(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 × 107M 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 3C 111

6.3.1 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 de-

creases 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 accre-

tion 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 disk-

corona 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, includ-

ing 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 prop-

erties 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 × 107M 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 ampli-

tude 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 108M. 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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149

Curriculum Vitae

Ritaban Chatterjee

Address: Department of Astronomy, Boston University, 725 Commonwealth Avenue,

Boston, MA 02215

Phone: (617) 353-7430

email: ritaban@bu.edu

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. Ex-

pected 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 : Fabrica-

tion and Characterization of Polymer LEDs.

3. Presidency College, University of Calcutta: B.Sc. in Physics (Major) with Math-

ematics and Chemistry in 2001.

Professional Experience

1. Graduate Research Assistant, Department of Astronomy, Boston University, 2005-

Present.

2. Graduate Teaching Fellow, Astronomy 102 (Stars and Galaxies), Department of

150

Astronomy, Boston University, 2003-2005.

3. Junior member, American Astronomical Society, 2006-Present.

4. Co-Investigator in the VLBA program BM256: Probing Blazars through Multi-

waveband Variability of Flux, Polarization, and Structure, which completed observa-

tions in September, 2008.

Awards and Fellowships

1. 1 year, $69,000 grant from Fermi Cycle 2 Guest Investigator Program for the pro-

posal “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 Na-

tional 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) examina-

tions, 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

151

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 Univer-

sity, 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.

152

Computer Skills

1. 6 years of experience in FORTRAN 77.

2. Other programming language used : C, perl, IDL.

3. Operating systems : Linux, Windows.