Abstract
Title of Dissertation: A Spectral Survey of Black Hole Spin
in Active Galactic Nuclei
Laura West Brenneman, Doctor of Philosophy, 2007
Dissertation directed by: Professor Christopher S. Reynolds
Department of Astronomy
This dissertation explores the question of whether broad iron lines from the accretion
disk can be used as viable diagnostic tools for constraining black hole spin. We begin
by giving an overview of the importance of black hole angular momentum as a signature
of General Relativity and as a means of testing this theory in the strong-field limit. We
discuss the anatomy of the typical black hole/accretion disk system, focusing on the com-
plex environments of active galactic nuclei, and in particular Seyfert-1 systems which we
pursue in this work. After developing a robust technique for fitting the continuum and
absorption parameters through a rigorous analysis of the XMM-Newton spectrum of the
Sy-1 galaxy NGC 4593, we then discuss a new model we have developed that fits broad
emission lines from the inner accretion disk. This model, kerrdisk, is fully relativistic
and allows the black hole spin to be a free parameter in the fit. Using this model, we
carefully analyze the 350 ks XMM-Newton spectrum of the Sy-1 source MCG?6-30-15,
which has the broadest and best-studied iron line observed to date. Fitting for the black
hole spin in this source, we conclude that a > 0.987 to 90% confidence. We then extend
our source list to analyze the XMM-Newton spectra of nine other radio-quiet Sy-1 AGN
that have previously been observed to harbor broad iron lines. We find that, given enough
photons and a broad line indicative of an origin in the inner disk where relativistic effects
are important, our new model enables us to place robust constraints on black hole spin.
Four of our sampled AGN meet the criteria necessary to constrain spin. Those constraints
are given, along with the full spectral fit to each source. Interestingly, the spins of these
sources range from moderate (a ? 0.5?0.7) to very high (a > 0.95), and we do not find
any AGN consistent with non-rotating black holes. For those objects that had marginal
spin constraints or none at all, we discuss the spectral fits and the probable reasons for the
lack of robustness of our results. This is the first ever survey of black hole spin in type-1
AGN.
A Spectral Survey of Black Hole Spin
in Active Galactic Nuclei
by
Laura West Brenneman
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland at College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2007
Advisory Committee:
Professor Christopher S. Reynolds, chair/advisor
Professor M. Coleman Miller
Professor Sylvain Veilleux
Professor Stacy S. McGaugh
Professor Theodore A. Jacobsen
Adjunct Professor Richard F. Mushotzky
c? Laura West Brenneman 2007
Preface
The final results presented in this thesis are unpublished, but will be submitted to the
Astrophysical Journal shortly after acceptance of this manuscript by the University of
Maryland Department of Astronomy. Work published in refereed journals includes the
material in Chapter 2 (Reynolds et al. 2004a), some of which is in press (Brenneman
et al. 2007), and Chapters 3-4 (Brenneman & Reynolds 2006). Preliminary results that
formed the basis of Chapter 5 were given at the AAS meetings in January 2006, January
2007 and May 2007, as well as the Triggering Relativistic Jets conference in Cozumel
(March 2005), the Conference on Supermassive Black Holes in Santa Fe (July 2006), and
the STScI Spring Symposium on Black Holes (April 2007).
ii
For Mom, who read me books on astronomy, and for Dad, who took me
outside to say goodnight to the moon.
iii
Acknowledgements
It really does take a village. This work would not have been possible without
the guidance, patience and wisdom of my advisor, Chris Reynolds. He has
helped me in countless ways: inspiring me with his talks and helping me
prepare my own, helping me focus my work and my thinking, teaching me
how to approach problems logically and creatively at the same time, grinding
through fortran code with me, and providing helpful words on everything
from XSPEC tricks to manuscript proofreading to career advice. I could not
have asked for a better mentor.
Many thanks also to the members of my committee for putting up with
all my emails and helping me to become a better scientist. Cole Miller, in par-
ticular, has taken the time to answer my questions whenever I?ve asked them
since my first year, and has always done so with clarity, grace and thoughtful-
ness. Though not a member of my committee, Derek Richardson has nicely
acted as a sounding board for my programming woes on several occasions,
even though my work couldn?t possibly have less to do with rubble piles.
iv
The faculty and staff of the Astronomy Department have been wonder-
ful teachers, colleagues and supporters for the duration of my time here. I am
indebted to them for their knowledge, caring and consideration. Likewise,
special thanks go out to my fellow graduate students, who have also doubled
as housemates, teammates and fellow sufferers through late nights and long
problem sets. Their scholarship has given me inspiration, and their humor
has given me much-needed relief.
My parents have provided me with unconditional love, support and con-
fidence, along with the occasional meal, wake-up call and spare bedroom to
escape to. Even though neither is a scientist, they both smile and nod politely
when I talk to them about my work. I would not be here without the lessons I
learned from them, most importantly that intelligence alone is nothing with-
out focus, discipline and determination.
I am grateful also to my family and friends, who have kept me sane and
grounded during all my years of education and who have never wavered in
their belief in me. And finally, thanks to Kathy, for more reasons than I can
count.
v
Contents
List of Tables viii
List of Figures ix
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The History of Black Hole Studies in X-rays . . . . . . . . . . . . . . . . 2
1.3 Anatomy of a Black Hole-Accretion Disk System . . . . . . . . . . . . . 7
1.3.1 Accretion Disk Properties . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 The Corona and Relativistic Jet Outflows . . . . . . . . . . . . . 12
1.3.3 The Disk Reflection Spectrum . . . . . . . . . . . . . . . . . . . 13
1.3.4 The Complication of Absorption . . . . . . . . . . . . . . . . . . 16
1.4 The History of Modeling Broad Iron Lines . . . . . . . . . . . . . . . . . 21
1.5 Purpose and Structure of this Work . . . . . . . . . . . . . . . . . . . . . 24
2 Modeling the X-ray Continuum in AGN: NGC 4593 26
2.1 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Continuum and Absorption . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 On the Lack of Accretion Disk Signatures in NGC 4593 . . . . . 38
2.3 Variable Nature of the Source . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.1 Spectral Variability . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.2 Continuum Power Spectrum and Spectral Lags . . . . . . . . . . 49
2.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 54
2.4.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . 54
2.4.2 Comparison with Previous Work . . . . . . . . . . . . . . . . . . 56
2.4.3 Implications for the X-ray Emission Region . . . . . . . . . . . . 57
2.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 A New Relativistic Line Emission Code 60
3.1 The kerrdisk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2 Comparison With Other Disk Line Models . . . . . . . . . . . . . . . . . 66
vi
3.2.1 The Convolution Model kerrconv . . . . . . . . . . . . . . . . . 71
4 MCG?6-30-15: The Broadest Iron Line Found to Date 74
4.1 A Brief History of Broad Iron Line Studies in MCG?6-30-15 . . . . . . . 75
4.2 Determining the Spin of the Black Hole in MCG?6-30-15 . . . . . . . . . 80
4.2.1 Simple Power-Law Continuum and Iron Lines . . . . . . . . . . 82
4.2.2 Modeling the Warm Absorber . . . . . . . . . . . . . . . . . . . 86
4.2.3 Model Including a Full Reflection Spectrum . . . . . . . . . . . . 93
4.2.4 Ruling out a Schwarzschild Black Hole . . . . . . . . . . . . . . 100
4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Spectral Fits to Other Broad Iron Line AGN 107
5.1 Data Reduction and Spectral Analysis Methodology . . . . . . . . . . . . 109
5.2 Results for Our Sample of Sy-1 AGN . . . . . . . . . . . . . . . . . . . 114
5.2.1 MCG?5-23-16 . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2.2 NGC 3783 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2.3 Mrk 766 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.2.4 3c273 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.2.5 3c120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2.6 NGC 2992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.2.7 NGC 4051 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.2.8 Ark 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.2.9 Fairall 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.3 Comparison of Sample Results . . . . . . . . . . . . . . . . . . . . . . . 156
6 Conclusions 165
6.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
A Computing kerrdisk Line Profiles 173
Bibliography 183
vii
List of Tables
2.1 Best fit parameters for the EPIC-pn spectrum of NGC 4593 . . . . . . . . 37
2.2 The cold and ionized iron lines in the EPIC-pn spectrum of NGC 4593 . . 49
4.1 Best fit parameters for MCG?6-30-15 . . . . . . . . . . . . . . . . . . . 99
5.1 Best fit parameters for MCG?5-23-16 . . . . . . . . . . . . . . . . . . . 118
5.2 Best fit parameters for NGC 3783. . . . . . . . . . . . . . . . . . . . . . 123
5.3 Best fit parameters for Mrk 766 . . . . . . . . . . . . . . . . . . . . . . . 128
5.4 Best fit parameters for 3c273 . . . . . . . . . . . . . . . . . . . . . . . . 136
5.5 Best fit parameters for 3c120 . . . . . . . . . . . . . . . . . . . . . . . . 138
5.6 Best fit parameters for NGC 2992 . . . . . . . . . . . . . . . . . . . . . 145
5.7 Best fit parameters for NGC 4051 . . . . . . . . . . . . . . . . . . . . . 147
5.8 Best fit parameters for Ark 120 . . . . . . . . . . . . . . . . . . . . . . . 152
5.9 Best fit parameters for Fairall 9 . . . . . . . . . . . . . . . . . . . . . . . 159
5.10 Comparison of laor and kerrdisk model fits for all sources. . . . . . . 162
5.11 Comparison of reflion and kdblur(refl) model fits for all sources. . . 163
5.12 Comparison of kerrconv(refl) model fits for all sources. . . . . . . . . 164
viii
List of Figures
1.1 Important X-ray missions. . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Anatomy of a BH system. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Diagram of coronal geometry. . . . . . . . . . . . . . . . . . . . . . . . 15
1.4 Reflection spectrum of an accretion disk. . . . . . . . . . . . . . . . . . . 16
1.5 Formation of a broad emission line. . . . . . . . . . . . . . . . . . . . . 17
1.6 Relativistic blurring of emission lines. . . . . . . . . . . . . . . . . . . . 18
1.7 AGN system with molecular torus. . . . . . . . . . . . . . . . . . . . . . 18
1.8 Spectral model of a warm absorber. . . . . . . . . . . . . . . . . . . . . 20
1.9 Broad iron line in MCG?6-30-15. . . . . . . . . . . . . . . . . . . . . . 21
1.10 Absorption near the Fe-K? line in MCG?6-30-15. . . . . . . . . . . . . . 22
2.1 Photoabsorbed power-law fit to the 2?10 keV spectrum of NGC 4593. . 31
2.2 Power-law and two Gaussians fit to the 0.5?10.0 keV spectrum of NGC 4593. 32
2.3 Model 1 global fit to NGC 4593. . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Model 2 global fit to NGC 4593. . . . . . . . . . . . . . . . . . . . . . . 36
2.5 Variation from the time-averaged Model 2 spectrum in 10 ks segments. . . 46
2.6 Variation of the cold and ionized iron lines from the Model 2 spectrum in
10 ks segments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.7 Flux and equivalent width variation of the cold iron line over the 76 ks
observation of NGC 4593. . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.8 Flux and equivalent width variation of the ionized iron line over the 76 ks
observation of NGC 4593. . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.9 Light curve and power spectrum for NGC 4593. . . . . . . . . . . . . . . 51
2.10 Soft, intermediate and hard band light curves. . . . . . . . . . . . . . . . 51
2.11 The cross-correlation function showing the hard-soft band time lag. . . . 53
2.12 Hardness ratios vs. time and energy for NGC 4593. . . . . . . . . . . . . 54
3.1 Variation of kerrdisk lines profiles with various parameters. . . . . . . . 67
3.2 Comparison of several accretion disk emission line models for a Schwarzschild
BH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3 Comparison of several accretion disk emission line models for a Kerr BH. 69
3.4 Comparison of the kerrdisk model profile to that of kerrconv(gauss). 72
ix
4.1 Photoabsorbed power-law fit to the X-ray spectrum of MCG?6-30-15. . . 83
4.2 Modeling the emission features in MCG?6-30-15. . . . . . . . . . . . . . 84
4.3 Modeling the WA in MCG?6-30-15. . . . . . . . . . . . . . . . . . . . . 88
4.4 Evidence for a multi-zone structure to the WA in MCG?6-30-15. . . . . . 90
4.5 Relative contribution of the various components in Model 4. . . . . . . . 92
4.6 Model for MCG?6-30-15 including a full ionized disk reflection spectrum. 94
4.7 Relative contributions of the components in Model 5. . . . . . . . . . . . 96
5.1 Fe-K? line residual in MCG?5-23-16. . . . . . . . . . . . . . . . . . . . 117
5.2 Best fit to the spectrum of MCG?5-23-16. . . . . . . . . . . . . . . . . . 119
5.3 Relative contributions of the model components in MCG?5-23-16. . . . . 120
5.4 Fe-K? line residual in NGC 3783. . . . . . . . . . . . . . . . . . . . . . 124
5.5 Best fit to the spectrum of NGC 3783. . . . . . . . . . . . . . . . . . . . 125
5.6 Relative contributions of the model components in NGC 3783. . . . . . . 126
5.7 Fe-K? line residual in Mrk 766. . . . . . . . . . . . . . . . . . . . . . . 129
5.8 Best fit to the spectrum of Mrk 766. . . . . . . . . . . . . . . . . . . . . 130
5.9 Relative contributions of the model components in Mrk 766. . . . . . . . 131
5.10 Fe-K? line residual in 3c273. . . . . . . . . . . . . . . . . . . . . . . . . 133
5.11 Best fit to the spectrum of 3c273. . . . . . . . . . . . . . . . . . . . . . . 134
5.12 Relative contributions of the model components in 3c273. . . . . . . . . . 135
5.13 Fe-K? line residual in 3c120. . . . . . . . . . . . . . . . . . . . . . . . . 139
5.14 Best fit to the spectrum of 3c120. . . . . . . . . . . . . . . . . . . . . . . 140
5.15 Relative contributions of the model components in 3c120. . . . . . . . . . 141
5.16 Fe-K? line residual in NGC 2992. . . . . . . . . . . . . . . . . . . . . . 142
5.17 Best fit to the spectrum of NGC 2992. . . . . . . . . . . . . . . . . . . . 143
5.18 Relative contributions of the model components in NGC 2992. . . . . . . 144
5.19 Fe-K? line residual in NGC 4051. . . . . . . . . . . . . . . . . . . . . . 146
5.20 Best fit to the spectrum of NGC 4051. . . . . . . . . . . . . . . . . . . . 148
5.21 Relative contributions of the model components in NGC 4051. . . . . . . 149
5.22 Fe-K? line residual in Ark 120. . . . . . . . . . . . . . . . . . . . . . . 153
5.23 Best fit to the spectrum of Ark 120. . . . . . . . . . . . . . . . . . . . . . 154
5.24 Relative contributions of the model components in Ark 120. . . . . . . . 155
5.25 Fe-K? line residual in Fairall 9. . . . . . . . . . . . . . . . . . . . . . . 156
5.26 Best fit to the spectrum of Fairall 9. . . . . . . . . . . . . . . . . . . . . 157
5.27 Relative contributions of the model components in Fairall 9. . . . . . . . 158
x
Chapter 1
Introduction
1.1 Overview
Accreting black holes (BHs) are the driving force behind some of the most powerful pro-
cesses in the universe. The central regions of active galactic nuclei (AGN) and Galactic
black holes (GBHs), in particular, are two BH-driven systems that are prodigious sources
of energy and radiation across the electromagnetic spectrum. Yet in spite of their ex-
treme nature and power, much about these objects remains unknown. The mechanism of
accretion onto the BH is a complex, magnetohydrodynamic (MHD) process whose de-
tailed workings will remain the subject of ambitious simulations for many years until a
computational marriage between General Relativity (GR) and MHD, including plasma
effects and radiative transfer, can be mastered. Accretion disks in BH systems can be
probed with observations, however, whereas (classically) BHs themselves emit no elec-
tromagnetic radiation. Fortunately BHs are mathematically simple objects that can be
fully defined by only their mass and spin. Unfortunately, while mass is comparatively
easy to calculate provided the BH has another object orbiting it, measuring spin requires
detecting strong-field GR effects and is not so straightforward to ascertain.
In the current absence of any gravitational wave signatures detected from BH systems,
1
which would provide a clean and robust measure of BH spin, we are left to look for indi-
rect electromagnetic evidence of this property in the spacetime immediately surrounding
the event horizon. GR predicts that one should observe several characteristic signatures in
the radiation from the material close to the event horizon (i.e., the central portions of the
accretion disk): frame dragging and gravitational time dilation are prominent examples.
Based on this theory, a powerful method for probing the properties of the BH is to observe
the degree to which emission lines in the spectrum of the inner accretion disk are altered
in their energy profiles by enhanced relativistic effects and extreme Doppler shifts. Proper
modeling of these emission features and fitting these models to data provides us with one
of the more robust and reliable diagnostic tools for constraining such relativistic effects
as BH spin. That is the subject of this thesis.
1.2 The History of Black Hole Studies in X-rays
X-rays provide the cleanest probe of the central engine in AGN: lower-energy radiation
is highly reprocessed before reaching the observer. The accretion disk itself typically
radiates as a blackbody peaking in the ultraviolet, but inverse Comptonization processes
involving the surrounding plasma boost these photons in energy until they become X-ray
emission. In smaller GBH systems the disk is hotter to begin with and has a blackbody
temperature in the X-ray range, compounding those X-rays produced by the Comptoniza-
tion processes at work. Unfortunately, our atmosphere is opaque to X-rays, so the scien-
tific study of these regions in BH systems simply was not possible until we were able to
put detectors into orbit in the latter half of the twentieth century.
An excellent history of the early years of X-ray astronomy was written by Bradt in
1992 (Bradt et al. 1992). Though the first detection of cosmic X-rays came in 1949
(Friedman et al. 1951), when X-ray Geiger counters aboard a sounding rocket were briefly
2
carried above the atmosphere and detected X-rays coming from the Sun, it was over ten
years later before improved technology enabled a detector to discover X-rays coming
from sources outside our solar system. This group, led by Riccardo Giacconi at American
Science and Engineering in 1962, discovered a bright X-ray source in the constellation of
Scorpius, which they consequently named Sco X-1 (Giacconi et al. 1962). Even though
the group had a scant few minutes of observing time, it was immediately apparent that the
source was cosmic in origin and had an X-ray luminosity ? 108 times stronger than the
Sun. This source is now known to be a low-mass X-ray binary neutron star system within
our own Milky Way.
Because successive sub-orbital rocket launches provided only brief glimpses of the X-
ray universe, a sustained orbital observatory was needed in order to begin to truly study the
sources found in detail. To this end, the first X-ray orbiting satellite, Uhuru, was launched
in 1970. The main instrument was a series of proportional counting arrays sensitive to X-
rays in the range of 2?20 keV. The final Uhuru catalog contained 339 objects, most
of which were binary stellar systems, supernova remnants, Seyfert galaxies and galaxy
clusters (Forman et al. 1978). Uhuru was followed by the HEAO missions beginning
in 1977, which marked the start of the era in which big X-ray payloads were being put
into orbit to make observations. HEAO-1 was primarily a scanning mission dedicated to
observing the entire X-ray sky and performing the first Large Area Sky Survey (LASS)
from 1?20 keV. Important discoveries included a catalog of 842 X-ray sources and
observations of aperiodic variability in the compact binary Cygnus X-1, which became
the first confirmed GBH after optical radial velocity studies of its secondary star proved
that the accreting object was too massive to be a neutron star. HEAO-1 also collected
numerous broad-band spectra of AGN of varying types (Worrall et al. 1981) , greatly
contributing to our knowledge of such objects. The mission was succeeded by HEAO-2
in 1978, which was later renamed Einstein. This X-ray observatory was the first of its
3
kind to employ grazing incidence optics, providing a significant advancement in imaging
and resolution capabilities. Its instruments combined to observe everything from coronal
stellar emission to X-ray jets emitted from massive galaxies to the warm/hot intergalactic
medium. But arguably some of the most important results were the spectral surveys of
AGN such as quasars and Seyfert galaxies, which showed tantalizing correlations between
radio flux and X-ray slope. These findings provided some of the best evidence that results
from the two wavebands might reflect two sides of the same beast, and helped support the
paradigm of the Unified Model of AGN (Bechtold et al. 1987; Kruper et al. 1990; Miller
& Antonucci 1983; Wilkes & Elvis 1987).
After Einstein deorbited in 1981, American involvement in X-ray astronomy took an
extended break. In the meantime, however, European and Japanese instruments made
significant progress in the field. In 1983, EXOSAT was successfully launched and began
an observing campaign from 1?50 keV. Notable among its many discoveries were the
first detailed observations of quasi-periodic oscillations (QPOs) in several low-mass X-ray
binary systems (Priedhorsky et al. 1986; van der Klis 1989), as well as a spectral survey
of 48 Seyfert galaxies revealing the prevalence of a soft X-ray component in these sources
(Turner & Pounds 1989). This soft component was thought to represent disk emission,
thereby substantiating theories that postulated AGN as BH/disk-related phenomena.
The Japanese observatory Ginga launched in 1987. Among its notable accomplish-
ments: detection of the systematic delay in variation of the hard X-ray to soft X-ray spec-
trum in Cyg X-1 (Miyamoto et al. 1988); detailed studies of iron emission and absorption
features common to many Seyfert-1 (Sy-1) spectra (Matsuoka et al. 1990; Pounds et al.
1990, 1989); and highly absorbed Sy-2 spectra in contrast to Sy-1s, which again sup-
ported the Unified Model (Awaki et al. 1990). Interestingly, both EXOSAT and Ginga
also discovered iron line emission and Compton reflection humps in BH spectra (Day
et al. 1990; Pounds et al. 1990; White et al. 1985).
4
The next decade brought the advent of the German-led ROSAT mission in June of
1990, with which the U.K. and U.S. were also affiliated. Conducting a rigorous all-sky
survey (the RASS), ROSAT expanded the X-ray source catalog to over 150,000 objects.
With over 1000 times the sensitivity of Uhuru, this observatory enabled even deeper ob-
servations of AGN and other BH systems as well as a multitude of other X-ray sources
(Boller et al. 1997; Wagner et al. 1994)). ROSAT was followed by the joint Japanese-
American satellite ASCA in 1993. This was the first X-ray telescope to combine imaging
capability with a broad pass band, moderately high spectral resolution (E/?E ?100) and
large effective area, as well as the first to employ CCDs as an X-ray detector. ASCA
revolutionized the study of iron emission lines around BHs, noting both the prevalence
of the feature in Sy-1 sources and enabling astronomers to use this feature to attempt to
constrain BH angular momentum (Mushotzky et al. 1995; Nandra et al. 1997).
The Rossi X-ray Timing Explorer (RXTE), launched in 1995, was designed specif-
ically to monitor X-ray sources such as AGN and GBHCs with high timing resolution,
since compact objects tend to display variability on short time scales in accordance with
their small light crossing times. With its very large collecting area and dedication to all-
sky monitoring, RXTE revolutionized the study of X-ray spectral and temporal variability
in BH systems, enabling astronomers to probe the nature of the accretion disk with un-
precedented detail (Lamer et al. 2001; Lee et al. 2000; Miller et al. 2004; Wilms et al.
1999). This mission is still active, as are two important, newer observatories in the X-ray
regime: XMM-Newton of ESA and Chandra of NASA, both launched in 1999. Although
both instruments offer superior resolution and throughput, Chandra excels more in the
area of precision X-ray imaging, whereas XMM-Newton enjoys a larger collecting area
and is more ideally suited for spectroscopy. The two observatories act as excellent com-
plements for each other and have enabled astronomers to examine the nature of accretion
and radiation within BH systems with unprecedented detail. Just as their predecessors did
5
before them, Chandra and XMM-Newton have focused on many different types of X-ray
phenomena during their lifetimes: everything from resonating galaxy clusters (Reynolds
et al. 2005) to millisecond pulsars (Juett et al. 2003) to the nature of the cosmic X-ray
background (Gilli et al. 2007). But some of the most important progress has been made
in the study of AGN and GBH systems. With the spectral resolution and throughput of
these two telescopes, scientists are coming closer than ever before to being able to de-
scribe the complex interaction between a BH and its accretion disk (Fabian et al. 2002;
Miller et al. 2006a; Wilms et al. 2001). Efforts to measure BH spin via detailed char-
acterization of the emission features from the disk are finally able to produce reliable
constraints due to the precision of the data (Brenneman & Reynolds 2006). These studies
are a central component of this thesis.
The next generation of X-ray telescopes promises to improve upon this legacy. Even
as RXTE, Chandra and XMM-Newton remain operable and active, new instruments such
as Swift (2004), Suzaku (2005) and the upcoming GLAST mission (2008) are already mak-
ing giant steps forward and adding more pieces to the puzzle of high energy phenomena
in the universe. While Swift is ostensibly a Gamma-ray burst mission, its X-ray telescope
(covering 0.2?10 keV) is ideally suited for examining the continuua and iron line regions
of AGN and GBHs. Suzaku is already contributing greatly to iron line studies itself: with
its spectral coverage of 0.3?600 keV and enhanced spectral resolution, it is already mak-
ing important distinctions between different models of emission and absorption from the
inner accretion disk (Miniutti et al. 2007; Reeves et al. 2007). These distinctions enable
astronomers to place vital constraints on the reflected emission from the accretion disk as
well as any intrinsic absorption within the system, thereby allowing BH spin to be more
robustly constrained.
The planned observatory Constellation-X, if it comes to fruition, will be another in-
valuable tool for probing BH spin and the BH-disk interaction. The microcalorimeters
6
generating the spectra for this mission will provide an order of magnitude enhancement
in resolution and will greatly lower the necessary integration time for any given object,
enabling deeper and more precise measurements to be made from spectral studies than
are possible with the instruments currently in orbit. And GLAST, the Gamma-ray Large
Area Space Telescope planned for launch later this year, will allow for an in-depth study
of jets and other relativistic outflows powered by BH systems, providing a unique view of
the transfer of angular momentum within these systems as well as the disk-jet interaction
and jet triggering mechanisms. Graphs charting the advent of X-ray missions with time
and with energy are shown in Fig. 1.1.
The aforementioned missions are giving us images and spectra of the X-ray universe
in unprecedented detail. Given enough photons and enough spectral resolution, we have
the necessary information to robustly constrain relativistic effects such as BH spin for the
first time, and to quantitatively probe the strong-gravity regime to test the accuracy of
GR?s predictions. But in order to separate out the evidence of spin from other manifes-
tations of the accretion disk or BH-disk interaction, we need to have an accurate model
for disk emission that correctly describes the intricate physics of the BH-disk system. In
creating such a model, it is imperative to begin with a physically consistent picture of the
accretion disk itself as well as the spacetime in which it resides.
1.3 Anatomy of a Black Hole-Accretion Disk System
The general picture of an accreting BH system, whether a GBH, AGN, or even an inter-
mediate mass black hole (IMBH; thought to be on the order of 102 ?104 Mcircledot (Miller &
Colbert 2004)), consists of a BH and surrounding accretion disk that can extend out to
tens of thousands of gravitational radii (rg = GM/c2 where M is the mass of the BH).
The disk forms by virtue of conservation of angular momentum in the material gravita-
7
Figure 1.1: X-ray missions plotted versus time (top) and energy range in
keV (bottom). Credits: http://heasarc.gsfc.nasa.gov/docs/heasarc/missions/time.html,
http://heasarc.gsfc.nasa.gov/docs/heasarc/missions/energy.html
8
tionally captured by the hole. In the case of a non-spinning BH pulling in material with
no preferred direction of net angular momentum, the material will be accreted via the
Bondi-Hoyle mechanism, i.e., in spherically symmetric fashion (Bondi & Hoyle 1944). It
is thought, however, that BHs totally lacking in angular momentum are quite rare if they
do indeed exist at all: statistically, there will almost always be enough angular momentum
in the accreted material to form a significant accretion disk, enabling the BH to accrete
material and its angular momentum, thus leaving the BH with a non-zero net spin.
1.3.1 Accretion Disk Properties
The classic picture of the accretion disk involves gaseous matter gaining in speed as it
falls toward the event horizon, and also being acted upon by the intense gravitational
field of the BH (Page & Thorne 1974; Shakura & Sunyaev 1973). The infalling material
forms an optically thick, geometrically thin disk around the BH, not unlike water spiraling
down a drain. Matter cannot be transported inwards unless it loses angular momentum,
however. This can be readily shown using the simplifying assumptions of Newtonian
gravity and Keplerian orbits within the disk: the velocity of a particle within the disk
at radius r is vK = (GM/r)1/2, where M is the mass of the accretion disk. The specific
angular momentum of the particle at this radius is then lK = (GMr)1/2, so in order for the
particle to be accreted (i.e., gain speed in its infall toward the BH) it must lose angular
momentum.
The exact mechanism by which mass is transported involves weak magnetic fields
threading the accretion disk (Balbus & Hawley 1991). In this scenario, a differentially ro-
tating disk possessing a weak magnetic field undergoes a local instability, which then gets
twisted within the disk as the magnetic field lines get progressively twisted and torqued
by the disk rotation. The instability propagates throughout the disk, growing according
to its rotational velocity. Motion of the disk material associated with the instability pro-
9
duces both poloidal and toroidal magnetic field components and propagates the instability,
which has the effect of transporting angular momentum outwards in the disk as it trans-
ports mass inwards. By virtue of this magneto-rotational instability (MRI), turbulence
within the disk is created, which then drives the angular momentum transport within the
disk, enabling matter to spiral inwards towards the BH until it reaches the innermost sta-
ble circular orbit (ISCO) in the disk. This radius, also known as the radius of marginal
stability (or rms), defines the last point at which a particle can orbit the BH before it enters
the plunging region and falls precipitously inward past the event horizon. The ISCO is a
direct function of the BH spin:
Z1 ? 1+(1?a2)1/3[(1+a)1/3 +(1?a)1/3] (1.1)
Z2 ? (3a2 +Z21)1/2 (1.2)
rms = 3+Z2?sgn(a)[(3?Z1)(3+Z1 +2Z2)]1/2 (1.3)
The variable a is the dimensionless spin parameter of the BH and is a unitless quantity
defined as a = cJ/GM2, where M is the mass of the BH and J is its angular momentum.
The radius rms is given in units of rg. As the spin of the hole increases, the radial coor-
dinate for the ISCO is pulled in closer to the event horizon, and this coordinate in turn is
also pulled closer in towards the singularity:
reh = 1+(1?a2)1/2 (1.4)
For a non-spinning BH rms = 6rg (event horizon at reh = 2rg), whereas for a BH
spinning in the prograde direction as fast as possible rms = 1rg (event horizon at reh =
1rg). The disk itself generates an ultraviolet blackbody component of radiation for AGN
and an X-ray blackbody for GBHs, based on the relative size difference between these
10
two classes of objects:
Tdisk ? M?1/4BH (L/LEdd)1/4 (1.5)
So assuming the disk of an AGN and GBH each accrete and radiate at the same fraction
of the Eddington luminosity, the disk temperature will be greater for the GBH because
of its smaller mass and associated smaller radiating area. The Eddington luminosity is
achieved by setting the inward force of gravity equal to the outward force of radiation for
a given body:
LEdd = 4piGMmpc/?T ? 1.3?1038(M/Mcircledot) erg s?1 (1.6)
where M is the mass of the body in question, mp is the mass of a hydrogen atom (or
proton), and ?T is the Thomson scattering cross-section. The Eddington luminosity is
believed to set an upper limit to the luminosity of a steadily accreting source such as a
BH.
In certain cases when the BH is not actively accreting material at such a prodigious
rate (i.e., well below the Eddington rate), it is thought that the optically thick accretion
disk may not extend all the way in to the ISCO. Rather, it would truncate at some radius
outside rms and the flow of material from this point to the event horizon would become
optically thin and geometrically thick, in contrast to the rest of the disk (Narayan & Yi
1994). In this advection dominated accretion flow (ADAF) scenario, most of the energy
stored in the accreted material is kept as entropy rather than being radiated. As a result,
ADAF models of accretion disks predict very low luminosities for their central engines
and are thought to be a leading candidate to explain the phenomenon of low-luminosity
AGN (LLAGN), in particular. Due to this net storing of energy and the ?puffing up? of
the accretion disk to accommodate the quasi-spherical flow that develops, net outflows
in the form of a wind from the disk are possible (Blandford & Begelman 1999). As a
11
consequence, only a small fraction of the material may actually fall into the BH, and the
binding energy it releases could blow off the remainder via a torque-induced wind.
1.3.2 The Corona and Relativistic Jet Outflows
In addition to the accretion disk, BH systems often have a plasma layer associated with
them, known as the ?corona.? It is unclear at present what geometrical form this sea of
charged particles might take, though possible options are a sandwich-type layer above and
below the disk, a ?pill-box? or clumpy distribution, or perhaps a more-or-less spherical
appearance (Paczynski 1978). The presence of the plasma itself in this picture likely
originates in magnetized outflows from the surface layer of an ionized disk as discussed
in the preceding paragraph. Alternatively, because BH systems are often associated with
bipolar outflows in the form of collimated jets (Blandford & Payne 1982; Blandford &
Znajek 1977), the plasma we think of as coronal material may indeed be charged particles
in the base of such a jet (Merloni & Fabian 2002; Miller et al. 2006b). Fig. 1.2 provides
an illustration of jets in relation to the disk and BH, and Fig. 1.3 diagrams four different
possible geometries for the corona that are often considered (Reynolds & Nowak 2003).
Whatever the origin of the plasma in question, the observed X-ray continuum (which
is accurately approximated by a power-law from ? 2 keV up to ? 100 keV in AGN and
GBHs) is thought to be produced by inverse Comptonization processes in the corona (or
base of a jet) surrounding the inner part of the accretion disk. As photons emitted from the
disk interact with energetic electrons in the surrounding plasma (moving at high speeds
due to the high temperature of the plasma), the photons receive a boost in energy from
each encounter. A given photon may undergo many such collisions depending on the
geometry and covering fraction of the plasma around the disk. If the electrons move rel-
ativistically, each collision increases the energy of the photon by a factor of ?2, where
? = (1?v2e/c2)?1/2, and ve is the velocity of the electrons or other charged particles in
12
the plasma. If the electrons are thermal in nature (with kT ? 100 keV), and therefore
sub-relativistic, each collision will change the fractional energy of the photon by a factor
of 4kT/mec2, where kT is the energy of an average electron and me is its mass (Ry-
bicki & Lightman 1979). Taking into account a thermal distribution of seed photons and
a relatively uniform distribution of electrons, the inverse Comptonization produces the
characteristic power-law form of the continuum seen in the X-ray spectrum of AGN and
GBHs. A portion of the X-ray photons produced in the corona are scattered outwards and
seen as continuum to the observer, while another fraction of the photons are backscat-
tered down onto the disk, irradiating it and producing the so-called ?X-ray reflection?
signatures in the observed spectrum (Guilbert & Rees 1988; Lightman & White 1988).
These X-ray reflection signatures consist of fluorescent and recombination emission lines
sitting on the continuum and the summed radiative recombination continua of the excited
ions in the photoionized disk surface (George & Fabian 1991; Ross & Fabian 2005). See
Fig. 1.4 for an example of spectra from a disk with varying levels of ionization.
1.3.3 The Disk Reflection Spectrum
The Fe-K? line is the most prominent of these features due to its energy (at 6.4 keV it
is visible above the direct power-law continuum), and the high astrophysical abundance
and fluorescent yield of iron. As high-energy reflected photons are absorbed by iron in
the accretion disk, they can kick electrons out of the K-shell of the atom, provided that
the iron is not so highly ionized that there are no K-shell electrons present. When the
K-shell electron is taken away, an L-shell electron preferentially drops down an energy
level to take its place (also assuming an L-shell electron is present), liberating a photon of
characteristic rest energy 6.4 keV (although if the iron in question is highly ionized this
energy can be as high as 6.97 keV for Fe-K?). This line is often significantly broadened
and skewed by both the standard Doppler effect, special relativistic time dilation and gen-
13
Figure 1.2: A BH is shown surrounded by an accretion disk, with bipolar magnetized jets
visible. The so-called ?corona? surrounding many BH systems may actually be plasma
in the base of such a jet, or the jet itself may grow out of coronal plasma collected in
some geometry around the inner disk. Credit: http://www.nasa.gov.
eral relativistic processes in the disk, the effects of which increase the closer the line is
emitted to the event horizon (Fabian et al. 1989; Laor 1991). These general relativistic
processes include light bending, beaming and gravitational redshifting, all of which result
in a greatly elongated and skewed line profile; in particular, the line profile can display
an extended low-energy tail primarily resulting from gravitational redshift. Because ac-
cretion disks generally radiate more copiously the closer one gets to the event horizon,
the principal line emission region is sufficiently close to the BH that frame-dragging ef-
14
Figure 1.3: Possible geometries for a simple AGN corona are presented. From top to bot-
tom, the corona is seen sandwiching the inner disk, truncating the inner disk, surrounding
the inner disk isotropically, and existing in a patchy form around the disk as a ?pill-box.?
The top configuration is often called a slab geometry, but tends to predict spectra that are
softer than observed. The bottom three schematics represent ?photon-starved? geome-
tries wherein the corona is less effectively cooled by inverse Compton scattering of disk
photons. Credit: Michael Nowak (2003).
fects associated with the BH spin can be important in determining the line profiles. As
stated above, increasing spin results in the inner edge of the disk being pulled in closer
to the event horizon such that its radiation is subject to greater relativistic effects and
more powerful Doppler shifts as it escapes this region. The broad iron line is therefore
a powerful probe of the relativistic effects on the spacetime immediately surrounding the
BH. As such, we are motivated to construct a new model to fit the Fe-K? line profiles
seen in BH systems; one which can extract best-fit values for parameters such as the BH
spin, disk inclination angle and inner radius of emission from the disk. An illustration
15
Figure 1.4: The spectrum resulting from irradiation of an ionized slab (e.g., an accretion
disk) with an incident power-law X-ray spectrum of spectral index ? = 2. The disk has
an iron abundance frozen at the solar value. As one increases the ionization of the disk,
note the decrease in observable emission features. Credit: Ross & Fabian (2005).
of how various effects combine to alter spectral line morphology is seen in Fig. 1.5, and
the effect of this type of smearing on an entire reflection spectrum from the disk is shown
in Fig. 1.6. The building of this iron line model is an important part of this thesis and is
presented in detail in Chapter 3.
1.3.4 The Complication of Absorption
Unfortunately, our view of the inner disk spectrum is often complicated by intervening
absorption lines and edges. These features can come from several sources: partly ion-
ized ?warm? absorption (Halpern 1984) within the BH system (most frequently seen in
AGN, though not totally ruled out in GBHs), a cooler dusty torus thought to surround
many BHs at large radii (? 104?105 rg; also more often seen in AGN), and cold absorp-
tion from neutral hydrogen in our own Galaxy. See Fig. 1.7 for schematic and artistic
representations of the anatomy of an AGN system, including the putative locations of
these absorbers. The lines and edges produced by photons traveling through these types
16
Figure 1.5: Schematic representation of the effects of Doppler shifting, special and gen-
eral relativity on the morphology of a spectral line emitted from an accretion disk around
a BH. Credit: A. Young (2001).
of intervening gases are superposed onto the intrinsic X-ray spectrum from the accretion
disk and corona and can often overlap with important diagnostic emission features such
as the Fe-K? line or soft excess emission from the seed disk photons. Absorption, if not
taken properly into account and modeled accordingly, can greatly complicate our ability
to constrain BH-disk properties such as BH spin (Reynolds 1997; Reynolds & Nowak
2003).
The absorption in question comes most often from neutral hydrogen atoms in the
17
Figure 1.6: The ionized disk spectral model of Ross & Fabian (2005; dotted line) con-
volved with a relativistic smearing kernel assuming a near-maximally-spinning Kerr BH
(solid line). Note the dulled, broadened appearance of the emission features when rela-
tivistic blurring is acting on the system.
Figure 1.7: A canonical AGN is thought to be surrounded by a cold, dusty torus of
neutral molecules and atoms at a distance on the order of ? 104 rg. In the unified model,
depending on the observer?s viewing angle, this torus may obscure the central parts of
the accretion disk and prevent broad lines from being seen in the X-ray spectrum of
the source. Absorption from ionized gas may also take place in the central region from
an ionized outflow or perhaps clouds of material in the broad line region. Image credits:
http://chandra.harvard.edu, Cork Institute of Technology Astronomy and Instrumentation
Group.
18
Milky Way and/or neutral atoms and molecules in the torus surrounding an AGN that fall
along our line of sight. However, very often the AGN will also exhibit absorption features
from warm, partly ionized material thought to reside in clouds or patches surrounding the
accretion disk; it has been proposed that these clouds become ionized by radiation emitted
from the AGN (Halpern 1984). More recent X-ray observations have indicated that per-
haps these warm absorbers are actually a multi-temperature wind created by photoionzed
evaporation of material from the inner edge of the torus (Krolik & Kriss 2001), or by
accretion disk outflows and/or winds (Blustin et al. 2005).
Warm absorbers (WAs) are often characterized by prominent edges of OVII and OVIII,
as well as by lines and edges from many other elements including neon, argon, calcium,
silicon, sulfur and nitrogen. The material in question has been found on many occasions
to possess a multi-layer structure with physically and kinematically distinct zones of dif-
fering temperature, column density and ionization level (Otani et al. 1996). This type of
structure is evident in many Sy-1 AGN (George et al. 1998b; Reynolds 1997; Reynolds &
Fabian 1995), e.g., MCG?6-30-15 (Brenneman & Reynolds 2006; Lee et al. 2001; Turner
et al. 2004) and NGC 3783 (Kaspi et al. 2001), and likely correlates with the distance
of the absorbing material from the central engine, which is the source of the ionizing
radiation. An example of a WA spectrum can be seen in Fig. 1.8.
Because these absorption features can exist simultaneously with emission features
in the AGN system, and because we see the spectrum filtered through several layers of
source and local absorption, it is imperative to model these features correctly in order
to separate out the true reflection spectrum of the accretion disk and isolate the Fe-K?
line for study. Absorption lines and edges from the WA can alter the shape of the overall
spectrum to such a degree that they can mimic the redshifted wing of a very broad Fe-
K? line in some cases, rendering proper modeling of this line nearly impossible unless
absorption has been adequately taken into account. In the case of the canonical broad iron
19
Figure 1.8: A template spectral model of a typical WA showing various lines and edges.
Galactic photoabsorption and absorption from neutral iron in the Fe-L3 edge are also
included, as is a power-law continuum from 0.5?10 keV. In this case, the Galactic
NH = 1020 cm?2 , NWA = 1022 cm?2 , ?WA = 100 erg cm?1 s?1 , NFe = 1016 cm?2 , ? = 2,
and the power-law flux is 10?2 ph cm?2 s?1 . Solar abundances are used for all elements
in the WA. WA model created by Brenneman & Reynolds (2006).
line Sy-1 galaxy MCG?6-30-15, for example, an iron feature is seen that extends down
to ? 3 keV on the red wing, making it the broadest iron line observed to date. Because
of the extreme breadth of this line, however, some within the astrophysical community
doubted that it could be a disk reflection feature, insisting that it could just as easily
be a faux emission line created by the juxtaposition of two adjacent absorption edges
of iron (Fe-K and Fe-L). This absorption hypothesis was finally laid to rest after a ?
522 ks Chandra/HETGS observation of the source (Young et al. 2005). In order for Fe-L
absorption edges to have the optical depth necessary to mimic a broad red wing of Fe-K?,
the overall amount of iron in the source would dictate the presence of a deep absorption
20
Figure 1.9: The continuum-subtracted spectrum from the Chandra/HETGS observation
of Sy-1 galaxy MCG?6-30-15 (Young et al. 2005) in black, XMM-Newton/EPIC-pn data
of the same object (Fabian et al. 2002) in red. Note the extent of the broad Fe-K? line.
line of iron at a rest energy between 6.4?6.6 keV. This line was not seen in the Chandra
data at a confidence level substantially above 99%, implying that the broad iron line seen
is in fact an emission feature from the accretion disk. This case is an excellent example of
the importance of modeling the WA properly in order to rule out the effects of absorption
on observed emission line profiles. The broad iron line and absorption model used in
fitting the X-ray spectrum of MCG?6-30-15 are shown in Figs. 1.9-1.10.
1.4 The History of Modeling Broad Iron Lines
Clearly, iron line fitting is a complicated process requiring due diligence in modeling
the rest of the X-ray spectrum in order to obtain reliable results and accurately measure
the accretion disk properties that affect line morphology. Better spectrographs and more
precise relativistic line modeling techniques are now allowing us to begin to place statis-
tical constraints on disk parameters such as BH spin for the first time, but the history of
broad iron line studies upon which our modern science was built dates back nearly two
21
Figure 1.10: The Chandra/HETGS data (Young et al. 2005) fit with a broad-iron-
line-mimicking ionized WA model. Note that lack of an absorption line between
6.4?6.6 keV, as would be expected if the apparent breadth of the Fe-K? emission line
is an artifact of nearby iron absorption edges.
decades. The first broad iron line robustly detected and resolved in an AGN was found
by ASCA in MCG?6-30-15 (Iwasawa et al. 1996; Tanaka et al. 1995), and since then has
been extensively studied with BeppoSAX (Guainazzi et al. 1999), RXTE (Lee et al. 1999,
2000), Chandra (Lee et al. 2002; Young et al. 2005) and XMM-Newton (Fabian et al.
2002; Wilms et al. 2001). All of these results show that the broad iron line feature is
consistent with a highly redshifted line from the inner parts of an accretion disk, and as
mentioned previously, no alternative hypothesis has yet explained the spectrum of MCG?
6-30-15 satisfactorily (Fabian et al. 1995; Reynolds & Wilms 2000; Vaughan & Fabian
2004; Young et al. 2005). Subsequent ASCA, Chandra and XMM-Newton studies have
discovered broad iron line profiles in several other Seyferts, such as MCG?5-23-16 (De-
wangan et al. 2003), NGC 3516 (Turner et al. 2002), Mrk 335 (Gondoin et al. 2002), and
Mrk 766 (Pounds et al. 2003b). The advent of Suzaku, in particular, promises to expand
this source list even further.
In addition to having a sample of objects that have been observed with robust broad
22
iron lines, it is equally important to have a precise model to use in fitting the data if one
wants to measure BH spin. The two line profiles currently included as standard in the
X-ray spectral fitting package XSPEC (Arnaud 1996) are useful as a starting point, but
ultimately quite limited in terms of their ability to accurately parameterize the line. The
diskline model (Fabian et al. 1989) describes the line profile from a disk around a non-
rotating Schwarzschild BH, and, due to the approximations employed, does not include
relativistic light bending. Similarly, the laor model (Laor 1991) has important limitations
as well: this is a fully-relativistic model, but the dimensionless spin parameter (a) of the
BH is hard-wired at a = 0.998, the equilibrium spin of a BH accreting from a standard
accretion disk (Thorne 1974). Furthermore, due to the computational realities of the early
1990s, the relativistic transfer functions underlying the laor model are pre-calculated and
tabulated rather sparsely, yielding noise (or even gross inaccuracies) in the line profiles
produced, especially at very high disk inclination angles. Given these limitations, as well
as the high quality of AGN spectra currently being obtained with Chandra, XMM-Newton
and Suzaku), it is imperative that X-ray astronomers have access to effective models that
are fully relativistic, accurate, and that allow BH spin to be fit as a free parameter.
Three new relativistic line models have recently been developed for this purpose and
implemented in a form that can be readily used by X-ray astronomers: the ky suite
(Dov?ciak et al. 2004) and two similar codes (Beckwith & Done 2004; ?Cade?z & Calvani
2005). These models achieve comparable results for the morphologies of the line pro-
files, and all offer significant improvements over the diskline and laor results in terms
of accuracy and precision over a wider range of physical parameters. Most importantly,
these models leave the spin of the BH as a free parameter and compute fully relativistic
photon transfer functions. These models, as well as my own, will be discussed more fully
in Chapter 3.
23
1.5 Purpose and Structure of this Work
Given the X-ray observatories currently in orbit and the vast improvement in computing
resources over the past decade, the time is ripe for exploring the details of BH-disk spec-
tra in greater detail than has previously been able to be attempted. In this dissertation,
under the guidance of my advisor, Chris Reynolds, I consider the question of BH spin in
AGN. As stated above, we have created a new relativistic emission line model taking into
account all major factors influencing the shapes of lines fluoresced by reflected X-rays
incident on the accretion disk. We have fit this model to several AGN from the XMM-
Newton archive that have been seen to harbor broad iron lines (Miller 2007; Nandra et al.
2006). We have extracted best-fit parameters for the properties of the accretion disk in all
these sources, including the spin parameter of the BHs in question. In so doing, we have
begun the first true survey of BH spin in AGN.
Herein, we assess the constraints on the iron line profiles and BH spins of each source
in question, taking into account the complications introduced by other spectral compo-
nents displayed by these systems, especially the substantial columns of absorbing pho-
toionized gas seen along the line of sight to the central disks in many of the sources in
my sample. We begin in Chapter 2 by describing the ?control? case of the Sy-1 galaxy
NGC 4593, which does not possess a broad iron line, in order to detail the algorithms
used to fit the continuum and absorption parameters in an AGN and to explore the in-
teresting spectral and temporal variability often found in Sy-1 AGN. In Chapter 3 we
present the new variable-spin accretion disk emission line profile model, kerrdisk, that
we have developed for public use in the XSPEC package. Chapter 4 describes the fit of the
new model to the much-studied broad iron line in MCG?6-30-15, which has the largest
number of counts of any of the observations presented here, enabling the most accurate
physical constraints to be placed on the spin parameter in this source. Chapter 5 expands
24
the source list to several other broad iron line AGN and presents the results of spectral
fitting and the BH spin constraints for each. Conclusions are presented in Chapter 6.
25
Chapter 2
Modeling the X-ray Continuum in
AGN: NGC 4593
As stated in Chapter 1, we present an X-ray spectral analysis of the central regions of the
canonical Seyfert-1 galaxy NGC 4593 as a ?control? case to illustrate the complexities
involved in modeling such systems. Sy-1 galaxies are of particular interest for the study
of accretion onto supermassive BHs since they are typically oriented such that we can
view the accreting BH free of substantial obscuration or absorption from surrounding cir-
cumnuclear material. Furthermore, we believe that significant amounts of the continuum
radiation seen in radio-quiet Sy-1 galaxies originate in the disk rather than, for example,
a relativistically beamed jet (as is the case for BL-Lac objects). As such, we are better
positioned to study the inner parts of the accretion disk in Sy-1 galaxies than in other sys-
tems. The following is an expansion of our published work on NGC 4593 in Brenneman
et al. (2007; in press).
NGC 4593 is a spiral galaxy with a central bar classified as Hubble type SBb. At a
redshift of z = 0.009, it lies at a proper distance of ? 38 Mpc toward the constellation
Virgo. This is consistent with the same angular size distance and a luminosity distance of
26
using H0 = 71 km s?1 Mpc?1, ?m = 0.27, and ?? = 0.73.1 The galaxy has an apparent
visual magnitude of 11.67 and an approximate angular diameter of 3.9?2.9 arcmin. As
already noted, it hosts an AGN of a Sy-1 type (Lewis et al. 1978). Previous studies of the
source with EXOSAT demonstrated a soft excess (Pounds & Turner 1988), and BeppoSAX
data confirm a broad absorption dip of 15% below 1 keV which may be attributable to the
presence of a warm absorber along the line of sight (Kaastra & Steenbrugge 2001). ASCA
spectra display a slightly broadened cold iron line at 6.4 keV, in addition to evidence for
a warm absorber within the system (Nandra et al. 1997; Reynolds 1997). The source also
displays significant variability in flux. Between two ASCA observations 3.5 years apart,
the 2?10 keV flux of this source increased by ? 25%, though no significant variability
of the iron line was detected between the two pointings (Weaver et al. 2001). Within the
ASCA observation, a count rate decrease of ? 60% in 10 ks was witnessed, with smaller
flares and dips throughout the data set (Reynolds 1997). In terms of the overall properties
of the system, this author calculated a luminosity of LX = 8.53?1042 erg s?1 (2?10 keV)
with ASCA, and more recently, McKernan et al. (McKernan et al. 2003) used Chandra to
derive a luminosity LX = 5.37?1042 erg s?1 (2?10 keV). It should be noted that this
change in LX is larger than the flux calibration uncertainty of the observation, so this does
appear to be a robust finding.
We examine results from a 76 ks exposure of NGC 4593 with the XMM-Newton/EPIC-
pn instrument from 2002 June 23/24. The spectral and temporal variability of NGC 4593
are discussed, as well as the soft X-ray features and their comparison with the ?typical?
parameters defining a warm absorber. We also weigh the consistency of our findings with
other observations of this source and compare it with similar Sy-1 galaxies, especially
with respect to the possible existence of a broad iron line originating in the accretion disk.
1These values have been obtained from Ned Wright?s Cosmology Calculator web page:
http://www.astro.ucla.edu/ wright/CosmoCalc.html.
27
2.1 Data Reduction
We use data taken with the European Photon Imaging Camera pn (EPIC-pn) camera on
board XMM-Newton. The data were obtained during revolution 465 of XMM-Newton,
during which the pn was operated in its small-window mode to prevent photon pile-up,
using the medium filter to avoid optical light contamination. The EPIC MOS-1 camera
took data in the fast uncompressed timing mode, and the MOS-2 camera operated in
prime partial W2 imaging mode. Although the MOS results will not be discussed further
here, they mirrored the EPIC-pn data within the expected errors of calibration effects.
The average EPIC-pn count rate for this source was 29.78 cts s?1. Due to calibration
difficulties between the pn and RGS instruments, the RGS data are also not discussed
further in this work. These data were analyzed, but the discrepancies between the pn
and RGS results, the relatively small number of counts for NGC 4593 and the calibration
issues at play between the pn and RGS forced us to exclude RGS spectra in our model fits
to the data. Kirsch et al. provide a detailed discussion of these calibration uncertainties
(Kirsch et al. 2005). 2
The pipeline data for the pn instrument were reprocessed using the Science Analysis
Software and the corresponding calibration files, version 6.5.0. From these, we rebuilt the
calibration index file using cifbuild. For the EPIC-pn data the event files were mildly
edited in spectral coverage to observe the region from 0.2?15 keV, and bad pixels and
cosmic ray spikes were removed via narrow time filtering using the evselect task within
the SAS. No background flares were detected during the observation. Extraction of spec-
tra followed the procedure used by Wilms et al. , in which source and background spectra
were generated using the xmmselect task (Wilms et al. 2001). Response matrices and
2See also http://xmm.vilspa.esa.es/external/xmm sw cal/calib/index.shtml for a thorough discussion of
these cross-calibration issues.
28
ancillary response files were created using rmfgen and arfgen, and the data were then
grouped using the grppha task with a binning factor of 25 cts bin?1. Binning is required
in order to get sufficient counts per bin to make ?2 spectral fitting a valid statistical pro-
cess. An indicator of the global goodness-of-fit of the model to the data, the ?2 statistic
for a given set of measurements is defined as the difference between the data and model
divided by the square of the uncertainty in the data, summed over all the measurments, or
?2 =
k?
i=1
(Xi??i)2
?2i . (2.1)
Spectral modeling and analysis from 0.5?10 keV was performed using the XSPEC pack-
age version 11.3.2 (Arnaud 1996). Timing studies were performed using various routines
in the XRONOS package (Stella & Angelini 1992).
We have used the SAS epatplot task to compute the fraction of single, double, triple
and quadruple events as a function of energy and compared these fractions to their nom-
inal values as measured from weak source observations. For sources that are affected by
pile-up, these fractions deviate from the nominal values due to the higher probability of
wrong pattern classification. No significant deviation from the nominal single and dou-
ble distributions was found, indicating that our EPIC-pn observation of NGC 4593 is not
affected by pile-up.
2.2 Spectral Analysis
2.2.1 Continuum and Absorption
We began our analysis by fitting the 2?10 keV EPIC-pn data with a simple photoabsorbed
(phabs; (Balucinska-Church & McCammon 1992)) power-law model with abundances
(Anders & Grevesse 1989), as shown in Fig. 2.1. Here we assume a Galactic hydrogen
29
column density of NH = 1.97?1020 cm?2 (Elvis et al. 1989). This initially yields a best-
fit power-law photon index of ? = 1.74?0.01 and a flux of 7.06?10?11 erg cm?2 s?1
from 2?10 keV. The spectrum above 2 keV is well described by this model (?2/dof =
1879/1450 (1.30)), with the exception of two residual emission features with rest frame
energies of 6.4 keV (identified as the fluorescent K? emission line of cold iron) and
6.97 keV (likely to be the Ly? recombination line of hydrogen-like iron). The cold iron
line likely arises from fluorescence on the surface layers of the outer accretion disk, op-
tically thick optical broad emission line clouds, or the putative ?molecular torus? in re-
sponse to hard X-ray irradiation from a hot corona in the inner accretion disk (Basko
1978; George & Fabian 1991; Guilbert & Rees 1988; Lightman & White 1988; Matt
et al. 1991). The ionized line, by contrast, could be formed either by ionized disk ir-
radiation or by radiative recombination in highly ionized outflowing material above the
plane of the disk. Because these two iron lines are relatively narrow, fitting them with
relativistic disk emission models such as diskline, laor or kerrdisk (Brenneman
& Reynolds 2006) has no statistical advantage over fitting them with Gaussians, and
the parameters governing the disk emission are not well constrained. Therefore, us-
ing Gaussians to describe the iron lines, the 6.4 keV line in this model has a flux of
5.71?0.53?10?13 erg cm?2 s?1 and an equivalent width of 131?12 eV, while the
6.97 keV line has a flux of 1.80?0.45?10?13 erg cm?2 s?1 and an equivalent width
of 45?13 eV. Inclusion of these components significantly improves the goodness-of-fit
to ?2/dof = 1424/1446 (0.98). The flux and luminosity for the 2?10 keV spectrum
are 4.11?10?11 erg cm?2 s?1 and 7.38?1042 erg s?1 , respectively. These values for the
continuum and iron line parameters are in keeping with those determined previously for
this data set by Reynolds et al. , within error bars, and these conclusions are therefore
robust to the calibration changes in the EPIC-pn that have occurred since publication of
our previous work (Reynolds et al. 2004a). The results from this study and the discussion
30
Figure 2.1: The 2?10 keV spectrum of NGC 4593 fit with a simple photoabsorbed
power-law (phabs po). Note the residual iron features at 6.4 keV and 6.97 keV. For this
fit, ?2/dof = 1879/1450(1.30).
of fitting a broad iron line to this source can be found in the following Section.
Below ? 2 keV there is significant spectral complexity beyond a simple power-law
form (Fig. 2.2) which is most likely due to a combination of a soft excess and the presence
of absorbing material along our line of sight within the X-ray continuum source. As a first,
purely phenomenological attempt to describe the soft excess component, we have em-
ployed a thermal bremsstrahlung emission model (zbremss). The best-fit value for the en-
ergy of this component is kT ?0.21+0.00?0.00 keV, with a flux of 2.01+0.33?0.11?10?14 erg cm?2 s?1 .
Addition of this component again improves the goodness-of-fit to ?2/dof = 2398/1738
(1.38) from 0.5?10.0 keV, down from 11423/1736 (6.58) before the bremsstrahlung
emission was included (and after the energies from 0.5?2.0 keV had been noticed in the
spectrum).
31
Figure 2.2: The 0.5?10.0 keV spectrum of NGC 4593 fit with a photoabsorbed power-
law and two Gaussians to model the iron lines. Note the clear evidence for a soft excess,
possibly complicated by absorption features from a ?warm absorber? within NGC 4593.
For this fit, ?2/dof = 11423/1736(6.58).
Evidence for a warm absorber in this source was initially found through approximat-
ing it simply with the O VII and O VIII K-shell photoelectric edges first observed with
ASCA (Reynolds 1997). This author quotes an O VII edge depth of ? = 0.26?0.04, and
an O VIII edge with ? = 0.09+0.04?0.03. Interestingly, we do not find similar edge depths in
the XMM-Newton data set here: employing this simple model gives for O VII at 0.74 keV,
? = 0.15+0.01?0.02. For O VIII at 0.87 keV, ? = 0.00+0.01?0.00 (error bars are at the 90% confidence
level). As with other components in our global fit, we elected to freeze the redshifts at the
cosmological value for the source: z = 0.009. Allowing the redshifts to fit as free param-
eters does not significantly improve the goodness-of-fit, and results in best-fit redshifts
with large error bars that allow outflow velocities on the order of many thousand km s?1 .
Adding the O VII edge to the model improves the goodness-of-fit to ?2/dof = 2018/1740
32
(1.16).
It is thought that a more physical representation of a typical warm absorber would
incorporate not just oxygen edges, but a host of edges and absorption lines from several
other elements as well (nitrogen, neon and silicon, to name a few). With this in mind,
ionized plasma codes such as XSTAR (version 2.1kn3; originally developed in Kallman &
Krolik (1995)3) can in principle model these warm absorbers much more accurately than
the O VII and O VIII edges alone. Using XSTAR, we have constructed a warm absorber
table as a function of the absorbed column density (NH) and ionization parameter (?)
local to a given area surrounding the source. The ionization parameter is given by the
usual definition,
? = Lin
er2
, (2.2)
where Li is the luminosity above the hydrogen Lyman limit, ne is the electron num-
ber density of the plasma and r is the distance from the (point) source. We have con-
structed 20?20 grids of models uniformly sampling the (log NH,log?) plane in the range
NH = 1020 ? 1024 cm?2 and ? = 1 ? 104 erg cm?1 s?1 . While these were made to be
multiplicative models and hence can be applied to any emission spectrum, the ioniza-
tion balance was solved assuming a power-law ionizing spectrum with a photon index of
? = 2, cut off at an energy Ec = 20 keV. This is a good approximation of the typical AGN
continuum.
Replacing the oxygen edges with our warm absorber model described above, we find
that the WA has a column density of NH = 3.54?1022 cm?2 and an ionization param-
eter of log? = 2.09 erg cm?1 s?1 . However, replacing both oxygen edges with one WA
table actually worsens the fit to ?2/dof = 2123/1740 (1.22), and significant residuals
remain. To address this issue, we added in a second WA component and re-fit. In-
cluding the second WA we find that ?2/dof = 1864/1742 (1.07), a substantial improve-
3XSTAR Manual, available at http://legacy.gsfc.nasa.gov.
33
ment over the one-WA model and the two-edge model. Furthermore, adding the sec-
ond WA produced a notable two-zone structure within the absorbing system, in terms
of the column densities and ionization states of the two components: NH1 = 1.64+0.07?0.09?
1023 cm?2 and log?1 = 0.57+0.13?0.17 erg cm?1 s?1 vs. NH2 = 2.97+0.31?0.73 ?1021 cm?2 and
log?2 = 2.54+0.03?0.04 erg cm?1 s?1 . A natural interpretation is that the WA has distinct com-
ponents at physically different distances from the central engine. We note that attempting
to add a third zone, or table, into the model results in no statistical improvement in fit.
Abundances for the WAs were kept frozen at the solar values for each element in question
throughout. Freeing these components added in too many additional degrees of freedom
and prevented us from obtaining a statistically meaningful fit.
Even utilizing two WAs to try and model the soft spectrum more accurately, we note
that residuals still remain between the data and model, especially around ?0.7?0.8 keV.
If there is significant dust in the WA, it is likely that iron absorption plays a role, given its
elemental abundance in most AGN systems. To gauge the importance of iron absorption
here, we added in another multiplicative table model to the fit, representing the Fe-L3
edge at 0.707 keV (kindly provided to us by Julia Lee). Indeed, including this component
greatly improved the fit: ?2/dof = 1830/1743 (1.05). The iron column density necessary
for this fit is logNFe = 16.81+0.02?0.05 cm?2 . Hereafter, we shall refer to this spectral model
simply as Model 1.
Model 1 describes the data quite well with a goodness-of-fit parameter of ?2/dof =
1813/1745 (1.04). However, we note that it is purely phenomenological in nature, espe-
cially with respect to the arbitrary thermal bremsstrahlung model that has been included to
model the soft excess. Ideally, we would like to describe the soft excess with a model that
has a direct physical interpretation. Initially, we attempt to describe the soft excess as soft
X-ray reflection from a mildly-ionized accretion disk (for a successful application of this
model to the Seyfert galaxy MCG?6-30-15 see Chapter 4 of this work, also published in
34
Figure 2.3: (a) The best fit for Model 1, including a zbremss component to represent
the soft emission: ?2/dof = 1813/1745 (1.04). (b) The relative strength of the model
components for Model 1. The 6.4 and 6.97 keV Gaussians are shown in red and green,
respectively. The zbremss soft emission is in dark blue, and the photoabsorbed power-
law is in light blue. Other absorption components are indicated in black.
Brenneman & Reynolds (2006)). Operationally, we replace the thermal bremsstrahlung
component in Model 1 with the ionized disk model reflion (Ross & Fabian 2005).
Because the irradiated matter is also responsible for producing the Fe-K? line in many
sources, this model has the potential for self-consistently describing the soft excess as
well as the 6.4 keV emission line feature. Interestingly, we find that we cannot success-
fully describe both the soft emission and the Fe-K? line with the disk reflection model.
The resulting best fit is ?2/dof = 2652/1745 (1.52), and we found that either significant
residuals remained on the soft or hard end, or that the 6.4 keV iron line was simply not
fit adequately. Even adding the Gaussian component back to explicitly model the 6.4 keV
iron line, the disk reflection model was unable to adequately fit the form of the soft excess.
We thus conclude that ionized disk reflection is not an important process in shaping the
soft X-ray spectrum of NGC 4593. Given the relative narrowness of the Fe-K? line in this
source (discussed further in the following Section, (Reynolds et al. 2004a)), we believe it
is not originating in the inner disk, and hence the above is not a surprising conclusion.
Another possibility is that the soft excess is due to thermal Comptonization by plasma
35
Figure 2.4: (a) The best fit for Model 2, including a comptt component to represent
the soft emission in place of the zbremss component of Model 1. ?2/dof = 1808/1744
(1.04). (b) The relative strength of the model components for Model 2. The color scheme
is the same as in Fig. 2.3.
at a temperature between that of the disk and the hard X-ray corona (possibly in a transi-
tion zone). To reflect this, we use the comptt model (Titarchuk 1994) to parameterize the
soft excess. Hereafter, we shall refer to this spectral model as Model 2. This preserves
the physical realism of the soft emission arising from the accretion disk, but allows the
iron line to be produced elsewhere, perhaps farther away in the molecular torus where it
would not be as intrinsically broad. Model 2 reaches a best fit of ?2/dof = 1759/1744
(1.01), a slight improvement over the statistical best fit of Model 1. The best fit and model
for Model 2 are shown in Fig. 2.4. Here we have frozen the seed photon temperature at
T0 = 50 eV and have kept a slab geometry for the corona. The best-fit Comptonizing
plasma temperature is kTc = 42 keV with an optical depth of ? = 0.12, though both pa-
rameters were not very well constrained by the fit. This is not surprising, given that both
are equally involved in shaping the spectrum via the Compton-y parameter: y ? ?Tc. We
note that for Model 2 the equivalent widths of the 6.4 and 6.97 keV Gaussians remain
approximately unchanged from their values in the Model 1 fit.
Table 2.1 reports the parameter values and goodness-of-fit for both the final best-
fitting phenomenological model (Model 1, with zbremss and including all other com-
36
Model Component Parameter Model 1 Value Model 2 Value
phabs NH ( cm?2 ) 1.97?1020 1.97?1020
WA 1 NH1 ( cm?2 ) 1.64+0.07?0.09?1023 9.29+1.46?9.15?1022
log ?1 ( erg cm s?1 ) 2.54+0.03?0.04 2.75+0.12?0.32
WA 2 NH2 ( cm?2 ) 2.47+0.31?0.73?1021 1.13+1.21?0.94?1022
log ?2 ( erg cm?1 s?1 ) 0.57+0.13?0.17 1.70+0.30?0.59
Fe-L3 edge log NFe( cm?2 ) 16.81+0.02?0.05 16.92+0.04?0.08
po ? 1.87?0.00 1.75+0.02?0.03
flux ( erg cm?2 s?1 ) 5.11+0.04?0.02?10?13 4.44+0.41?0.54?10?13
zgauss E( keV) 6.4 6.4
?( keV) 0.10?0.08 0.10?0.01
flux ( erg cm?2 s?1 ) 4.46?0.32?10?15 4.15+0.33?0.34?10?15
E( keV) 6.97 6.97
?( keV) 0.10?0.02 0.10?0.06
flux ( erg cm?2 s?1 ) 9.47+2.00?2.07?10?16 7.77+2.07?2.37?10?16
zbremss kT( keV) 0.21+0.00?0.01
flux ( erg cm?2 s?1 ) 2.01+0.33?0.11?10?14
comptt T0( keV) 0.05
kT( keV) 42.19+140.67?40.19
? 0.12+0.06?0.11
flux ( erg cm?2 s?1 ) 6.46+0.90?0.92?10?14
?2/dof 1813/1745(1.04) 1759/1744(1.01)
Table 2.1: The energy range from 0.5?10.0 keV is considered for the EPIC-pn. Best fit
Model 1 contains a zbremss component to parameterize the soft excess below ? 2 keV,
while best fit Model 2 represents this component with a comptt model. All quoted error
bars are at the 90% confidence level. All redshifts used were frozen at the cosmological
value for NGC 4593: z = 0.009.
ponents added in), and the more physical model (Model 2, including comptt and all
other components). Using the Model 2 fit from Table 2.1, the total 0.5?10 keV flux
is FX = 6.74?10?11 erg cm?2 s?1 . Assuming a flat universe WMAP cosmology, this
corresponds to a luminosity of LX = 1.21?1043 erg s?1 . Considering only the energy
range from 2?10 keV, L2?10 = 7.40?1042 erg s?1 . This is roughly 21% greater than
the 2?10 keV luminosity observed by McKernan et al. (2003), but only about 86% of the
value from the ASCA observation reported by Reynolds (1997).
37
2.2.2 On the Lack of Accretion Disk Signatures in NGC 4593
As noted in the previous Section, the 2?10 keV spectrum of NGC 4593 is well-fit by
a photoabsorbed power-law form to within 3?5%. The only two significant devia-
tions from this model occur from 6?7 keV, and modeling these features with Gaus-
sian emission lines provides a much better fit and significantly reduces the value of
?2. Though we have frozen the rest-frame energies of these two components in our
global fit, we performed a more rigorous statistical analysis on the hard spectrum of
NGC 4593 (Reynolds et al. 2004a). Revisiting and expanding upon that work (forth-
coming in Brenneman et al. 2007), we find that the first line corresponds to cold Fe-K? at
E1 = 6.39?0.01 keV with a flux of F1 = 5.71?0.53?10?13 erg cm?2 s?1 and an equiv-
alent width of EW1 = 131?12 eV. The second line, corresponding to hydrogen-like
Fe-K?, has E2 = 6.95?0.05 keV and a flux of F2 = 1.80?0.45?10?13 erg cm?2 s?1
with an equivalent width of EW2 = 45?13 eV. We do not detect a helium-like Fe line at
6.67 keV: the upper limit on the equivalent width of such a feature would have to be less
than 13 eV.
These relatively narrow emission lines most likely originate from material that is com-
paratively distant from the central BH. The cold iron line is centered on the systemic ve-
locity of NGC 4593 and is well resolved (FWHM = 10900?2200 km s?1 ). For compar-
ison, the broad optical H? line in this source has a FWHM = 4910?300 km s?1 (Grupe
et al. 2004), roughly half of the velocity width of cold Fe-K? here. Thus, it seems clear
that the cold iron line is originating from a region that lies significantly inside the optical
broad emission line region (OBLR), and hence cannot be identified with X-ray reflection
from the putative ?molecular gas torus? theorized by Seyfert unification schemes. We
note that the XMM-Newton data sets no useful constraints on the presence of a Comp-
ton back-scattered continuum expected from X-ray reflection by cold matter. Thus the
38
possibility remains that this line might be formed by the fluorescence of optically thin
accretion disk material (as opposed to the optically thick material normally envisaged in
the scenario of X-ray reflection).
The hydrogen-like Fe-K? line, on the other hand, is only marginally resolved (FWHM =
12200+11200?9400 km s?1 ). It is therefore not possible to conclude where this ionized emis-
sion originates relative to the OBLR. It is, however, possible to say something about the
physical process underlying this emission. If we suppose that this line is emitted by a
collisionally ionized thermal plasma (described by the mekal model in XSPEC; (Liedahl
et al. 1995; Mewe et al. 1985, 1986)), the EPIC-pn data dictate that the plasma must pos-
sess a temperature of at least kT ? 50 keV in order to reproduce the constraint on the
hydrogen-like/helium-like equivalent width while simultaneously not curving the overall
continuum excessively. The required emission measure would then be EM ?integraltext n2e dV =
1.6?1067 cm?3 , where ne is the electron number density and V is the volume of the
thermal plasma. If we also suppose that this plasma surrounds the central engine in a
spherical geometry which is optically thin to Compton scattering (or else we would not
observe rapid X-ray variability from the AGN), we can use the column density and emis-
sion measure constraints to conclude that the thermal plasma must have an extent of at
least 4?1016 cm. It is hard to rationalize the existence of such hot plasma many thousands
of gravitational radii from the central BH. We therefore largely rule out this origin for the
ionized Fe-K? line. It is more likely that this feature originates via radiative recombina-
tion and resonant scattering in strongly photoionized gas within the central engine of the
AGN. While a detailed exploration of this postulate is beyond the scope of this paper, it
is tempting to identify this feature with the same plasma that produces the highly ionized
absorption features seen in several other AGN (Pounds et al. 2003a; Reeves et al. 2003).
We do not find evidence for additional broad emission features once these narrow
ones have been modeled. In addressing this issue, we added a relativistic iron line to
39
the spectral fit using two different models: the Schwarzschild model (Fabian et al. 1989),
known as diskline in the XSPEC package, and the near-extreme Kerr model (Laor 1991),
known as laor. The energy of the emission line (Ebroad) was allowed to vary across the
range of possible Fe-K? transition energies (from 6.40?6.97 keV in the rest-frame). The
inner radius of the emitting region (rin), the emissivity index of the disk (?), the viewing
inclination (i) and the line normalization were also free parameters in the fit. The outer
radius of the line-emitting region was fixed at rout = 1000rg. The improvement in the
goodness-of-fit was ??2/?dof =?11/?5 and ??2/?dof =?10/?5 for the diskline
and laor models, respectively. Such a change is not significant at the 90% confidence
level, indication that we have not robustly detected any broad Fe-K? lines in the fit.
In order to obtain a meaningful upper limit to the equivalent width of any broad iron
line, we must specify its shape (since the data cannot statistically make such a distinction
themselves). Empirically, we can proceed assuming that any such line has the ?typical?
profile found in co-added ASCA data (Nandra et al. 1997), i.e., the diskline model with
Ebroad = 6.4 keV, rin = 6rg, ? = 2.5 and i = 29?. Using these assumptions, we can set
an upper limit (with a 90% confidence level for one interesting parameter) to the broad
line equivalent width of EWbroad = 87 eV. Taking a theoretical approach, we assume the
simplest model (Novikov & Thorne 1974; Page & Thorne 1974; Shakura & Sunyaev
1973) is one in which the accretion disk is geometrically thin and radiatively efficient,
extends from the radius of marginal stability to large radii, and possesses an iron line
emissivity that tracks the underlying dissipation (Reynolds & Nowak 2003). Applying
such a line profile to the NGC 4593 data in the case of a near-extreme Kerr BH (with
dimensionless spin parameter a = 0.998) results in an upper limit to the equivalent width
of EWbroad = 99 eV. These are significantly less than the values expected from theoretical
reflection models (?200 eV for solar abundances (Matt et al. 1997) or than those observed
in the Seyfert galaxy MCG?6-30-15 (?400 eV; (Fabian et al. 2002)). Thus, there appears
40
to be a significant absence of spectral features from a relativistic accretion disk.
Given that the BH accretion paradigm of AGN is very well established and supported
by a significant body of evidence, the results of our spectral analysis of NGC 4593 de-
mand that we consider why we are not seeing the X-ray reflection signatures of a rel-
ativistic accretion disk, given that we believe it exists and is responsible for the AGN
emission features that we observe. A straightforward solution to this problem would be
to postulate subsolar abundances of iron in the BH accretion disk (Reynolds et al. 2004a).
However, it would be surprising if the solution to the lack of a broad iron line was simply
an underabundance of iron, given the highly evolved nature of stellar populations in the
nuclei of galaxies such as NGC 4593. With this motivation, we explore modifications of
the canonical line models discussed above and show that it is, in fact, rather easy to bury
relativistic spectral features in the noise even if they are present at the level associated
with cosmic abundance material.
One possibility is that the disk reflection signatures are present in the spectrum, but are
so broad that they are lost in the continuum. Such broad features can be produced when
the emission is very centrally concentrated (i.e., coming from deep within the potential
well of the BH and therefore subject to intense gravitational redshift). Alternatively, if
the disk is viewed at high inclination, the spectral lines will be especially broadened.
An example of the former can be found in the Sy-1 AGN MCG?6-30-15 (Brenneman &
Reynolds 2006; Reynolds et al. 2004b; Wilms et al. 2001). Using the models of Agol &
Krolik (Agol & Krolik 2000), Reynolds et al. suggest that the highly centrally concen-
trated emission profile of the disk seen when this source is in its ?Deep Minimum? state
(also found in (Brenneman & Reynolds 2006): for the inner disk, ?1 > 6) may be due to
a magnetic torque exerted on the inner disk by field lines threading the disk and BH. Such
a torque would explain the observed enhanced energy loss from this region of the disk.
Because the disk inclination of MCG?6-30-15 has been constrained at i ? 30? (Brenne-
41
man & Reynolds 2006; Fabian et al. 2002), however, the extremely broad iron line is
still discernible above the continuum. With lower signal-to-noise and a higher inclina-
tion angle this would not be the case. Perhaps this is the scenario at work in NGC 4593.
To test this possibility, we added to the spectral fit a cold iron line with a profile corre-
sponding to an infinite-efficiency (torqued) accretion disk around a near-extreme Kerr BH
(a = 0.998). The inclination and normalization of the line were left as free parameters.
This led to only a slight improvement in the goodness-of-fit over the simple power-law
plus narrow-line model (??2/?dof =?3/?2). The upper limit on the equivalent width
is EWbroad < 250 eV. Thus, a broad line with the strength expected from a cosmic abun-
dance accretion disk is consistent with these data if the emissivity profile is very centrally
concentrated.
An increase in the ionization level of the disk surface could also repress fluorescent
emission features. We address this question (Reynolds et al. 2004a) using the ionized
reflection models of Ballantyne et al. (2001) convolved with the relativistic smearing
model corresponding to a ?standard? Novikov-Page-Thorne accretion disk around a near-
extremal Kerr BH. We found that in the ionization range log? = 1.5?2.5, the fluorescent
iron line is strongly suppressed by resonant scattering followed by Auger destruction
(Matt et al. 1993). A standard Novikov-Page-Thorne accretion disk is permissible in this
object as long as it is either highly ionized (in which case the iron atoms are fully stripped)
or moderately ionized (when the fluorescent line is strongly suppressed by resonant scat-
tering and Auger destruction).
Limb-darkening and coronal attenuation could also be at fault. It is believed that
any broad iron line is produced via fluorescence in the outer few Thomson depths of the
optically thick part of the accretion disk. If viewed at high inclination (i.e., almost edge-
on), there are two distinct limb-darkening effects that can suppress the observed line flux
(Reynolds & Wilms 2000). First, iron line photons can be photoelectrically absorbed on
42
their passage through the outer layers of the disk, either by the K-shell edges of elements
lighter than iron or the L-shell edges of iron. The resulting excited ion will then de-excite
either via the Auger effect or through the emission of new fluorescent line photons, each
resulting in a net loss of iron line photons from the observed spectrum. Secondly, iron
line photons can be Compton scattered by energetic electrons in the corona, as discussed
in Chapter 1. The fractional energy gained by a photon in each interaction with a coronal
electron is of order unity for a thermal plasma with kT ? 100 keV. Thus, Compton scat-
tering effectively removes photons from the iron line, spreading them out in energy space
until they become indistinguishable from the power-law continuum. Both photoelectric
absorption in the disk and Compton scattering in the corona are strongly accentuated for
high-inclination observers since the photons then have to follow trajectories that graze
the disk atmosphere and corona. The primary continuum photons, on the other hand, are
not subject to limb-darkening since the corona is optically thin. Hence, the equivalent
width of a broad iron line would be expected to drop as the disk is viewed increasingly
edge-on. While there is little evidence that the inner disk of NGC 4593 is viewed at high
inclination, the possibility that limb-darkening is responsible for the absence of a broad
line in this object cannot be ruled out with current data.
If the broad iron line is genuinely absent from the data, perhaps the accretion disk is in
a radiatively inefficient state, e.g., possessing an advection-dominated accretion flow, or
ADAF (Blandford & Begelman 1999; Ichimaru 1977; Narayan & Yi 1994; Rees 1982).
In such a state, the disk does not radiate the dissipated energy locally due to a low ac-
cretion rate, leading to narrower emission line profiles since the lines would not originate
in the inner part of the disk. Indeed, it is possible that we are seeing just such a com-
ponent in the form of the narrow 6.4 keV line modeled in this Section. If we model
this feature with a diskline profile possessing an inner truncation radius, instead of a
narrow Gaussian profile, we determine that the inner truncation radius to the line emit-
43
ting region is rin > 200rg. In deriving this number, we have fitted the diskline model
assuming an emissivity index of ? = 3 (appropriate for illumination of a flat disk by
a central raised corona or advection-dominated region), and a rest-frame line energy of
6.4 keV. The equivalent width of this feature is EW = 113?13 eV with a goodness-of-fit
of ?2/dof = 1529/1470; i.e., the truncated diskline profile produces very comparable
results to the narrow Gaussian profile.
It is possible that the observed X-ray continuum does not originate from or irradiate
the accretion disk. The most likely alternative is that the continuum has its origins in
a relativistic jet flowing from the central engine; the primary X-rays are then beamed
away from the accretion disk, strongly suppressing any X-ray reflection features. Given
the high-amplitude variability seen on hour-long timescales within this object, the X-rays
would have to originate from the inner parts of any jet.
2.3 Variable Nature of the Source
NGC 4593 displays significant variability (over a factor of two in 0.5?10 keV flux)
during the course of this observation. In this Section, we examine the detailed variability
properties of this source.
2.3.1 Spectral Variability
We have analyzed the spectral variability of the source as seen in the EPIC-pn data. As
an initial assessment of spectral variability, Fig. 2.5 plots the data-to-model ratios of con-
secutive 10 ks segments of the EPIC-pn data using the comptt best-fit spectrum model
discussed in ?2.2.1. Experimentation suggested that intervals smaller than 10 ks contain
insufficient counts to maintain the integrity of the spectrum. As well as the obvious vari-
ations in the normalization of the spectrum, there are clear changes in slope between seg-
44
ments (with the source becoming softer as it brightens). There is also a feature of variable
equivalent width seen at ? 6.4 keV, corresponding to the cold Fe-K? line. Interestingly,
though, we see no variable discrete features in the soft X-ray spectrum suggesting that
there is no significant warm absorber variability during our observations.
To examine variability of the iron lines in more detail, Fig. 2.6 plots the renormalized
interval data over the time-averaged data from 2?10 keV. Direct spectral fitting of the
cold and ionized Fe-K lines in each interval with Gaussian profiles illuminates the nature
of their variability (or lack thereof). As can be seen in Table 2.2, the data show that the
cold line exhibits only slight variations in flux. In other words, the cold iron line flux does
not appear to respond to changes in the X-ray continuum. Its equivalent width, however,
shows significant variability, as we illustrate in Fig. 2.7. Constraints on the ionized line
are not strong enough to rule out a constant flux and equivalent width, as is shown in
Fig. 2.8 and Table 2.2.
The simplest way to interpret the lack of continuum response of the cold iron line is
to suppose that it exists on spatial scales with light travel times greater than the duration
of our observation. For an observation time of 76 ks, as is the case here, the light would
travel approximately 150 AU, or roughly 1.9?103 rg if NGC 4593 harbors a 8.1?106 Mcircledot
BH at its core (see discussion at the end of ?2.4.3). The lack of response for the iron line
flux would suggest that this size is a lower limit for the size of the line emitting source.
This would place the line emission in the outer regions of the accretion disk or the putative
molecular torus of the Seyfert unification scheme.
45
Figure 2.5: Variation of the EPIC-pn time-averaged spectrum from the comptt best-fit
model discussed in ?2.2.1. Time intervals are 10 ks in length except for the last, which is
? 6.1 ks. Segments a) - h) are shown in chronological order of the observation.
46
Figure 2.6: The cold and ionized Fe-K? lines from the time-separated EPIC-pn spec-
trum. Time intervals are as above in Fig. 2.5. Lines are above a phabs po continuum.
The time-averaged data appear in black squares, interval data in red triangles.
47
Figure 2.7: Variation of the flux (a) and equivalent width (b) of the cold Fe-K? line
(6.4 keV) over the course of the 76 ks observation. Note that a fit to the data with a
constant model is marginally robust for the flux: ?2/dof = 10/7 (1.43). This translates to
a ?20% chance of the data agreeing with a constant model. Also note that the data point
with the greatest offset corresponds to the point of lowest flux on the source light curve,
unsurprisingly, but is still statistically valid. The constant fit is not statistically robust
for the equivalent width plot: ?2/dof = 22/7 (3.14). This indicates a < 1% chance of
agreement between the data and model.
Figure 2.8: Variation of the flux (a) and equivalent width (b) of the ionized Fe-K? line
(6.97 keV) over the course of the observation. Here the uncertainty in the data is so great
that a constant flux cannot be ruled out: ?2/dof = 3/7 (0.43). A constant equivalent
width is similarly likely: ?2/dof = 3/7 (0.43).
48
Line FWHM ( km s?1 ) Flux ( erg cm?2 s?1 ) EW ( eV)
Cold Fe-K? 13245?2208 7.41?0.86?10?13 232?27
(6.40 keV) 8831?2208 4.98?0.89?10?13 126?22
9934?2208 5.76?0.85?10?13 134?20
13246?3311 7.26?1.04?10?13 153?22
8831?2208 5.27?0.86?10?13 105?17
11038?4415 4.08?0.93?10?13 88?20
8831?2208 5.61?0.88?10?13 137?22
11038?3311 5.82?1.17?10?13 124?25
Ionized Fe-K? 7095?6081 1.97?1.41?10?13 64?46
(6.97 keV) 50678?83111 2.89?5.05?10?13 80?140
6081?6081 2.09?1.54?10?13 52?38
14190?11149 2.04?2.22?10?13 46?50
9122?6081 2.52?1.85?10?13 54?39
18244?9122 3.06?3.48?10?13 71?58
24325?9122 4.90?3.00?10?13 132?81
??- ??- ??-
Table 2.2: Each row represents a time interval of 10 ks in the observation. Fits were
done in XSPEC using a phabs po model for the continuum and two Gaussian lines with
parameters fit to the data in each time interval. Error bars are at 1?. The blank lines in
the ionized Fe-K? table represent time intervals for which a robust fit to the data could
not be achieved.
2.3.2 Continuum Power Spectrum and Spectral Lags
The light curve for the full-band (0.5?10.0 keV) data set is shown in Fig. 2.9a. The
light curve is characterized by an initial rapid drop up to ? 5 ks, followed by a relatively
steady increase peaking at ? 45 ks, a drop until ? 65 ks, and then a final increase that
shows possible signs of tapering off around the end of the observation at 76 ks. There are
indications of smaller scale variability on time scales of < 1000 s, with slight flares and
drops occurring throughout the data set.
Fig. 2.9b shows the Leahy normalized power spectrum of the 0.5?10.0 keV EPIC-pn
light curve. The power spectrum demonstrates that the variability of the source becomes
dominated by Poisson statistics on timescales of about 200 s once it drops to a power of
? 2, as expected. Before this point, the slope of the power spectrum for low frequen-
49
cies is ?2.63+0.66?0.25. This value for the PSD slope is consistent with results from several
other Sy-1 AGN such as NGC 3783 (Markowitz 2005), MCG?6-30-15 (Papadakis et al.
2005; Vaughan et al. 2003), NGC 4051 (at high frequencies; (McHardy et al. 2004)), and
Mrk 766 (also at high frequencies; (Vaughan et al. 2003)).
Given the range of X-ray energies available in this data set, it is also useful to study the
continuum variability in different energy bands. Hardness ratios and time lags between
different energy bands in the continuum, in particular, can help constrain the emission
mechanisms of the source as well as the physical scale of the emitting region(s). We
divided the X-ray spectrum into three energy bands, each with an approximately equal
number of counts (? 5?105). The soft band ranges from 0.50?0.84 keV, the mid band
extends from 0.84?1.50 keV, and the hard band covers 1.50?10.00 keV. The light
curves for all three bands are represented in Fig. 2.10. In order to test whether a time lag
exists between these energy bands, we computed the cross-correlation function between
the three energy bands using the XRONOS package as well as the discrete correlation
function (DCF; (Edelson & Krolik 1988)). We measured the hard-to-soft band lag to be
226?53 s (i.e., the hard band lags the soft band by this amount of time; Fig. 2.11).
The most straightforward interpretation of this time delay envisions it as representing
the finite scattering time within the Comptonizing disk-corona system that is thought to
be responsible for the primary X-ray production. One should be cautioned, however, that
this interpretation invokes numerous underlying simplifications with regard to the physi-
cal mechanism that produces such a time lag. See Pottschmidt et al. and Nowak et al. for
more detailed accounts of other factors that can be responsible for or affect the observed
time lag between the hard and soft energy bands (Nowak et al. 2002, 1999; Pottschmidt
et al. 2003). We assume here that both the hard and soft X-ray photons originate from
seed UV photons from the disk, which are then Comptonized by a corona of relativistic
electrons surrounding the accretion disk. The energy of a given photon in our simplified
50
Figure 2.9: The light curve (a) and power spectrum (b) for the time-averaged pn data from
NGC 4593. Variations on timescales as small as hundreds of seconds appear visible in
the source. Note that the frequency at which the power spectrum flattens into Poisson
noise is about 5?10?3 Hz. Inverting this means that the smallest timescale of variability
we can reliably observe from this source is ? 200 s. At low frequencies, the slope of the
power spectral density curve is ?2.63+0.66?0.25.
Figure 2.10: Light curves for the different energy bands: the soft band runs from 0.50?
0.84 keV (solid black), the mid band runs from 0.84?1.50 keV (dashed red), and the
hard band runs from 1.50?10.00 keV (dotted green).
51
scheme will thus depend on the number of scatterings it undergoes with the electrons, and
one may therefore infer that the more energetic photons have experienced more interac-
tions. It is thus possible to estimate the size of the coronal region by measuring the time
lag between the peaks of the hard and soft photon light curves of the source, as we have
done, and making the simplified assumption that the corona possesses a slab or spheri-
cal geometry. With each scattering, a seed photon gains on average a fractional energy
?E/E ? 4kBT/mec2, where T is the temperature of the electrons in the corona. So the
energy of a Comptonized photon after a given number of scatterings will be:
E ? E0
parenleftbigg
1+ 4kBTm
ec2
parenrightbiggn
(2.3)
where E0 is the initial seed photon energy and n is the number of scatterings (Chiang
et al. 2000; Rybicki & Lightman 1979). The time delay of this photon relative to the
seed photon source will be roughly proportional to the number of scatterings, t ? nt0.
Here t0 ? lT/c where lT is the mean free path for Thomson scattering in an optically
thick corona or, if the corona is optically thin, simply the size of the corona. We take
the effective photon energy in the soft range (0.50?0.84 keV) to be 0.67 keV. For the
hard range (1.5?10.0 keV) we calculate the effective photon energy to be 2.17 keV. Both
estimates are based on taking weighted averages (based on flux) of the energies in the soft
and hard ranges, and accounting for the energy-dependent effective area of the EPIC-pn.
Assuming that the energy of the coronal electrons ranges anywhere from 50?100 keV,
our measured soft-hard time lag of ? 226 s suggests that the corona occupies a region
around the disk 1.91?3.34?1012 cm in size. This is derived assuming the size of the
corona is given by
r ?tc
log
parenleftBig
1+ 4kBTm
ec2
parenrightBig
log EE0 (2.4)
We will assume that the central BH in NGC 4593 has a mass of 8.1?106 Mcircledot based on
52
Figure 2.11: The cross-correlation function for the soft-to-hard energy bands in
NGC 4593 in red (with data points), plotted with the best fit curve in solid black. The
vertical line represents a zero time delay between the two bands; the off-centeredness
of the curve peak indicates that the hard band lags the soft band by 226?53 s at 90%
confidence.
reverberation mapping (Gebhardt et al. 2000; Nelson & Whittle 1995). Using this mass
for the NGC 4593 BH, the characteristic length scale of the corona would be in the range
of 1.6?2.8rg.
The hardness ratio for the source also varied with respect to both time and energy flux
(soft band flux was used since it had the highest photon count): see Fig. 2.12 for details.
Note the downward trend of the hardness ratio in both the time and energy graphs. It
looks as if the ratio fluctuates almost periodically in time, tracking the variations in the
light curve. Over the course of the observation the hardness ratios decrease by a factor of
? 1.28.
53
Figure 2.12: a) The hardness ratio of the source vs. observation time. The ratio is
determined by taking the ratio of the counts in the hard band to the counts in the soft
band. b) The hardness ratio of the source vs. energy flux. Ratios were computed in the
same way as above.
2.4 Discussion and Conclusions
2.4.1 Summary of Results
We have obtained a 76 ks XMM-Newton observation of the Sy-1 galaxy NGC 4593. An
examination of the best-fitting EPIC-pn spectrum shows that the continuum is well mod-
eled by a photoabsorbed power-law with NH = 1.97?1020 cm?2 , ? = 1.75, and a flux of
4.44?10?13 erg cm?2 s?1 . The best fit to the hard spectrum can be achieved by includ-
ing two Gaussian emission lines representing cold and ionized fluorescent iron at 6.4 and
6.97 keV, respectively.
We see clear evidence for a complex warm absorber in the EPIC-pn spectrum. Fit-
ting a grid of photoionization models computed using the XSTAR code, we infer a warm
absorber with two physically and kinematically distinct zones: one with a column den-
sity of NH = 9.29?1022 cm?2 and an ionization parameter of log? = 2.75, the other
with NH = 1.13?1022 cm?2 and log? = 1.70, which is likely more distant from the
central engine. We robustly detect the L3 edge of neutral iron presumed to exist in the
54
form of dust grains along the line-of-sight to the central engine, as cited by McKernan et
al. (McKernan et al. 2003). The iron associated with this edge has a column density of
NFe = 8.32?1016 cm?2 .
A soft excess below ? 2 keV is also seen in the data, and can be accounted for either
phenomenologically by a redshifted bremsstrahlung component (Model 1) or, more effec-
tively and physically, a component of Comptonized emission from an accretion disk of
seed photons upscattered by a plasma of relativistic electrons existing in either a corona or
the base of a jet near the disk in some geometry (Model 2). The latter scenario yields the
best statistical fit to the data, with a seed photon temperature of T0 = 50 eV, an elec-
tron temperature of kT = 42 keV, a plasma optical depth of ?p = 0.12 and a flux of
6.46?10?14 erg cm?2 s?1 .
We do not detect any X-ray reflection features from a relativistic accretion disk (Reynolds
et al. 2004a). However, we show that, even if a radiatively efficient geometrically thin
disk exists, its X-ray reflection signatures would be buried in the noise if the disk has
either a very centrally concentrated irradiation profile or an appropriately ionized surface.
Either of these models can be tested by longer EPIC observations which would be sen-
sitive to the subtle features displayed by a highly blurred or ionized reflection spectrum.
If longer observations still fail to detect any accretion disk signatures, we are forced to
consider other possibilities. The inner disk may be very hot and optically thin, thereby
being incapable of producing any X-ray reflection features. Alternatively, the observed
X-ray continuum might be highly anisotropic and beamed away from the disk, thereby
rendering any reflection features undetectable.
In terms of variability, the cold line Gaussian had a time-averaged equivalent width
of EW = 131 eV, while the ionized component had an EW = 45 eV. Although the con-
tinuum varied with time over the course of our observation, the flux of the cold Fe-K?
showed marginal evidence for variability between successive 10 ks intervals. The equiva-
55
lent width of this line, on the other hand, is shown to vary significantly. The simplest inter-
pretation of this result is to suppose that the cold line originates from a region with a light-
crossing time larger that the length of our observation. For a BH mass of 8.1?106 Mcircledot
this places the cold line emitting region beyond about 2000rg from the BH, i.e., in the
outer accretion disk or the putative molecular torus of Seyfert unification schemes. Our
statistics on the ionized Fe-K line are insufficient to constrain its variability properties ?
these data are consistent with both constant flux and constant equivalent width.
We have detected a 226 s time-lag between the hard and soft EPIC-pn bands, with
the hard band lagging the soft. In a simple model in which this corresponds to scattering
times within a Comptonizing corona, we conclude that the corona can only possess a size
of ? 1.6?2.8rg.
2.4.2 Comparison with Previous Work
Previous studies of NGC 4593 with EXOSAT demonstrated a soft excess below 2 keV,
and ASCA spectra display a slightly broadened cold iron line at ? 6.4 keV. BeppoSAX
data confirm a broad absorption dip of 15% below 1 keV which may be attributable to the
presence of a warm absorber, characterized by an optical depth of ? = 0.32 for the O VII
edge, and ? < 0.22 for the O VIII edge (Kaastra & Steenbrugge 2001). Reynolds quotes
ASCA values for these edges of ? = 0.26 and 0.09, respectively (Reynolds 1997).
McKernan et al. calculated a 2?10 keV Chandra luminosity of LX = 6.10?1042 erg s?1
for H0 = 70 km s?1 Mpc?1 and q0 = 0, versus LX = 8.53?1042 erg s?1 as determined
by Reynolds with ASCA. The latest Chandra data from McKernan et al. states that the
0.5?5 keV spectrum is well modeled by a single-zone warm absorber with broken power-
law of hard index ? = 1.79, soft index ? = 2.27 and a break energy of E = 1.07 keV. The
soft spectrum is complicated by the presence of absorption edges of O VII, O VIII and
Fe-L3 below ? 2 keV, as well as some weaker emission features.
56
Our observed 2?10 keV luminosity is LX = 7.40?1042 erg s?1 (H0 = 70, q0 = 0,
? = 0.7), which is roughly 21% above that observed with Chandra by McKernan et al. ,
or 13% below that recorded with ASCA by Reynolds.
The optical depth of our O VII edge is ? = 0.15, 57% of the value obtained by Reynolds
and 46% of that calculated by Kaastra & Steenbrugge, but matching that found by McKer-
nan et al. within errors. The O VIII edge is not wanted statistically by the fit, in contrast to
the McKernan et al. observation (? = 0.14) and the Reynolds data, and the 2001 Kaastra
observation. Our best-fit value for the galactic absorption is NH = 1.97?1020 cm?2 ,
closely resembling that used by McKernan in the hard band Chandra data. McKer-
nan?s value for the column density of the soft emission from the warm absorber was
significantly lower than our own two-zone model: NH = 5.37?1021 cm?2 versus our
9.29?1022 cm?2 and 1.13?1022 cm?2 . It should be noted, however, that the authors
based this value on the RGS data rather than the EPIC-pn.
2.4.3 Implications for the X-ray Emission Region
The narrowness of the fluorescent iron line together with the lack of response of this line
to changes in the hard X-ray continuum suggest an absence of a cold, optically thick
matter within the central ? 103 rg of the accretion disk. The standard framework for
accommodating such a result is to postulate that the inner regions (r ? 103 rg) of the
accretion flow have entered into a radiatively inefficient mode which is extremely hot
(electron temperatures of T ? 1010 K), optically thin, and geometrically thick (Narayan
& Yi 1994; Rees 1982). Within this framework, the hard X-ray source is identified as
thermal bremsstrahlung or Comptonization in origin. However, the variability of the X-
ray continuum is inconsistent with X-ray emission from a structure which is ? 1000rg in
extent. The rapid continuum variability and the short time lag between the hard and soft
X-ray photons dictate that, at any given time, the X-ray emission region is only ?1?3rg
57
in extent.
We are therefore led to consider alternative geometries and/or origins for the X-ray
source. We consider three possibilities. Firstly, the inner accretion flow may indeed be in
the form of a radiatively inefficient flow, but the observed X-ray emission may come from
the compact base of a relativistic jet powered by BH spin. Secondly, the X-ray emission
may indeed originate from the body of the radiatively inefficient flow but, at any given
instant in time, be dominated by very compact emission regions within the flow. Such
emission regions may arise naturally from the turbulent flow or, instead, may be related
to a magnetic interaction between the inner parts of the flow and the central spinning BH
(Wilms et al. 2001; Ye et al. 2007). In this case the iron line could still plausibly originate
at a distance of thousands of rg and thus be quite narrow. Finally, it is possible that the
accretion disk is radiatively efficient (and hence optically thick and geometrically thin)
close to the BH and supports a compact accretion disk corona. Of course, an immediate
objection to this scenario is the lack of a broadened iron line. However, as demonstrated in
Reynolds et al. (2004b) and discussed in ?2.2.2, it is possible the iron line is so broad that
it is buried in the noise of the continuum. Alternatively, the accretion disk surface may
have an ionization state such that iron line photons are effectively trapped by resonant
scattering and destroyed by the Auger effect. Longer observations with better spectral
and timing resolution will be necessary in order to confirm our results and differentiate
between these different possible scenarios.
2.4.4 Conclusions
We have shown that the Sy-1 galaxy NGC 4593 has a continuum spectrum that is fit
remarkably well by a simple photoabsorbed power-law above?2 keV. Below this energy,
we see evidence for spectral complexity that can be attributed to the presence of a possible
multi-zone layer of absorbing material intrinsic to the source, as well as a soft excess that
58
cannot be explained by a reflection model from an ionized disk. Also arguing against a
disk-reflection-dominated source is that unlike other sources of its kind (e.g., MCG?6-
30-15), NGC 4593 has relatively narrow cold and ionized Fe-K? line features at 6.4 and
6.97 keV, respectively. We can say that the cold line is most likely formed quite far out
in the accretion disk based on its narrowness and lack of significant variability over the
76 ks duration of our observation. We find no evidence for reflection features from the
inner accretion disk (e.g., a ?broad iron line?) in the spectrum.
Based on the time lag between the soft and hard spectral bands, we estimate that
the corona occupies a region around the central source on the order of ? 1.6?2.8rg,
assuming that NGC 4593 harbors a 8.1?106 Mcircledot BH at its core and that the energies
of the electrons in the corona range from ? 50?100 keV. This estimate for the coronal
size is reinforced by our measurements of continuum variability on timescales as small as
? 200 s, equivalent to a light travel time of ? 4rg for the BH mass in question.
Taken together, the implications of a narrow iron line emitted far out in the disk or
torus and the small coronal size in NGC 4593 present an atypical picture of an AGN.
We postulate that the primary X-ray source is associated with the compact base of a jet
or compact emission regions within a much larger optically thin accretion flow. Alter-
natively, the accretion disk may be radiatively-efficient with a compact corona but not
display a broad iron line due to the effects of extreme broadening or disk ionization.
59
Chapter 3
A New Relativistic Line Emission Code
As discussed in Chapter 1, we now have access to X-ray spectral data of sufficient quality
that we are motivated to construct an iron line model that allows the spin of a BH to be a
free parameter in the fit. Emission lines from an accretion disk around a BH vary greatly
from their standard Voigt profiles seen in an Earth-bound laboratory: they are strongly
influenced by the effects of extreme Doppler shifting as well as those of Special and
General Relativity. As such, a fully relativistic computational treatment of these effects
is necessary in order to accurately parameterize the line shapes and extract meaningful
constraints on those parameters in question, such as BH spin.
3.1 The kerrdisk Model
As mentioned in ?1.4, other groups have recently been developing similar models for the
purpose of fitting for BH spin as well. These models (Beckwith & Done 2004; ?Cade?z &
Calvani 2005; Dov?ciak et al. 2004) all produce consistent results with each other and with
our new model, kerrdisk, in terms of the line profiles produced for a given set of input
parameters. However, kerrdisk has the added advantage of portability. In practice, the
XSPEC modules that implement both the ky and Beckwith & Done models use relativistic
60
transfer functions stored in very large (multi-gigabyte) pre-calculated tables. By contrast,
kerrdisk uses much smaller pre-calculated tables of transfer function values and lin-
early interpolates between them. This technique enables accurate line profile calculations
while also saving the user disk space and computing power. A more detailed comparison
between kerrdisk and these other available models will be made in ?3.2.
Using their respective models, both the Dov?ciak and Beckwith groups conclude that
fitting broad iron lines cannot truly constrain the spin of the BH. We argue that this is not
the case. Since their models allow emission from any radius of the accretion disk out-
side of the event horizon, the aforementioned groups can produce iron line profiles with
arbitrarily redshifted wings even if the underlying BH spacetime has no spin. One must
consider the physicality of this assumption, however: it is not possible to get line emis-
sion from radii deep within the plunging region for several reasons. Firstly, the closer one
gets to the event horizon, the smaller the geometrical area of the disk available for emis-
sion becomes, while the gravitational redshift affecting any emission from such regions
increases correspondingly. Both of these effects would tend to minimize the contribution
to the line profile from most of the emission inside the radius of marginal stability. Fur-
ther, the ionization of the disk material within ? 4rg of a Schwarzschild BH is inevitably
too high to produce significant line emission in the first place, and the optical depth of
this material also decreases rapidly within the radius of marginal stability (Reynolds &
Begelman 1997; Young et al. 1998). For all of these reasons, one simply cannot produce
significant line emission from any arbitrary radius outside the event horizon. This must
be taken into account when modeling such line emission.
Our new relativistic emission line code, kerrdisk, is written in FORTRAN77 so that
it can be easily meshed with XSPEC, and has now been compiled successfully on Solaris,
Linux and Apple-MAC platforms. The dimensionless spin parameter of the BH (a) can
take on any value in the range ?1?a?1, where negative values of a correspond to a BH
61
that is rotating in a retrograde sense relative to the accretion disk. Although, according to
the equations of GR, a could have any arbitrary value, the cosmic censorship hypothesis
states that naked singularities cannot exist in the universe, so a BH must be shrouded by
an event horizon. This limits the acceptable range of spin parameters to ?1 ? a ? 1. For
simplicity we consider only prograde spins up to the theoretical spin-equilibrium limit,
i.e., 0 ? a ? 0.998.
The limiting value of a = 0.998 for BH spins was first discussed by Kip Thorne
(Thorne 1974). Therein, the author contends that if BHs were simply accreting mat-
ter, their spins would ascend to a?1 rather quickly, but because material in the accretion
disk radiates, and some of that emitted radiation is swallowed by the hole, a counteract-
ing torque is produced. The origin of this counteracting torque lies in the photon capture
cross-section of the hole: BHs have a higher capture cross-section for photons of nega-
tive angular momentum (opposite to that of the hole itself) than for photons of positive
angular momentum. Thus, the accretion of emitted radiation from the disk results in an
overall reduction in the angular momentum of the hole until it reaches a theoretical equi-
librium value of a = 0.998. Recent work on magnetohydrodynamic (MHD) accretion
disks suggest that the continued transport of angular momentum from matter within the
radius of marginal stability, as well as angular momentum lost from the rotating BH it-
self via Blandford-Zjanek-like mechanisms (Blandford & Znajek 1977), may lead to a
rather lower equilibrium spin (e.g., see recent GR MHD simulations (Krolik et al. 2005)).
Equilibrium spins as low as a ? 0.90 are within the realm of possibility.
Following the method of Cunningham, we compute the line profile by employing a
relativistic transfer function (Cunningham 1975). For a given BH spin a and disk inclina-
tion i, the observed accretion disk spectrum can be written as
Fobs(Eo) ?
integraldisplay g2
radicalbigg?(1?g?)I(Eo/g,?e,re)?(re,g?;a,i)dg?redre. (3.1)
62
Here, I(E,?e,re) is the rest-frame specific intensity of the disk at radius re and energy E
emitted at an angle ?e to the disk normal, ? is the Cunningham transfer function which
accounts for the effects of light-bending on the observed solid angle from each part of the
disk, g is the ratio of the observed to the emitted photon energy (g = Eo/Eem), and g? is
the relative value of g with respect to the redshift extremes obtained from the disk annulus
in question,
g? = g?gmin(re)g
max(re)?gmin(re)
. (3.2)
This formulation is attractive from the computational point of view; light bending ef-
fects are isolated from relativistic beaming effects and encoded in the transfer function
?(re,g?;a,i) which is a slowly varying function of its variables. This allows us to perform
full computations of the transfer function at a relatively sparse set of points in parameter
space, and then use linear interpolation to accurately determine the transfer function at a
general point.
Specializing to the case of a ?-function emission line allows us to eliminate the g?
integration from Eqn. (3.1). Assuming that the surface emissivity of the emission line is
a function of emission radius re and angle ?e is f(re,?e), this gives
Fobs(Eo) ?
rmaxintegraldisplay
rmin
g3radicalbig
g?(1?g?)
1
gmax?gmin ?(re,g
?;a,i) f(re,?e)redre. (3.3)
We use the algorithms of Speith to compute the transfer function ?(re,g?;a,i) as well
as gmin(re) and gmax(re), thereby allowing us to perform this integration (Speith et al.
1995). Following laor, we assume a limb-darkening law of I ? 1 + 2.06(cos?e) (Laor
1991), though this is trivial to change in the driver code. For a given spin a and inclination
i, high quality line profiles (including all those presented herein) are produced using a
transfer function computed at 50 radial bins, equally spaced in the variable 1/?re, and
20 linearly spaced relative redshift bins (g?) across the line profile at any given radius.
63
These values were determined via extensive trial and error to make the best, smoothest
possible line profile while keeping computation time to a reasonable length. Increasing ei-
ther the number of radial or relative redshift bins did not significantly improve the integrity
of the line profiles produced. Also, because the transfer function varies quite slowly with
radius, relative redshift, a and i, greater frequency of sampling was not warranted.
Our choice for the radial spacing corresponds to equal spacing of non-relativistic Ke-
plerian velocities. We then evaluate the line profile integral (Eqn. (3.3) with a densely
spaced logarithmic grid in re, using linear interpolation in re of the (rather sparsely sam-
pled but slowly varying) transfer function. In practice, we use 5ne-zones per decade of
re where ne is the number of frequency elements in the output line profile (specified by
the response matrix of the data being fit). Experimentation shows that this produces high
quality line profiles even at very high resolution (i.e., large ne).
The Cunningham transfer function ?(re,g?;a,i) is computed for a 20?20 grid in
(a,i)-space and is stored in a 40 MB table that is accessed by the driver script for kerrdisk.
The grid of spins is spaced in a weighted fashion by the square root of the gridpoint such
that more sampling takes place as the spin parameter increases. The grid of inclination
angles in spaced linearly in terms of cosi. Again, due to the slowly varying nature of
the transfer function, simple linear interpolation to arbitrary spins and inclination angles
produces accurate and high quality line profiles.
To parameterize the emissivity function of the accretion disk, we follow Fabian et
al. (Fabian et al. 2002) and assume a line emissivity characterized by a broken power-law
64
between some inner radius rmin and outer radius rmax, i.e.,
f(re) =
?
????
???
?
???
????
?
0 re < rmin
(re/rbr)??1 rmin ? re < rbr
(re/rbr)??2 rbr ? re < rmax
0 re ? rmax
(3.4)
That is, the accretion disk is expected to behave qualitatively as a Page-Thorne (Page
& Thorne 1974) disk and radiate more copiously at smaller radii (i.e., deeper within
the gravitational well where more potential energy is being liberated). In reality, we
would expect the disk to exhibit a continuous range of emissivity indices (??s), but for
computational simplicity we arbitrarily split the disk into an outer and inner portion, each
with their corresponding emissivity index that can be fit to the data.
We note that, at present, the publicly available Speith algorithms on which this work
is based do not support the proper computation of emission from within the radius of
marginal stability, i.e., we are restricted to rmin ? rms. Hence, all kerrdisk line profiles
currently assume that the emission profile is truncated within r = rms. As discussed in
?1.4, truncating the emission in this way will not significantly affect the resulting line
profile due to the high ionization and low optical depth of material within the plunge
region.
The code takes ? 4 s to produce a single line profile on a 2 GHz processor linux ma-
chine. When the model is used to fit data within XSPEC, several hundreds or thousands of
iterations of the code are often needed to get a good fit, resulting in run times that can be
on the order of an hour or more. In principle, this run time can be significantly reduced
by employing a parallelization scheme when fitting. Such a parallelization scheme is pos-
sible to implement in the ISIS spectral analysis package (Houck 2002) using the PVM
module (Michael Nowak and Andrew Young, private communication).
65
The best way to examine the results of the code?s line profile simulations is to look at
how the morphology of the line changes with alterations made in certain important param-
eters. For illustrative purposes, Fig. 3.1 shows model line profiles with a rest-frame energy
of E = 1 keV. The line profiles shown in this figure have the same parameter settings as
those shown in the review by Reynolds & Nowak (Reynolds & Nowak 2003) to enable
easy comparison. The Reynolds & Nowak profiles are also based on the Speith algorithms
but sample the transfer function more sparsely and employ a cruder integration technique
to evaluate the line profile. The fact that our line profiles agree with, but are much less
noisy than the Reynolds & Nowak profiles validates our newer integration/interpolation
technique.
3.2 Comparison With Other Disk Line Models
Verification of our new line profile code can be demonstrated through detailed compar-
isons with existing public models, such as laor and diskline ? where a = 0.998 and
0.0, respectively ? as well as those of the newer models we have mentioned (Beckwith
& Done 2004; ?Cade?z & Calvani 2005; Dov?ciak et al. 2004). Since the kyrline model
of Dov?ciak has already been compared with the kdline model of Beckwith & Done
and that of ?Cade?z & Calvani, we need only to compare kerrdisk with kyrline. These
comparisons are shown in Figs. 3.2-3.3 and discussed in this Section.
Given the lack of relativistic light bending in the diskline model, we expect our
fully relativistic kerrdisk line profiles with a = 0 to differ slightly from those computed
with diskline, especially at large inclination angles. We indeed see slight differences
(Fig. 3.2). We should stress, however, that the differences are minor and that diskline
should still be considered a perfectly acceptable model for disks around Schwarzschild
BHs for all but the highest signal-to-noise data. Examining the comparison of the laor
66
Figure 3.1: Variation of the kerrdisk line profile with (a) disk inclination angle, (b)
disk emissivity index, and (c) BH spin parameter. In each case the range of emission in
the disk is from r = rms?50rg. In (a), a = 0.998, ? = 0.5. In (b), a = 0.5, i = 40. In (c),
i = 40, ? = 3, and the lines are normalized the the same flux the illustrate the effects of
gravitational redshift on the line profile with an increase in spin.
67
Figure 3.2: Various iron line models for a Schwarzschild BH. The inclination angles
represented are 5? for (a), 45? for (b), and 80? for (c). Here ?1 = ?2 = 3.0, and rmin and
rmax are held constant at 6rg and 50rg, respectively. The diskline profile is in solid
black, the kerrdisk profile is in dashed red, the kyrline profile including emission
from within the ISCO is in dash-dotted green and the kyrline profile not including
ISCO radiation is in dotted blue.
68
Figure 3.3: Various iron line models for a maximally spinning Kerr black hole. The in-
clination angles vary as above for the Schwarzschild case in (a)-(c). Other parameters
are the same as those used in the Schwarzschild case, but now rmin = 1.235rg, corre-
sponding to the radius of marginal stability for a maximal Kerr BH, rather than the 6rg
Schwarzschild rms. The laor profile is in solid black and the rest of the color scheme is
the same as that used in Fig. 3.2 above.
69
models with the a = 0.998 kerrdisk model, we note good agreement (Fig. 3.3). The
slight differences that do exist are caused by an artificial smoothing of the laor line due
to interpolation of a sparsely sampled transfer function. Again, however, we note that the
laor model is perfectly acceptable model for disks around a = 0.998 BHs for all but the
highest signal-to-noise data.
The real power of this new generation of line profile models is the freedom in the spin
parameter of the BH. Therefore, the real verification of our code lies in a detailed com-
parison of kerrdisk and kyrline. Indeed, as shown in Figs. 3.2-3.3, the line profiles for
kerrdisk and kyrline are virtually indistinguishable when one does not include radia-
tion from within the radius of marginal stability in kyrline. Also shown in these figures
are the effects of including emission from within the radius of marginal stability (down
to the horizon, for the sake of illustration), as computed by Dov?ciak et al. This has the
greatest effect on the line profiles from the slowly spinning holes since it is only in these
systems that an appreciable fraction of the plunging region is subject to modest gravita-
tional redshift (as opposed to the extremely large redshift experienced by the material in
the plunging region of a Kerr BH; in this case the BH spin has pulled rms down quite close
to the event horizon and much deeper within the gravitational potential well). We intend
to extend our model to include the region within the radius of marginal stability in future
work, carefully considering the effects of both the level of ionization and the optical depth
of the material within the plunging region, in particular, as discussed in Chapter 1. Both
of these effects can have a substantial impact on the contribution of emission from this
region to the overall line profile.
70
3.2.1 The Convolution Model kerrconv
As mentioned in ?1.3.2, the irradiation of the accretion disk by the primary X-ray source
results in a whole X-ray reflection spectrum consisting of Compton and radiative recombi-
nation continua plus numerous fluorescent and radiative recombination lines. The Fe-K?
line is the most prominent due to its high rest-frame energy and its intrinsic strength, but
many other species are also excited (e.g., oxygen, nitrogen, silicon and sulfur). The whole
X-ray reflection spectrum from the disk will be subject to the same extreme Doppler and
relativistic processes that combine to alter the morphology of the iron line. The most
physically realistic simulation of the reflected spectrum from a photoionized disk surface
has been presented by Ross & Fabian. These high-quality models capture the ?traditional?
X-ray reflection processes (Compton scattering, photoelectric absorption and fluorescent
line emission) as well as the powerful soft X-ray radiative-recombination line emission
expected from an X-ray irradiated photoionized surface of an optically thick accretion
disk (Ross & Fabian 2005). These authors have provided their results in the form of
tabulated spectra that can be used in XSPEC. We then wish to apply the Doppler and
relativistic effects discussed to the reflected spectrum by convolving it in velocity space
with a relativistic smearing kernel such as the one used to generate the kerrdisk line
profile. To facilitate this, we have also produced a convolution form of our line profile
model, kerrconv, whose results mirror those of the kyconv model designed by Dov?ciak
et al. and the kdconv model of Beckwith & Done, provided that no radiation from within
the ISCO is included in the latter two models, as was the case for the comparison of
kerrdisk with kyrline and kdline in ?3.2 above. As with kerrdisk, the kerrconv
parameters include emissivity indices for the inner and outer disk separated by a break
radius, inner and outer radii for the disk emission, the spin parameter of the BH, and the
inclination angle of the disk with respect to our line of sight. The kerrconv model is
71
Figure 3.4: A simulated Fe-K? line at 6.4 keV. The kerrdisk results are shown in solid
red, the kerrconv(gauss) results in dashed green. Both lines are given the same set of
input parameters: ?1 = ?2 = 3, a = 0.998, i = 30?, rmin = rms, rmax = 50rms. The fact
that kerrconv reproduces the kerrdisk results verifies its accuracy.
readily validated by applying it to a narrow Gaussian emission line and comparing the
resulting spectrum with the regular kerrdisk model, as in Fig. 3.4.
The kerrconv model applies relativistic smearing to the entire reflected accretion disk
spectrum, and as such is quite computationally expensive when used in a fit to real data of
high quality (i.e., high count number). It is therefore advisable to use this model as a final
step in a rigorous spectral analysis such as that performed on MCG?6-30-15 (Chapter 4)
or any of the other Sy-1 AGN discussed in Chapter 5. For sources with broad iron lines
such as the ones analyzed herein, a reliable technique that can speed the fitting process
is to first attempt to fit the spectrum with one of the unsmeared ionized disk reflection
72
models. Initially freezing the iron abundance at the solar value (Fe/solar = 1) and the
ionization level at neutral (? = 30) can also help constrain the relevant parameter space.
These variables can be freed at a later time. If it is clear that a broader iron feature is
present ? one that is not accounted for by the model ? then applying a kdblur smearing
kernel is a logical next step. This convolution model is similar to kerrconv, but employs
a laor kernel (a = 0.998) rather than a kerrdisk kernel (arbitrary spin). Because laor
is a pretabulated model, this fit to the data will be quite a bit faster than kerrconv and
will allow some further preliminary constraints to be placed on the disk emissivity profile,
disk inclination, and reflection parameters. Finally, once a good fit has been achieved with
kdblur, one can substitute in kerrconv using the kdblur best-fit parameters as a starting
point. This will cut down fitting time considerably and also produce a more reliable fit
by gradually narrowing down the relevant regions of parameter space in the model. This
step-wise modeling technique is detailed in Chapter 5.
73
Chapter 4
MCG?6-30-15: The Broadest Iron Line
Found to Date
As mentioned in Chapter 3, the Seyfert-1 galaxy MCG?6-30-15 is considered the bench-
mark in broad iron line AGN studies, possessing the broadest Fe-K? feature yet observed.
The extreme width of the line is almost certainly an indication of relativistic origin in the
inner accretion disk of this source, making it an ideal candidate on which to test our new
kerrdisk model. Because MCG?6-30-15 has also been so extensively studied, in large
part because of its extreme Fe-K feature, we are fortunate to have more photons to work
with than in any other broad iron line AGN (350 ks with XMM-Newton; (Fabian et al.
2002)). This allows us to place viable statistical constraints on the angular momentum of
the BH in this source.
74
4.1 A Brief History of Broad Iron Line Studies in MCG?
6-30-15
MCG?6-30-15 is an S0-type galaxy in the constellation of Centaurus that hosts a Sy-1.2
nucleus. It has a measured redshift of z = 0.008, placing it at a distance of d ? 37 Mpc
using WMAP cosmological parameters. X-ray studies of this AGN have revealed a pow-
erful central source along with a significantly broadened Fe-K? feature. As mentioned
above, this broad line has led MCG?6-30-15 to become one of the most studied AGN
in the X-ray band due to its potential as a probe of BH and accretion disk physics. Al-
though the mass of the hole is not yet well constrained, estimates based on X-ray studies
have placed it in the range of 106?2?107 Mcircledot (Nowak & Chiang 2000; Reynolds 2000).
McHardy et al. have further narrowed this mass range to 3?6?106 Mcircledot using a variety of
methods such as the M-? relation, line widths from optical spectra, BLR photoionization
arguments and X-ray variability (McHardy et al. 2005).
Reflection signatures from neutral material had been observed with EXOSAT (Nandra
et al. 1989) and Ginga (Matsuoka et al. 1990; Nandra et al. 1990), but it was not until
deep observations of MCG?6-30-15 by ASCA that the broadened and skewed iron line
was robustly detected (Tanaka et al. 1995). It was determined that the line profile matched
that expected due to X-ray reflection from the surface of a relativistic accretion disk; the
robustness of this interpretation was demonstrated by Fabian et al. (Fabian et al. 1995).
Broad-band BeppoSAX data (Guainazzi et al. 1999) confirmed the Tanaka et al. detection
of a broadened and redshifted iron line with an equivalent width of EW ? 200 eV.
A detailed re-analysis of this observation (Iwasawa et al. 1996) identified a period of
time when the source entered the so-called ?deep minimum? state, marked by low con-
tinuum emission. While in this state, the iron line width (and especially the extent of the
red wing of the line) markedly increased to the point that emission from a disk around
75
a Schwarzschild BH truncated at the radius of marginal stability (rms = 6rg) could no
longer reproduce the observed line profile. Noting that the radius of marginal stabil-
ity moves inwards (to a location characterized by higher gravitational redshift) as the
BH spin is increased, it was subsequently argued that the BH in MCG?6-30-15 must be
rapidly rotating. Fitting sequences of Novikov-Thorne (Novikov & Thorne 1974; Thorne
1974) models to the deep minimum ASCA data (and assuming that the X-ray irradia-
tion tracks the local dissipation in the underlying disk), Dabrowski et al. derived a lower
limit of a > 0.94 on the rotation of the BH (Dabrowski et al. 1997). At this point, how-
ever, Reynolds & Begelman noted that physically plausible scenarios could result in suf-
ficient X-ray reprocessing (including ionized iron line emission) from within the radius
of marginal stability to fit the ASCA deep minimum state with even a Schwarzschild BH
(Reynolds & Begelman 1997). In order to illuminate the region of the disk within rms, the
authors hypothesized an X-ray source on the symmetry axis some height above the disk,
and suggested that iron line profile changes (and some part of the X-ray continuum flux
changes) could be attributed simply to changes in the height of this X-ray source.
After the discovery of its broad iron line feature, MCG?6-30-15 became the sub-
ject of many more observations. With the first observations of XMM-Newton in 2000,
astronomers had a new tool with unparalleled throughput with which to examine this
source in finer detail. The first XMM-Newton observation of MCG?6-30-15 was fortunate
enough to catch the source in its ?deep minimum? state characterized by low contin-
uum flux and a broader than normal Fe-K? profile. The resulting high signal-to-noise
spectrum revealed an extremely extended red wing to the line profile extending down to
3?4 keV (Wilms et al. 2001). Because so much emission seemed to be coming from
radii deep within the gravitational potential well, and because the emissivity index was
correspondingly quite high, the authors hypothesized an interaction between the spinning
BH and its accretion disk. Magnetic torquing effects between the two could result in the
76
extraction of rotational energy from the BH which would, in turn, power the high coronal
emission seen from the inner radii of the disk (Agol & Krolik 2000; Garofalo & Reynolds
2005). An alternative mechanism consists of the strong gravitational focusing of a high-
latitude source above a rapidly rotating BH (Martocchia & Matt 1996; Miniutti & Fabian
2004). In contrast with data from the ASCA era, a Schwarzschild model appeared not
to work for these data ? a line extending down to ? 3 keV would require line emission
from extremely deep within the plunge region: r ? 3rg = 0.5rms, a situation which ap-
pears unphysical due to the high ionization expected in this part of the flow (Reynolds &
Begelman 1997).
Reynolds et al. performed a follow-up and more detailed analysis of the XMM-Newton
observation of MCG?6-30-15 taken by Wilms et al. (Wilms et al. 2001). They explicitly
demonstrated that the iron line profile was inconsistent with an X-ray irradiation profile
that follows a Novikov-Thorne (Novikov & Thorne 1974) dissipation law, even for an ex-
tremal Kerr BH (Reynolds et al. 2004b). Employing a generalized thin disk model (Agol
& Krolik 2000) that includes a torque applied at r = rms, Reynolds et al. suggested that
this torque has a great impact on the disk emission seen in this observation. In the ?deep
minimum? state, the torqued-disk scenario requires that the disk is largely emitting via
the extraction of rotational energy from the BH rather than via accretion. These authors
also examined spectral variability during the deep minimum state. By studying difference
spectra and direct spectral fits to 10 ks segments of data from this observation, Reynolds
et al. concluded that the intensity of the broad line seems to be proportional to the hard
2?10 keV flux of the source: the equivalent width of the line remains approximately con-
stant while the source fluctuates substantially in amplitude. Such behavior is consistent
with simple X-ray reflection models.
The longest XMM-Newton observation of the source to date was recorded by Fabian et
al. in 2001. This group found MCG?6-30-15 in its normal state, and recorded data for over
77
87 hours (Fabian et al. 2002). In this state, the bulk of the iron line emission was in a nar-
rower line compared with the ?deep minimum? state, although a very extended red wing
was still evident. The time-averaged EPIC-pn spectrum again showed that the Fe-K?
feature was very strong, and the long data set was of sufficient resolution and quality that
the spectrum demanded a fit incorporating a full reflection model. Relativistic smearing
needed to be applied not just to the cold iron line, but to the entire reflection continuum.
Taking this into account, the iron line was once again found to produce emission within
the radius of marginal stability for a Schwarzschild BH. Fitting the line with the maxi-
mally spinning (a = 0.998) BH laor model suggested that the line emissivity followed
a ? ? r?? dependence with ? = 4.5?6 between an inner radius rmin < 2rg and a break
radius rbr ? 6rg. Beyond the break radius, the emissivity profile flattened to ? ? 2.5.
This broken power-law form was strongly preferred by the data over the usual simple
power-law emissivity functions usually fitted to such data ? again, this reflects the high
quality of the data. Fabian et al. also note that, in its normal state, difference spectra of
MCG?6-30-15 show spectral variability from 2?10 keV in the form of a power-law: the
iron line flux changed little between successive 10 ks frames of the observation, whereas
the continuum flux varied by as much as a factor of ? 2. This result is in contrast to that
found by Reynolds et al. , who observed an iron line flux proportional to the 2?10 keV
continuum flux when MCG?6-30-15 was in its ?deep minimum? state (Reynolds et al.
2004b). Comparing these two studies, it appears that the iron line flux is proportional
to the observed X-ray power-law continuum at low fluxes and then ?saturates? to an ap-
proximately constant level once the observed X-ray continuum exceeds a certain level.
This complexity could be due to light-bending effects if the power-law X-ray continuum
source is situated close to the spin axis of the BH (Miniutti & Fabian 2004). Alternatively,
patchy ionization of the disk surface might produce such a saturation (Reynolds 2000).
The ky suite of iron line profile models (Dov?ciak et al. 2004) was used to fit the
78
time-averaged spectrum of MCG?6-30-15 as well, also using data from the long XMM-
Newton observation (Fabian et al. 2002). They fit the 3?10 keV spectrum with four
combinations of ky models, all involving a broad Fe-K? kyrline, a narrow Gaussian
emission line at 6.9 keV (likely an ionized line of iron, as cited in Fabian et al. ), and a
Compton-reflection continuum from a relativistic disk (smeared using a kyconv kernel).
The authors also found that models describing the disk emissivity as a broken power-
law rather than a single power-law in radius achieved significantly better statistical fits,
though among these broken power-law models, comparable fits can be obtained for a
wide variety of BH spin values. These authors therefore concluded that iron line profiles
are not a good way to constrain BH spin. At some level, this objection amounts to the
obvious point that arbitrarily large redshifts can be obtained around any BH (rotating or
not) if one is at liberty to produce emission from any radius arbitrarily close to the event
horizon. As stated in Chapter 3, however, one must consider the physical realism of this
assumption in general, and the best-fit spectral parameters determined by these authors
in particular. For their low-spin (a = 0.25) best-fitting model, Dov?ciak et al. concluded
that a substantial amount of iron line emission had to originate from deep within the
radius of marginal stability; translating the fit parameters of Dov?ciak et al. into standard
quantities, they require an inner emissivity profile of ? ? r?9 starting at an inner radius
of rin = 3.2rg, to be compared with the radius of marginal stability for a a = 0.25 BH
which is at rms ? 5.2rg. As has already been noted and will be explored further in ?4.2,
it is hard to understand how this region of the accretion flow could contribute to any part
of the observed iron emission given that the fact it will be very tenuous and extremely
highly photoionized (Reynolds & Begelman 1997; Young et al. 1998).
The medium resolution (CCD) data discussed so far leave ambiguous the possible
role of complex ionized absorption in distorting the observed X-ray continuum shape
and hence the inferred iron line profile. To assess the role of this absorption, Young et
79
al. performed and analyzed a deep, 522 ks grating observation of MCG?6-30-15 in May
2004 with the HETGS instrument on Chandra (Young et al. 2005). This observation
produced two important results: first, the authors found that the difference in the hard
continuum spectrum between the high and low flux states was well described by a power-
law of photon index ? = 2.0+0.2?0.1. This finding agreed with previous studies that indicated
that the spectral variability of MCG?6-30-15 in its normal state is dominated by a power-
law component (Fabian et al. 2002). Second, and most importantly, ionized absorption
models whose continuum curvature mimics the red wing of a broad iron line from 3?
6 keV were ruled out. Such models generically predict strong K? absorption lines of
intermediately ionized iron. Young et al. showed that these lines are conclusively absent,
falsifying the ionized absorption model and further strengthening the relativistic smearing
hypothesis.
4.2 Determining the Spin of the Black Hole in MCG?6-
30-15
In this Section, we use our new models (kerrdisk and kerrconv) along with the ky
models of Dov?ciak et al. to confront the issue of determining the spin of the BH in MCG?
6-30-15. Because of the extremely robust, broad, well-studied iron line in this system,
MCG?6-30-15 is an excellent candidate for such a study. Given the complexity of the
spectrum displayed by the source, it is important to perform this exercise in a step-by-
step manner, clearly enumerating all of the assumptions at each stage, and employing
physical models to represent the spectral complexity whenever possible.
This guides the study presented in this Section. Due to the unprecedented signal-to-
noise, we use the EPIC-pn data from the aforementioned long XMM-Newton observation
of MCG?6-30-15 (Fabian et al. 2002). Data preparation and reduction followed Vaughan
80
& Fabian exactly (Vaughan & Fabian 2004). We present a step-by-step analysis of these
data using models of increasing complexity and physical realism. Initially, to illustrate
the potential power of broad iron lines for spin determination, we modeled the 2?10 keV
EPIC-pn as a simple power-law continuum modified by a broad iron line (and absorp-
tion by the Galactic column of 4.1?1020 cm?2 toward this source); this is comparable
to the study performed by Dov?ciak et al. It does, however, neglect the significant effects
that continuum curvature due to ionized absorption could have on the inferred iron line
parameters (and hence inferred BH spin). To assess these effects, we next model the ef-
fects of multiple warm absorbers and dust on first the 2?10 keV spectrum and then the
full 0.6?10.0 keV spectrum. In our most sophisticated spectral model, we describe the
0.6?10.0 keV band including multiple absorption components and augmenting the sim-
ple broadened iron line with a relativistically smeared ionized X-ray reflection spectrum
(Ross & Fabian 2005).
The best-fit parameters and error bars for each progressive model fit are shown in
Table 4.1. Each fit and the corresponding change in the global goodness-of-fit (??2) with
respect to changes in a in each case are shown in Figs. 4.1-4.6. The unfolded spectrum
and the best-fit model components for both the single kerrdisk case and the full ionized
reflection spectrum convolved with kyconv are shown in Figs. 4.5-4.7. For the warm
absorber tables described in Table 4.1 and ?4.2.2, all abundances are frozen at the solar
value. For all model components, the redshift is set to z = 0.008, the optically determined
value for MCG?6-30-15 (Reynolds et al. 1997). In all of the fitting below, the inner disk
radius contributing to the iron line emission (or X-ray reflection spectrum in the case of
Model 5) was not allowed to be smaller than the radius of marginal stability.
81
4.2.1 Simple Power-Law Continuum and Iron Lines
Initially, we perform an analysis of the 2?10 keV spectrum assuming that the underlying
continuum is a simple power-law (absorbed by the Galactic hydrogen column along our
line of sight) and that the disk spectrum is just a single iron line (rather than a whole
reflection spectrum). Fig. 4.1 shows the hard spectrum as fit by this photoabsorbed power-
law (Model 1). To accurately model the continuum we have initially ignored the 4?7 keV
range when fitting this component. This prevents any contamination of the fit by the
presence of an iron line reflection signature. Once the fit was complete, energies from
4?7 keV were included again. As suspected, the data/model ratio shown in the lower
panel demonstrates a significant residual feature above the continuum, which appears to
have the form of a highly broadened iron line peaking at 6.4 keV. The presence of this
large residual feature results in a poor fit, ?2/dof = 4577/1106(4.14).
Fig. 4.2a plots the data/model ratio again, this time for a model including a single,
broad kerrdisk line with a rest-frame energy of 6.4 keV (Model 2). Two narrow red-
shifted Gaussians representing a cold Fe-K? line and an ionized line of iron are also
included at 6.4 and 6.9 keV, respectively (Fabian et al. 2002). The 6.4 and 6.9 keV lines
both have equivalent widths of ? 14 eV.
It should be noted here that Fabian et al. acknowledged that a 6.74 keV absorption
line of EW =?138?35 eV fit the data as well as an emission line at 6.9 keV and EW =
18?6 eV. This absorption feature was also preferentially used in the MCG?6-30-15
work of Vaughan & Fabian, and was consistent with the prediction of Sako et al. based
on an RGS observation of this source in 2001 (Sako et al. 2003). However, the 6.7 keV
absorption line detected in the deep high-resolution Chandra/HETGS spectrum (Young
et al. 2005) is significantly weaker than that fitted by Fabian et al. , with equivalent widths
of EW = ?18+7?5, EW = ?13?9, and EW = ?25?9 eV during the average, low and
82
Figure 4.1: The phabs(po) fit to MCG?6-30-15. Notice the significant deviations of the
data from this model, especially around 6.4 keV. Formal ?2/dof = 4577/1106 (4.14).
high flux states of the source, respectively. Thus, the high-resolution Chandra spectrum
does not support a spectral model for the EPIC spectrum in which the complexity in the
6.6?7.0 keV range includes a very strong absorption line. Two possible loopholes in this
argument are: (1) an order of magnitude temporal change in the helium-like iron column
density between the XMM-Newton and Chandra grating observations, and (2) extreme
? 104 km s?1 velocity broadening of the absorption feature which would diminish its
detectability in the high-resolution spectrum. More plausible is the notion of a weak
(EW ?40 eV) and slightly broad emission line from hydrogen like iron (Fe XXVI). Given
that Chandra shows there to be a weak (EW ??20 eV) narrow Fe XXVI absorption line
at 6.97 keV, the EPIC-pn spectrum would be expected to show a net emission feature with
EW ? 20 eV.
Most importantly, however, the details of whether this spectrum complexity is de-
83
0.0 0.2 0.4 0.6 0.8 1.0
Spin Parameter
0
200
400
600
Delta Chisq
b)
Figure 4.2: (a) A kerrdisk line near 6.4 keV has been added to the phabs(po) fit, as
have two zgauss lines modeling out the narrow, cold iron line at 6.4 keV as well as the
narrow, ionized iron line at 6.9 keV. Formal ?2/dof = 960/1096 (0.88). Note the flatness
of the ratio plot shown here as compared with that shown above for the phabs(po) case.
(b) The corresponding plot of the change in ?2 vs. a for this model. Formally at 90%
confidence, a = 0.970+0.003?0.015.
84
scribed by an ionized iron emission or absorption line has almost negligible effect on the
broad iron line. In terms of the effect on the overall fit, Fabian et al. note that the relativis-
tic line parameters differ insignificantly when one employs an absorption line rather than
an emission line in the model. Getting ahead of ourselves slightly, we have checked this
result in our own analysis by replacing the 6.9 keV Gaussian in Model 4 with a 6.74 keV
Gaussian in absorption (i.e., negative flux). The result was a ??2/?dof = +26/0, indi-
cating a marginal decrease in the overall goodness-of-fit. Visually, this fit was indistin-
guishable from the best fit from Model 4, and as per Fabian et al. , we also found minimal
change in the relativistic line parameters. The inner emissivity index of the disk became
marginally steeper and its inclination angle increased very slightly, but the changes were
well within the statistical error bars. The most interesting point, however, is that the best-
fit equivalent width of this absorption line was only EW =?21.3 eV; much less than the
EW = ?138 eV found by Fabian et al. Such a modest equivalent width in comparison
to what should be necessary suggests that this line is not robustly wanted in our fit to the
data.
Returning to Model 2, the three iron lines (two narrow and one broad) that we do
choose to include significantly improve the fit (?2/dof = 960/1096(0.88)), and succeed
in modeling out the residual feature shown in Fig. 4.1. Formally at 90% confidence for
one interesting parameter, our best fit for Model 2 indicates a very rapidly rotating BH
(a = 0.970+0.003?0.015). To gauge the sensitivity of this fit to the spin of the BH, Fig. 4.2b
plots the change in the goodness-of-fit parameter ??2 as a function of BH spin parameter
a. This clearly demonstrates that ?2 improves dramatically as one approaches very rapid
spins. The equivalent width of the broad iron line in our best-fitting model is ? 729 eV,
quite a bit higher than the?550 eV cited by Fabian et al. , the 450 eV found by Ballantyne
et al. (Ballantyne et al. 2003), or the ? 250 eV found by Dov?ciak et al. (Dov?ciak et al.
2004). This unphysically high equivalent width is due to the simplicity of this model ?
85
the effects of absorption and the X-ray reflection continuum, in particular, will introduce
additional curvature into the continuum, thereby alleviating the need for such a strong
line.
4.2.2 Modeling the Warm Absorber
As discussed in Chapter 2, in order to accurately assess the width and morphology of the
iron line in an AGN, it is imperative that the soft portion of the spectrum be modeled cor-
rectly. One must be concerned about confusing a broad red wing of a relativistic iron line
with continuum curvature resulting from a putative ?warm absorber? present within the
AGN system. In fact, it has been argued that broad iron lines may be entirely unnecessary
once one correctly accounts for the effects of a WA (see Sako et al. for a discussion of
MCG?6-30-15 (Sako et al. 2003); see Turner et al. for a discussion of NGC 3516 (Turner
et al. 2005)). As mentioned in ?4.1, a deep Chandra/HETGS observation of MCG?6-
30-15 fails to find the K-shell absorption lines of the intermediate charge states of iron
predicted from a model in which a WA is mimicking the whole relativistic red wing of
the iron line. However, the question remains as to the effects that warm absorption has
on fitting of the extreme red wing of the iron line which drives BH spin constraints. Very
long data sets are needed in order to obtain spectra with enough signal to put both broad
line and WA models to the test and pursue the question of their overlap with statistical
validity. The ? 350 ks observation of MCG?6-30-15 (Fabian et al. 2002), which we use
here, is ideal for such a study because of its large number of counts and its resolution of
the broad iron feature this galaxy is thought to possess.
We have used the XSTAR spectral synthesis package for photoionized gases to con-
struct a grid of WA models as a function of the absorbed column density NH and ioniza-
tion parameter ?. This is the same grid we use and reference in Chapter 2 for the spectral
analysis of the warm absorber in NGC 4593.
86
Initially, we side-step the complexities of the soft (< 2 keV) spectrum and apply this
WA model to the 2?10 keV only. In many ways, neglecting any constraints from the
spectrum below 2 keV maximizes the impact that it may have on the broad iron line; the
sole ?job? of the absorption component in this setting is to attempt to fit the curvature
of the spectrum otherwise attributed to the broad iron line. We do notice a modest re-
duction in the goodness-of-fit parameter compared with Model 2 (the simple power-law
and kerrdisk model) ??2/?dof =?26/?2. The warm absorber in Model 3 is of mod-
est optical depth and rather weakly ionized: NH = 4.22?1022 cm?2 and log ? = 0.84.
Although the change in the goodness-of-fit is not dramatic, the additional continuum cur-
vature introduced by the warm absorber leads to a reduction in the equivalent width of the
iron line from EW = 729 eV down to the more physically reasonable value EW = 521 eV.
As can be seen from Table 4.1, the parameters that determine the best-fitting shape of the
iron line (the emissivity indices, inner radius, break radius, outer radius, inclination of the
disk and BH spin) are essentially unaffected by the inclusion of this warm absorbing com-
ponent. As shown in Fig. 4.3, a rapidly rotating BH is still preferred in this case (formal
90% confidence constraints being a = 0.997+0.001?0.035). However, in contrast to the case with
Model 2, the inclusion of a WA to the 2?10 keV spectrum allows models with low BH
spin to fit the data adequately (with low-spin cases producing a goodness-of-fit parame-
ter which is only ??2 ? 40 worse that high-spin cases) ? in these cases, the 3?4 keV
curvature is being modeled as the effects of warm absorption rather than the extreme red
wing of the iron line.
Of course, the soft X-ray band (< 2 keV) is extremely important for constraining the
properties of WAs; the opacity of most well-studied WAs is dominated by oxygen and
iron edge/line absorption in this band. Hence, to be complete, we must extend our study
of the effects of warm absorption on X-ray reflection features to the full 0.6?10.0 keV
band.
87
0.0 0.2 0.4 0.6 0.8 1.0
Spin Parameter
0
20
40
60
80
100
Delta Chisq
b)
Figure 4.3: (a) A WA table has been added to the fit to try and model the soft end of
the spectrum more accurately. Formal ?2/dof = 934/1094 (0.85). (b) ??2 vs. a plot.
Formally at 90% confidence, a = 0.997+0.001?0.035.
88
When fitting the 0.6?10.0 keV band, we find that we cannot produce an acceptable fit
with a model consisting of a simple power-law and kerrdisk line subjected to the effects
of Galactic absorption and a one-zone WA. This is not surprising: it is generally thought
that WAs must be physically more complex than a one-zone model can account for, i.e.,
they cannot be well described by a single value of the column density and ionization
parameter. Physically, the WA likely represents a wind emanating from the accretion disk
and/or cold torus surrounding the central engine and may well contain dust. A continuum
of ionization parameters likely exists along the line of sight. For computational purposes,
however, it is convenient to approximate this as a discrete number of zones, each of which
is characterized by a single column density and ionization parameter. Adding in a second
WA dramatically improves the fit and, indeed, the two absorbers do seem to represent
distinct ?zones? of material based on their physical properties (see Table 4.1 for details).
Even taking both WA models into account, however, there still appears to be signif-
icant remaining absorption in the spectrum below 2 keV, as well as a strong soft excess
below ? 0.7 keV. A strong edge due to the L3-edge of neutral iron (presumably in dust
grains embedded within the WA) has already been noted in high-resolution Chandra and
XMM-Newton grating spectra of MCG?6-30-15 (Lee et al. 2002; Turner et al. 2003). In-
corporating this edge into our fit (employing spectral tables provided to us by Julia Lee)
makes a significant visual and statistical improvement, largely explaining the unmodeled
absorption mentioned above. It is worth noting that the edge demands quite a high column
density of iron: logNFe = 17.54, which is approximately a factor of two higher than that
found by Turner et al. (Turner et al. 2003). To address the soft excess seen below 0.7 keV,
we employ a simple blackbody model. Since the data are only sensitive to the tail of this
component, the other parameters describing the spectrum are completely insensitive to
the precise model used for this soft excess. Table 4.1 details the fit, which includes two
warm absorption zones, the Fe-L3 edge and the additional soft excess.
89
0.0 0.2 0.4 0.6 0.8 1.0
Spin Parameter
0
100
200
300
400
Delta Chisq
b)
Figure 4.4: (a) A second WA has been added, as well as an iron edge at 0.707 keV and
a blackbody component to model direct disk emission below ? 1 keV. The data now
include energies from 0.6?2.0 keV. The residual feature at ? 1.8 keV is a calibration
artifact (the Si-K edge). Formal ?2/dof = 1742/1375 (1.27). (b) ??2 vs. a plot. For-
mally at 90% confidence, a = 0.997?0.001.
90
Although we cannot statistically compare the Model 3 and Model 4 fits (since we
have expanded the energy range of study between these models), Model 4 does appear
to describe the full 0.6?10 keV spectrum very well (see Fig. 4.4). As before, the data
strongly prefer a rapidly rotating BH. The inclusion of the 0.6?2.0 keV data apply extra
constraints on the WAs; the partial degeneracy found in Model 3 between the red wing
of the iron line and the curvature introduced by warm absorption is now removed. At
90% confidence, Model 4 gives formal constraints on the BH spin of a = 0.997?0.001,
and the broad iron line has an equivalent width of ? 926 eV. This is significantly higher
than we find for Models 2-3, or in any of the other analyses of this data set, and reflects
the breadth of the red wing of the iron line feature in this fit. The values for the best-fit
parameters for Model 4 are shown in Table 4.1.
Fig. 4.5 shows the unfolded spectrum for MCG?6-30-15 fit with Model 4 using a sim-
ple kerrdisk line. Each model component is colored and labeled separately to highlight
its relative contribution to the fit. Note the relatively strong blackbody component that
must be included at ? 0.1 keV in order to accurately model the spectrum below ? 2 keV,
as well as the redshifted Gaussian emission lines at 6.4 and 6.9 keV that must be added to
the broad neutral iron line to fully capture the shape of the hard spectrum.
Turner et al. have approached the question of absorption in MCG?6-30-15 by analyz-
ing the RGS spectrum from the same XMM-Newton observation used here (Turner et al.
2003). In fitting the 0.32?1.7 keV range, these authors have identified six components
of absorption: absorption by the cold Galactic column, four ?zones? of warm absorbing
plasma, and an absorbing L3 edge of neutral iron (from dust embedded in one or more
of the warm absorbing zones). Considering this detail in structure identified by Turner
et al. , it might appear that our spectral model (which only requires two WA zones plus
the neutral Fe-L3 edge to describe the spectrum) is inconsistent with the picture painted
by the RGS. Upon closer inspection, however, we see that this is not the case. Firstly,
91
Figure 4.5: A ?F? plot of the relative contributions of the model components for Model 4.
The two redshifted Gaussian components (zgauss) are shown in green and dark blue, the
kerrdisk line is in light blue, the blackbody component (bbody) representing soft emis-
sion from the disk is in purple, and the power-law continuum (powerlaw) is in red. The
soft components labeled ?abs combo? in black represent the combination of absorption
features present in the spectrum: Galactic photoabsorption, two WA models and an iron
absorption edge. The solid black line represents the combined model including all the
dashed components.
the lowest ionization WA seen in the RGS (log? ??4.42) cannot be distinguished from
neutral absorption by our 0.6?10.0 keV EPIC-pn spectrum and hence is accounted for
through the neutral absorption column present in our model. Secondly, the two high-
est ionization WAs identified by the RGS actually have rather similar ionization states
(log? ? 1.6?1.7 for Model 2 of Turner et al. ) and are only separated into two zones
through their kinematics; they are separated by ? 2000 km s?1 in velocity space by the
RGS. The EPIC-pn instrument, however, would not be able to resolve the velocity differ-
ence of these two zones. Accounting for these two facts, we would expect the Turner et
92
al. four-zone RGS model to reduce to a two-zone model when applied to EPIC-pn data.
The column densities and ionization parameters are lower in the Turner et al. fit than
in ours but, unfortunately, it is difficult to compare these values in a meaningful way
due to calibration issues in the continuum response that presently exist with RGS data.
This renders it nearly impossible to perform simultaneous RGS/EPIC-pn fits in XSPEC,
which is why we have chosen not to address such a joint fit within the scope of this
work. Cross-calibration issues similarly affect our ability to compare EPIC-pn data with
Chandra/HETGS results, making it difficult to obtain a more precise, independent check
on the model fit to energies below ? 2 keV.
4.2.3 Model Including a Full Reflection Spectrum
The broadened iron emission line of Models 1-4 is, of course, just the tip of the iceberg;
the disk produces a whole spectrum of fluorescent and recombination lines, radiation-
recombination continua and Compton backscattered continuum. To obtain truly reliable
constraints, we must consider the full X-ray reflection spectrum.
In Model 5, we take the basic continuum/absorption components of Model 4 and
augment the simple iron line with the full X-ray reflection spectrum from an ionized
disk surface (Ross & Fabian 2005). The Ross & Fabian models describe the reflected
spectrum emitted by an optically thick atmosphere (here, the surface of an accretion disk)
of constant density that is illuminated by radiation with a power-law spectrum (here,
photons that have been inverse Compton-scattered by relativistic electrons in the corona
or base of a jet). We then convolve this reflection spectrum with the effects of relativistic
smearing via kerrconv. Interestingly, as will be noted below, the soft X-ray emission
associated with the photoionized disk surface naturally explains the soft excess without
the need for an additional ad hoc blackbody component. Hence, Model 5 does not include
the blackbody component of Model 4.
93
0.0 0.2 0.4 0.6 0.8 1.0
Spin Parameter
0
100
200
300
400
500
Delta Chisq
b)
Figure 4.6: (a) The bbody component has been replaced by a smeared ionized disk re-
flection spectrum. Formal ?2/dof = 1793/1374 (1.30). Again, the residual feature at
? 1.8 keV is a calibration artifact (the Si-K edge). While this fit statistically seems less
robust than that achieved with Model 4, the ionized reflection model is thought to be more
physically accurate in its ability to account for both the soft excess as well as the broad
iron feature at 6.4 keV. (b) ??2 vs. a plot. Formally at 90% confidence, a = 0.989+0.009?0.002.
94
The best-fit parameters for this model are shown in Table 1, and in comparison with
Models 1-4 it appears that Model 5 provides a statistical fit to the data that is not as
good: (?2/dof = 1793/1374; ??2 = +51 for one more degree of freedom compared
with Model 4). Model 5 is, however, our most physical model in the sense that the whole
reflection spectrum is treated as opposed to just the iron line, resulting in a natural ex-
planation for the soft excess. That is to say that both the somewhat arbitrary blackbody
component and the broad kerrdisk line of Model 4 are not required in this fit; the soft
excess and broad iron feature are instead both fully described by the smeared radiative
recombination line/continuum emission from the irradiated accretion disk. This change
in the modeling of the soft excess increases the photon index of the continuum power-law
component to ? = 2.09, and also results in an increase in the inferred depth of the neutral
Fe-L3 edge to an iron column density of log NFe = 17.68 (over 17.54 in Model 4). The
column densities and ionization parameters of the two included WAs also vary somewhat
from Model 4, but the clear delineation between them remains evident. See Table 4.1 for
details.
The inclusion of an ionized X-ray reflection spectrum also has important implications
for the derived spin parameter, as can be seen in Fig. 4.7. The fact that a significant com-
ponent of the line broadening in this model is now due to Compton scattering reduces the
inferred BH spin to a = 0.989+0.009?0.002, slightly lower than the value determined in Model 4,
but still consistent with a very rapidly spinning BH. We do find, again, that a narrow
Fe-K? line at 6.4 keV is necessary in order to properly model the shape of the spectrum,
as well as a 6.9 keV line of ionized iron as in Model 4. The equivalent widths of these
narrow lines are 24.7 eV and 27.3 eV, respectively. Including all of these components, we
find that the total 0.6?10 keV luminosity of MCG?6-30-15 is LX = 9.34?1042 erg s?1
using WMAP cosmological parameters.
Fig. 4.7 shows the plot of the relative contributions of the best-fit model components
95
Figure 4.7: A ?F? plot of the relative contributions of the model components for MCG?
6-30-15, as above in Fig. 4.5. Now the fit is from Model 5, as shown in Fig. 4.6a. The
color scheme is the same as for Fig. 4.5, but in this case the blackbody component has
been replaced by an ionized reflection spectrum to model the soft emission as well as the
broad neutral iron line. This component appears in light blue.
for Model 5. The main features are an ionized disk reflection spectrum relativistically
blurred with a kerrconv convolution model to represent the soft emission and ionized
iron features, as well as two zgauss components to model the cold, neutral iron line at
6.4 keV and the 6.9 keV line included in previous fits (Fabian et al. 2002). The absorption
components in the soft spectrum are the same as those used for Model 4. Note that the
presence of the ionized disk reflection negates the need for the blackbody component of
Model 4 shown in Fig. 4.5.
While not essential for the principal issue of this thesis (i.e., determining BH spin),
it is instructive to estimate the ?reflection fraction? of the ionized reflection spectrum,
frefl. This parameter is defined to be proportional to the ratio of the normalization of the
96
reflection spectrum to that of the intrinsic spectrum, and normalized such that frefl = 1
corresponds to a reflector that subtends half of the sky as seen from the X-ray source.
Operationally, the ionized reflection model of Ross & Fabian is characterized by an abso-
lute normalization and hence one cannot fit trivially for frefl. We estimate this parameter
by extending Model 5 out to 100 keV and setting frefl to be the ratio of the normaliza-
tion of the reflected and intrinsic spectra at the peak of the Compton reflection hump at
35 keV. This technique yields frefl ?1.25. Previous studies have also found the reflection
parameter to be in this range for MCG?6-30-15, but it should be noted that in these cases
frefl = ?/2pi has been a fitted parameter in the reflection model used, and as such has
been considered an indication of the covering fraction of the reflecting material. For ex-
ample, Fabian et al. began their spectral fitting by assuming frefl = 1, but discovered that
when this parameter was left free they achieved better statistical fits to the data (Fabian
et al. 2002). The best-fit value determined by these authors was frefl = 2.2+1.1?0.7, which is
roughly consistent with our own, within error bars. By contrast, Lee et al. used a ?400 ks
simultaneous ASCA/RXTE observation of MCG?6-30-15 to identify four distinct spectral
states for the source (Lee et al. 2000). These authors noted that as the flux increased,
?3?10 steepened while ?10?20 gradually flattened at approximately the same rate. Lee et
al. modeled the reflection with a pexrav component in XSPEC, using a reflection inclina-
tion angle matching that of the accretion disk at i = 30? and possessing an exponential
cutoff for the Comptonizing source power-law at 100 keV. The iron abundance was main-
tained at twice the solar value. These authors found that as the source flux increased, frefl
did as well, beginning at 0.35+0.15?0.16 and topping off at 1.37+0.23?0.14. The last two flux states
are consistent with our result within error bars.
A very high iron abundance in this disk is required by our Model 5 fit (ZFe > 9.8Zcircledot
at 90% confidence). Previous studies have also detected an overabundance of iron in the
disk of MCG?6-30-15 (Ballantyne et al. 2003), though none have proposed this high an
97
abundance. If we freeze the iron abundance to be 3Zcircledot and re-fit, as in Ballantyne et al. ,
the goodness of fit parameter is increased by ??2 =+463 for one more degree of freedom,
and there are obvious residual features created in the model fit by employing this tactic.
Most of the absorption parameters remain relatively unchanged, but the disk parameters
are altered considerably: rmin = 1.88rg and rmax = 12.26rg, so the disk only radiates over
a fairly thin ring near the radius of marginal stability. The emission profile consists of
?1 = 5.60, ?2 = 1.00, and rbr = 3.22rg, reinforcing this conclusion. The inclination angle
of the disk is reduced to ? 20? from ? 30? in the best-fitting Model 5, and the spin of the
BH is considerably lowered to a = 0.31. Even though this is the best fit with ZFe = 3Zcircledot, it
is clear from the form of the residuals around 6.4 keV that the reflection spectrum is being
insufficiently broadened. Based on this fact and the substantial worsening of ?2, it appears
that our fit indeed prefers a higher abundance of iron than that found by Ballantyne et al.
Our confidence in the goodness-of-fit provided by Model 5 is strengthened by the
consistency with which the continuum model we have employed extends to fit the Bep-
poSAX/PDS spectrum of MCG?6-30-15 at high energies. The BeppoSAX observation
was taken simultaneously with the XMM-Newton in 2001 (Fabian et al. 2002), acting
as a valued ?sanity check? to the derived EPIC-pn fit by providing spectral data from
? 15?100 keV. We have performed a joint fit to the PDS and pn data within XSPEC,
applying our Model 5 to both sets of data. Even with the paucity of counts at high ener-
gies, the results of this fit clearly show that Model 5 provides an excellent description of
both the pn and the PDS continuum. The ability to place such additional constraints on
our continuum and absorption parameters gives us greater confidence in the constraints
we have correspondingly derived for the broad iron line parameters, including BH spin.
98
Model
Component
Parameter
Model
1
Model
2
Model
3
Model
4
Model
5
ph
abs
NH
(cm
?2
)
4.10
?
10
?2
4.10
?
10
?2
4.10
?
10
?2
4.10
?
10
?2
4.10
?
10
?2
WA
1
NH1
(cm
?2
)
4.22
?
10
22
2.00
?
10
22
4.17
?
10
22
log
?1
0.84
?
0.49
1.76
?
0.09
1.6
?
0.03
WA
2
NH2
(cm
?2
)
3.49
?
10
23
2.19
?
10
23
log
?2
3.90
?
0.17
3.45
?
0.09
Fe
edg
e
log
NFe
(cm
?2
)
17
.54
?
0.03
17
.68
?
0.01
bb
ody
kT
(k
eV)
9.36
?
0.28
?
10
?2
flux
(ph
cm
?2
s?
1)
3.38
?
0.68
?
10
?6
po
?po
1.91
?
0.01
1.90
?
0.01
1.97
?
0.01
1.95
?
0.07
2.09
?
0.01
flux
(ph
cm
?2
s?
1)
1.39
?
0.01
?
10
?2
1.36
?
0.01
?
10
?2
1.30
?
0.06
?
10
?3
1.07
?
0.03
?
10
?4
1.18
?
0.03
?
10
?4
ke
rrdi
sk
E(
keV)
6.58
?
0.04
6.50
?
0.04
6.40
?
0.06
ke
rrco
nv
?1
5.65
?
0.63
5.46
?
1.13
6.56
?
0.43
6.06
?
0.26
?2
2.86
?
0.11
2.66
?
0.26
2.44
?
0.27
2.78
?
0.18
rbr
(rg
)
5.75
?
0.82
5.68
?
1.6228
5.14
?
0.87
5.56
?
0.66
a
0.970
+0
.003
?0
.015
0.997
+0
.001
?0
.035
0.997
?
0.001
0.989
+0
.009
?0
.002
i(?
)
20
?
2
23
?
2
29
?
2
30
?
1
rmin
(rg
)
1.74
?
0.24
1.28
?
0.18
1.28
?
0.16
1.62
?
0.08
rmax
(rg
)
113
?
2
102
?
1
134
?
1
397
?
495
flux
(ph
cm
?2
s?
1)
2.98
?
0.36
?
10
?4
1.78
?
0.33
?
10
?5
2.68
?
0.52
?
10
?6
re
fl
Fe/solar
10
.00
?
0.72
log
?refl
2.03
?
0.00
?refl
2.09
?
0.01
flux
(ph
cm
?2
s?
1)
1.51
?
0.32
?
10
?7
?2
/dof
4577
/1106
(4.
14)
960
/1096
(0.
88)
934
/1094
(0.
85)
1742
/1375
(1.
27)
1793
/1374
(1.
31)
Table
4.1:
Models
1?
3are
from
2?
10
keV,
Models
4?
5also
include
ener
gies
from
0.6
?
2.0
keV.
Error
bars
quoted
are
all
at
the
1?
lev
el
except
for
those
on
the
spin
parameter
,which
are
all
at
formal
90%
confidence.
1?
errors
for
the
column
densities
of
the
WAs
were
not
well
constrained.
For
Model
5,
the
kerrconv
component
has
no
line
ener
gy
or
flux
parameters,
and
the
lar
ge
error
bars
on
the
maximum
disk
radius
indicates
that
this
parameter
is
not
rob
ustly
constrained.
99
4.2.4 Ruling out a Schwarzschild Black Hole
As mentioned above, Dov?ciak et al. and Beckwith & Done argue that broad lines cannot
be used as BH spin diagnostics due to the degeneracy that exists between the physical
parameters that go into composing the line profile (Beckwith & Done 2004; Dov?ciak
et al. 2004). We contend that this is not necessarily the case; broad lines can be used to
constrain BH spin if one takes into account the physical realism of the best-fit parameters.
The degeneracy between parameters makes it difficult to calculate the precise angular
momentum for a given BH, but we can nonetheless statistically rule out certain regions of
parameter space provided that the data used has the spectral resolution to enable accurate
model fitting.
In the case of MCG?6-30-15, the Fabian et al. data set is noteworthy for its length
and unprecedented resolution of the broad iron feature. This makes it an ideal candidate
for examining the parameter space of the new models in question. The width of the iron
line implies that this feature is produced in the accretion disk immediately surrounding a
rapidly spinning BH, and indeed the best-fit kerrdisk parameters for the simplest model
including an iron line (Model 2, from 2?10 keV) suggest that a = 0.970+0.003?0.015 with 90%
confidence (see Fig. 4.2a). The kerrdisk parameters are consistent with those of the
kyrline best fit as well. Given that the fits excluding emission from within the radius of
marginal stability imply a near-maximal spin for the BH, here we pose the question ?can
we rule out the non-spinning case if we relax the restriction of no emission from within
the radius of marginal stability??
To answer this question we utilize the kyrline model, since kerrdisk does not yet
include emission from within the ISCO. In previous fits to MCG?6-30-15 using low-spin
BH models, it has been found that the fit demands an inner emission radius well within
the radius of marginal stability (Dov?ciak et al. 2004). Substituting two kyrline model
100
components for the kerrdisk component in the 2?10 keV fit, we freeze a = 0.0 and re-fit
the data as in Model 2. Two kyrline components are used because the publicly released
version of kyrline does not support a broken power-law emissivity index for the disk (as
does kerrdisk), so we must divide the disk up into two effective regions: one extending
outwards from rms, and one interior to rms representing the plunging region. Because
the plunging region is physically distinct from the disk proper, any lack of continuity
between either the emissivity indices or the fluxes of the two components is not considered
problematic.
The simplest kyrline fit for a Schwarzschild BH is based on Model 2. Visually it
does not differ perceptibly from the kerrdisk best fit for Model 2, and statistically it
is a slightly better fit: ??2/?dof = ?15/0 between the two fits. Most notable about
the fit, however, is that when we force a = 0.0, the fit demands an inner radius that is
deep within the plunging region (rmin = 3.43?0.19rg as compared with rms = 6rg for
a Schwarzschild BH) with an extremely high inner emissivity index ?1 = 9.08?1.36.
Within the plunging region of a Schwarzschild BH, we expect the radial component of
the 4-velocity to be
ur =?c
radicalBigg
8
9 ?
parenleftbigg
1? 2r
parenrightbiggparenleftbigg
1+ 12r2
parenrightbigg
(4.1)
where, here, r is measured in units of rg = GM/c2 (Reynolds & Begelman 1997). For
r ? 3.43 we have ur ??0.22c, i.e., the material is already inflowing at mildly relativistic
velocities. Hence, conservation of baryon number demands that this part of the accretion
flow be extremely tenuous and, given that by assumption it is subjected to an intense X-
ray irradiation, this material must be fully ionized (Reynolds & Begelman 1997; Young
et al. 1998). More quantitatively, the analysis of Reynolds & Begelman shows that the
ionization parameter of the accreting matter at this radius will exceed log? = 4 for any
reasonable accretion efficiency; this is essentially fully ionized and will not imprint any
obvious atomic signatures on the backscattered spectrum. It is therefore extremely un-
101
likely that a disk with such a steep emissivity profile and an inner radius so deep within
the plunging region is an accurate physical model of the real system.
We have also performed a Schwarzschild fit to the data based on the more complex
best-fitting model from 0.6?10.0 keV (Model 5). Recall that in this case we have in-
troduced an ionized disk reflection component to the fit, which serves the dual purpose
of modeling the soft excess and the broad Fe-K? line at 6.4 keV. Whereas before in
Model 5 we convolved our reflection spectrum with a kerrconv component, here we use
a kyconv model instead because we are demanding that a = 0.0 in this case, and antic-
ipate that a large fraction of the emission will come from within the ISCO, as was the
case for our Schwarzschild fit based on Model 2 above. Following the approach outlined
above, we use two kerrconv components to allow for a broken power-law emissivity
index in the disk. Qualitatively similar results are obtained; the inner radius of the X-ray
reflection in such a model is rmin = 3.02?0.31rg with an extremely steep inner emis-
sivity index (?1 = 15.00?3.12). As before with the simpler case of a Schwarzschild
fit to Model 2, this implies that the vast majority of the emission of this model compo-
nent originates well inside the ISCO, which is not physically realistic. The ionization
parameter for the reflector has also risen marginally for the Schwarzschild case from
log?refl = 2.03?0.03 to 2.26?1.13. The iron abundance has remained very high at
Fe/solar = 10.0?0.23, as was the case in Model 5. Even with these adjustments in pa-
rameters, however, the Schwarzschild fit visually fails to account for the entire breadth
and shape of the 6.4 keV iron line. In this case, the formal ?2/dof = 2855/1377 (2.08),
as compared with 1793/1374 (1.35) for the Model 5 fit where BH spin is a free parameter.
Based on these arguments for Model 2 and Model 5 (the best-fitting cases for 2?
10 keV and 0.6?10 keV, respectively) we can make a strong case that a non-rotating BH
cannot viably produce the broad iron feature in MCG?6-30-15.
102
4.3 Discussion
4.3.1 Summary of Results
In fitting the hard spectrum of MCG?6-30-15 with the kerrdisk model, we have shown
that the data prefer a fit with a spin parameter that tends towards the maximum value.
A non-spinning BH can produce a formally adequate fit (although still statistically worse
than that achieved with a free spin parameter), but further requires a significant fraction of
the X-ray reflection to originate unphysically deep within the plunging region. One might
argue that for flows accreting at close to the Eddington rate, the radius of dynamical
stability might be pushed to the marginally bound orbit, rather than the marginally stable
orbit (Abramowicz et al. 1990; Chen et al. 1997). In principle this would mean that
the optically thick part of the flow could come substantially closer to the event horizon,
resulting in significantly more broad line contribution from this region. However, in the
case of a Schwarzschild hole the marginally bound orbit is still at a radius of rmb =
4rg, which is well outside the minimum radius of emission we get for the Schwarzschild
fit based on Model 5, where rmin = 3.02?0.31rg. The radial velocity of the infalling
material at this point would be nearly c/3 if released from rmb, so the material itself
would be quite optically thin and highly ionized, and so would not be likely to contribute
much to the overall iron line profile. Also, it is unlikely that MCG?6-30-15 is accreting
close to the Eddington rate.
In fact, for the rapidly-spinning BH preferred by our spectral fitting, the issue of un-
modeled emission from within the radius of marginal stability diminishes in importance.
For such rapidly spinning BHs, the geometric area of the disk within this radius is small
and the gravitational redshift of this region is extreme. Hence, we suspect that the inclu-
sion of reasonable amounts of emission from within the radius of marginal stability will
103
have negligible impact on our best-fitting spectral parameters, including the spin of the
BH.
The best-fitting model for the full 0.6?10 keV data set appears to be Model 5. The
hard spectrum is best represented by a power-law continuum and two Gaussian features
of iron at 6.4 (neutral) and 6.9 keV (ionized). The soft portion of the spectrum below
? 2 keV is well fit by relativistically blurred emission reflected from the surface of an
ionized disk that is modified by a two-zone WA, an iron absorption edge, and Galactic
photoabsorption. This ionized emission also contributes to the breadth and morphol-
ogy of the observed iron feature near 6.4 keV. As described above in ?4.2.3, this model
yields a formal, 90% confidence best-fit spin parameter for the BH in MCG?6-30-15 of
a = 0.989+0.009?0.002. Due to the aforementioned degeneracies in the broad iron line model
parameters (Chapter 3) this value should not be interpreted as exact, but the fact that near-
maximal spin is approached in each of the Models 2-5 strongly indicates that the data
prefer a rapidly spinning BH.
4.3.2 Conclusions
Both Dov?ciak et al. and Beckwith & Done make valid points about the difficulty of accu-
rately calculating the spin parameter of a BH based on broad line profiles from the disk
alone (Beckwith & Done 2004; Dov?ciak et al. 2004). Given the number of parameters
governing the kerrdisk line profile (nine, to be exact), some degeneracy between them
is certainly to be expected, and it is possible to generate statistically indistinguishable line
profiles using different combinations of parameters. This does not render the use of broad
lines as spin diagnostics obsolete, however: provided that one uses care in determining
whether parameter values are physically reasonable, it is possible to at least constrain the
spin parameter to be within a certain range of values. In the example of MCG?6-30-15
above, we have clearly shown that the data rule out a non-spinning black hole if we also
104
demand that the values for the disk emissivity indices are physically realistic. The plots of
??2 vs. a clearly show the improvement in fit achieved when one frees the spin parameter.
In this case the fit strongly tends toward maximal spin.
The combination of such a high spin and such a high iron abundance in the disk may
understandably give one pause when considering the precision of our best-fitting Model 5.
Both a and ZFe push the upper limits of their respective parameter spaces in order to try
to account for the extreme breadth and strength of the Fe-K? feature in the spectrum. As
we have mentioned, however, in this thesis we are seeking to establish a robust method
for constraining BH spin via X-ray spectroscopy and are not claiming that our best-fit
parameter values should be interpreted as exact. The spin of the BH may indeed reach
a = 0.989, but there could also be some contribution to the line from highly redshifted
radiation originating from within the ISCO that we have not yet accounted for, which
could reduce the need for such a high spin value. What we can say with confidence is
that fits to the data with a Schwarzschild BH are not physically sound. Likewise, the
disk may indeed have nearly ten times the solar value of iron, but underabundances in
some of the lighter elements may also simulate an effectively iron-rich environment which
could contribute to the observed width of the Fe-K? line (Reynolds et al. 1995). Suzaku
observations of this source are already proving invaluable for untangling the parameters
of the ionized reflection model (Miniutti et al. 2007). Much work remains to be done on
the subjects of modeling accretion disks and isolating black hole spins, and improvements
in the former will undoubtedly help us place more accurate constraints on the latter.
If MCG?6-30-15 is indeed a rapidly spinning BH, as seems likely given our spec-
tral modeling, it is astrophysically interesting for several reasons. As mentioned in ?4.1,
rapidly spinning holes can, in principle, experience a magnetic torque by the fields thread-
ing the accretion disk at the radius of marginal stability. This torque can theoretically
extract rotational energy from the hole itself, significantly enhancing the amount of dis-
105
sipation in the inner accretion disk. The steepest dissipation profiles would be obtained
if the magnetic torque is applied completely at the radius of marginal stability (Agol &
Krolik 2000). Therefore, only for rapidly spinning BHs would one expect to observe such
a steep dissipation profile: in this scenario rms is dragged inward very close to the event
horizon, so the torque is strongest here. Such an effect would manifest itself via strongly
redshifted reflection features in the spectrum, since the strong dissipation very close to
the event horizon would mean that most of the emission would originate from this re-
gion. Based on its own best-fit emission profile, MCG?6-30-15 may in fact be giving us
a glimpse of this phenomenon at work (Wilms et al. 2001). It should be noted, however,
that interpreting the detected reflection features in this way demands that little of the ob-
served emission originate from the plunging region within rms. Taken in this context, the
relatively steep emissivity index we found for the ionized disk in our best-fitting Model 5
(a = 0.989, ?1 = 6.06) is not unexpected, and may be indicative of this type of magnetic
torquing.
Finally, it is important to note that the 350 ks observation employed here for our spec-
tral modeling provided us with an extraordinary number of photons to work with: well
over 106 counts. This is due in part to the length of the exposure, but also to the intrinsic
brightness of MCG?6-30-15 (FX ?6?10?11 erg cm?2 s?1 ). With such a high number of
counts we are able to better constrain the parameters in kerrdisk and kerrconv. Unfor-
tunately, for many other AGN not as bright in X-rays and not as well-studied, we simply
do not have enough data to constrain parameters such as BH spin as robustly as we would
like. In the following Chapter we detail our analyses of several other broad iron line AGN
using the techniques outlined in our studies of NGC 4593 and MCG?6-30-15.
106
Chapter 5
Spectral Fits to Other Broad Iron Line
AGN
We have presented detailed spectral fits for two quite different Sy-1 AGN: NGC 4593 (no
evidence to support a broad iron line) and MCG?6-30-15 (evidence for the broadest iron
line yet observed). These two sources represent opposite ends of the parameter space in
terms of our ability to constrain BH angular momentum. Because we detect no broad Fe-
K? feature in NGC 4593, we are unable to apply the kerrdisk and kerrconv models to
fit for BH spin since we are not observing a line signature from the inner part of the disk
where relativistic effects are important. It could be that the accretion disk is truncated at
some large distance in this source, perhaps transitioning to an ADAF-type flow close to
the event horizon. In the case of MGC?6-30-15, by contrast, we have an abundance of X-
ray photons that clearly resolve a line with a broad red wing extending down to ? 3 keV.
These data have allowed us to place formal constraints on the BH spin of a > 0.987 (90%
confidence level) although, as explained in the previous chapter, this constraint might
weaken somewhat if the iron line emission region does in fact bleed inside of the ISCO.
In order to begin probing the question of BH spin distribution across the AGN pop-
107
ulation we clearly need to expand our sample. In this thesis we restrict our attention to
several other nearby Sy-1 AGN in an effort to reduce the number of environmental vari-
ables that may be involved in spin determination (e.g., no GBHs, though we do intend to
expand our source list further in the future to accommodate such objects and compare the
results to those of our AGN sample). Because the kerrdisk and kerrconv models rely
on the presence of broad iron lines in the X-ray spectrum in order to constrain BH spin,
we have also restricted our source list to include only those Sy-1 AGN that have robustly
been observed to harbor broad iron lines based on previous studies with XMM-Newton
and/or Chandra (Miller 2007; Nandra et al. 2006).
The question of what BH spin distribution we should expect to see among Sy-1 AGN
is not a simple one. Unlike GBHs, whose spins are thought to be chiefly natal due to
the small masses and/or short lifetimes of their stellar companions, AGN are quite old
and massive, and are thought to have grown from a combination of mergers and accretion
over their long histories. By comparing observations of BHs in local galaxies and AGN
to a model of what the BH mass function would look like for a given local population
whose BHs were grown solely by accretion, Marconi et al. find that mergers are not sig-
nificant in the evolution of local supermassive BHs. The authors suggest that mergers
might play a more prominent role for SMBHs beyond z = 3 (Marconi et al. 2004). Deter-
mining the spin of such sources would therefore provide us with a new parameter to use
in constraining the role and efficiency of accretion in evolving local SMBHs, and would
also aid in assessing the relative contributions of accretion vs. mergers in higher redshift
sources. Similarly, Volonteri et al. have used numerical simulations to predict how mas-
sive BHs should form and evolve. They find that the coalescence of comparable-mass
BHs increases their BH spins, while the capture of smaller BH companions in randomly
oriented orbits reduces the spin of the primary BH. Given the distribution of massive BH
binary mass ratios in hierarchical models, binary mergers alone do not lead to a system-
108
atic spin-up or spin-down of SMBHs with time. By contrast, because of the alignment of
a SMBH with the angular momentum of the outer accretion disk, gas accretion tends to
increase BH spin over time. Overall in the Volonteri et al. models, accretion dominates
over mergers and efficiently increases BH spin. The spin distribution is heavily skewed
toward rapidly rotating holes, is already in place at early epochs, and does not change
much below z = 5. If accretion occurs via a geometrically thin disk, about 70% of all
massive BHs are maximally rotating. Even in the conservative case in which accretion
is via a geometrically thick disk, about 80% of all massive BHs have a > 0.8 (Volonteri
et al. 2005). Given these predictions and the increasing computing power of such complex
numerical simulations, the time is ripe for culling observational evidence to see whether
the data support such hypotheses.
In the following Section we outline the method used for the data reduction and spectral
analysis of the AGN in our sample. We then discuss the modeling and results from each
source in its own subsection. Finally, we compare the results from all the sources in
our sample and discuss their physical implications for BH spin distribution and evolution
among Sy-1 AGN.
5.1 Data Reduction and Spectral Analysis Methodology
Our source selection was based on recent work by Nandra et al. and a review by Jon Miller,
both of whom consider the robustness of broad iron line detections across different source
populations (Miller 2007; Nandra et al. 2006). The Miller review, in particular, collects
all the recent X-ray data published on Seyfert sources and categorizes these objects by the
strength and robustness of their broad iron line features. We have used these two studies
as a guide for selecting the candidates for our sample.
Our data have been collected from the XMM-Newton Science Archive, using only
109
publicly available observations. XMM-Newton data were preferentially used as opposed
to Chandra data because of the superior collecting area of XMM-Newton in the 2?10 keV
band where the broad Fe-K? feature is the most prominent. Though Suzaku is producing
very interesting results, there are not enough publicly available data collected by that
instrument to undertake such a study at this time, though whenever possible we intend to
use Suzaku data to supplement our XMM-Newton results in the future.
We focus our study exclusively on the EPIC-pn data due to cross-calibration issues
mentioned previously in Chapter 2 between the pn, MOS and RGS instruments. Though
the RGS spectra in particular can provide detailed insight into the 0.3?2.0 keV spectrum
and help illuminate the nature of the soft absorption and excess seen in so many Sy-1
AGN, the cross-calibration issues unfortunately render it nearly impossible to correlate
those results with the continuum and iron line spectrum observed by the EPIC-pn instru-
ment. Because of the higher effective area of the pn, these data are more useful in our
work.
For each source in question we have performed reprocessing (when necessary) and
data reduction with the SAS version 7.0.0 software, including the latest CCF calibra-
tion files. Source and background spectra and light curves were extracted using the
xmmselect task from the SAS GUI. Response matrices and ancillary response files were
generated using the rmfgen and arfgen tasks. These were then grouped with the spectral
files using the FTOOLS package grppha with a minimum of 25 counts/bin in order to use
?2 as a meaningful goodness-of-fit statistic. Spectral analysis was carried out as before
for NGC 4593 and MCG?6-30-15 with XSPEC version 11.3.2 and our local kerrdisk
and kerrconv models installed.
We have made the spectral analysis method as uniform as possible for all the AGN
examined. There are, however, certain intrinsic physical differences between the sources
that must be taken into account in order to properly model the continuum and isolate
110
the iron line(s) in each case. Though all our sources are Sy-1 AGN, each system is
unique in its physical properties. Some have more photons than others to work with,
either because of higher flux, longer observation time or both. Some exhibit evidence
for complex, multi-zone warm absorbers, whereas some show only cold absorption from
neutral hydrogen along our line of sight. A soft excess is seen in some sources but not
others. And of course, the strength and breadth of the Fe-K? line varies from source to
source as well, though all have been chosen because they have previously shown evidence
for broad iron lines.
In order to examine the iron line(s) in detail the continuum must first be accurately
modeled. After excluding the energy ranges relevant to the iron line (?4.0?8.0 keV) and
the mirror edges (? 1.5?2.5 keV), we examine the rest of the 0.6?10.0 keV spectrum,
fitting it with a power-law continuum typical of an AGN which is then modified by cold
photoabsorption from neutral hydrogen. We typically set the minimum value of NH equal
to the Galactic column density along our line of sight to the source1 and allow it to vary
as necessary to accommodate the cold absorption in the system. Some sources require a
second, unabsorbed power-law component as well to properly model the basic continuum
shape. We disregard energies below ? 0.6 keV due to calibration uncertainties in this
range for the EPIC-pn instrument.
If significant residual features remain after fitting this absorbed power-law which in-
dicate the presence of a soft excess and/or warm absorption, we include these components
one by one as long as they make a significant difference in the global goodness-of-fit ac-
cording to the f-test (??2 ??4 for each new parameter introduced into the fit (Bevington
1969)). The soft excess is typically parameterized by a blackbody component represent-
ing the thermal disk emission, but may also be modeled by bremsstrahlung emission or
Comptonized emission from a thermal disk if either of these more complex forms gives
1This parameter is determined from H I 21 cm surveys. See http://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3nh/w3nh.pl for the column density calculator and relevant references.
111
a significantly better reduction in ?2. The warm absorption is modeled using the same
XSTAR-generated multiplicative table model described in Chapters 2 and 4 in the analysis
of NGC 4593 and MCG?6-30-15. Solar abundances are assumed for all elements and the
redshift is set at the source value. Some sources show no need for a WA model, while
others statistically require up to two physically separate WA components, each exhibiting
a distinct column density (NH) and ionization parameter (?).
Once the continuum has been properly modeled, we freeze the parameter values
for all components except the power-law spectral index (?) and normalization (flux in
ph cm?2 s?1 ) and restrict our energy range from 2.5?10.0 keV in order to focus on the
hard X-ray spectrum and the iron line region. Including the energies from 4.0?8.0 keV
again, we check for residual emission (or absorption) lines from 6.4?6.97 keV, indi-
cating the presence of unmodeled neutral and/or partly ionized Fe-K? in the spectrum.
Because these sources have been pre-determined to possess significant, broadened iron
emission, such residual emission features are seen in each case. We begin by attempting
to fit the 6.4 keV line of neutral iron (and any other ionized lines) with a simple Gaussian
feature, with the line width frozen at ? = 0 keV (i.e., intrinsically narrow) and the red-
shift again set to the source value. As expected, in each case we note significant residual
?wings? remaining around the Fe-K? feature after this narrow core was fit, indicating the
presence of a broad component to the line.
To assess the robustness of this broad iron component and to obtain constraints on the
BH spin, if possible, we then run each source through an ?analysis tree? of progressively
more complex modeling. Our procedure is outlined below:
1. Add in a laor component (a = 0.998) at the energy of the Fe-K? line and refit,
noting the corresponding change in ?2/dof to verify whether a broad line is sta-
tistically warranted in the model. Also note the inner radius of disk emission: a
broad line with the potential to diagnose BH spin should have an inner disk radius
112
of rmin lessorsimilar 6rg. We relax this restriction here to allow for differences in fit that may
be achieved through different models, requiring that rmin lessorsimilar 20rg.
? If the broad line is not statistically warranted, simply constrain the upper limit
of the equivalent width of the line.
? If the broad line is at least marginally statistically warranted, replace the laor
component with a kerrdisk component (a = 0?0.998) and refit, noting
again the corresponding change in ?2/dof. The inner disk radius and BH
spin as well as their statistical constraints should also be noted.
2. Rather than simply modeling the Fe-K? line in isolation, replace the broad line
component with a static ionized disk reflection spectrum (Ross & Fabian 2005).
3. To the static ionized disk reflection spectrum, add in the effects of relativistic smear-
ing from the spacetime around a maximally rotating BH using the kdblur convolu-
tion model (a = 0.998). Again note the statistical difference in the goodness-of-fit
to determine the importance of relativistic effects, as well as the inner radius of disk
emission. This gives us a rigorous measure of the degree to which broadening is
required even when reflection is accounted for.
? If the inner radius of disk emission is sufficiently close to the event horizon
(again using rmin lessorsimilar 20rg), the line may be sufficiently broad and relativistic
effects may be sufficiently important to allow us to constrain BH spin. Re-
place the kdblur component with kerrconv (a = 0?0.998) in order to place
statistical constraints on rmin and a.
It should be noted that we force the outer radius of disk emission to be rmax = 400rg
(or 400rms in the case of kerrdisk and kerrconv, which parameterize disk emission
radius in units of the radius of marginal stability) in all the broad line fits. The value
113
itself is somewhat arbitrary; the purpose of freezing this component at a large value is
to force the inner portions of the disk to determine the line profile morphology. For
the ionized disk component, we begin with the assumption of solar iron abundance and
relative neutrality (Fe/solar = 1 and ? = 30). If the fit is sufficiently robust, we then
relax these assumptions and allow these two parameters to fit freely. For kerrdisk and
kerrconv, we initially assume that the inner and outer portions of the disk emit under
the same emissivity index: ?1 = ?2, where the disk radiates as r?? at any given radius.
Again, if the fit is sufficiently robust, these indices are ?untied? and allowed to each fit
freely, but due to limitations in the number of photons we have for each data set, the only
source with enough counts to support a scenario where ?1 negationslash= ?2 is MCG?6-30-15.
5.2 Results for Our Sample of Sy-1 AGN
As mentioned in the previous Section, we have selected the AGN for our sample primarily
based on the research performed by other groups on the robustness of broad iron line
observations in various AGN and the likelihood of obtaining viable spin constraints from
these sources using the iron line method (Miller 2007; Nandra et al. 2006). In particular,
Jon Miller discusses recent results from 30 Seyfert AGN in which relativistic disk lines
have been detected and published, and divides those sources up into three ?tiers? based
on the nature and robustness of the detections. Many of the sources overlap with those
presented in Nandra et al. Though we have examined observed spectra from all of the 9
AGN listed in Tier 1 (the most robust cases), NGC 3516 and NGC 4151 were not included
in our study due to their extremely complex soft spectra (Schurch et al. 2004; Turner et al.
2005). We did analyze the other 7 sources in full: 3c120, MCG?6-30-15, MCG?5-23-16,
NGC 2992, NGC 4051, NGC 3783 and Mrk 766. Additionally, we have examined 3 other
sources from Tier 3 that are mentioned prominently in Nandra et al. : Fairall 9, Ark 120
114
and 3c273.
We present the results of our spectral analysis of these sources in the following Sec-
tions.
5.2.1 MCG?5-23-16
MCG?5-23-16 is a moderately absorbed Seyfert galaxy of intermediate type (Sy-1.9). It is
relatively nearby at a redshift of z = 0.0085, and with a typical 2?10 keV flux of F2?10 ?
8?10?11 erg cm?2 s?1 it is one of the brightest known Seyfert galaxies (Reeves et al.
2006). The source has been observed previously to have a soft excess below ? 1 keV and
an absorbing column of NH ?1022 cm?2 (Balestra et al. 2004; Dewangan et al. 2003), and
ASCA observations have indicated the presence of a broad Fe-K? line of EW ? 200 eV
(Weaver et al. 1998, 1997). The line was successfully modeled with a narrow core at the
rest-frame energy of 6.4 keV and a broad component superposed on it. This feature was
modeled with similar success in the XMM-Newton observations of Dewangen et al. and
Reeves et al. , as well as the Suzaku observation also published by these authors (Reeves
et al. 2007).
In December 2005, MCG?5-23-16 was simultaneously observed with XMM-Newton,
Chandra, Suzaku and RXTE. The XMM-Newton results are reported by Reeves et al. , and
our data reduction followed that work (Reeves et al. 2006). The EPIC-pn instrument had
a net exposure of 96 ks and returned ? 2.2?106 photons after filtering.
As suggested by Reeves et al. , a simple photoabsorbed power-law fit does not model
the continuum well, especially below ? 1 keV. Adding in a source of soft thermal emis-
sion also leaves prominent residuals and does not adequately account for the shape of
the soft excess, so following the lead of Reeves et al. we have employed a two-power-
law model (Reeves et al. 2006): one of the power-law components is affected only by
Galactic photoabsorption (NH = 8?1020 cm?2 as per Reeves et al. ), and hence leaves
115
the AGN system effectively unscattered, while the other component is also subject to
absorption intrinsic to the AGN, in this case with a fitted absorbing column density of
NH = 1.19?1022 cm?2 . This component also experiences scattering within the system.
Both power-law indices are locked together, indicating that the two components originate
from the same physical reservoir of photons with ? = 1.66. Calculating the ratio of the
flux of the scattered power-law component to the unscattered power-law component (from
0.6?10.0 keV, fitting only the continuum) yields an estimate of the optical depth of the
scattering plasma. In this case ? = 7.37?10?4 ph cm?2 s?1 /1.83?10?2 ph cm?2 s?1 ?
0.04, so the scattered fraction is low, implying that the electron plasma is optically thin.
The continuum spectrum also shows evidence for two prominent, narrow emission
lines of iron K? and K? (at EK? = 6.4 keV and EK? = 7.0 keV, with EWK? = 167 eV and
EWK? = 104 eV, respectively), as well as three narrow absorption lines of intermediately
ionized iron at E1 = 7.24 keV, E2 = 7.48 keV and E3 = 7.85 keV (EW1 =?79 eV, EW2 =
?121 eV, and EW3 =?143 eV, respectively).
After successfully modeling the continuum and narrow line parameters for MCG?5-
23-16, we restricted our attention to the hard spectrum (2.5?10.0 keV) and analyzed
the broad line component of this source using the method outlined above in ?5.1. Note
that eliminating soft energies from the fit removed the statistical need for a second, soft
power-law in the fit. For a full listing of best-fit model parameters and error bars for
MCG?5-23-16, see Table 5.1. The residual iron line feature in the hard spectrum is shown
in Fig. 5.1. Our best fit to this feature is shown in Fig. 5.2, and the relative contributions
of the individual model components are shown in Fig. 5.3. The best-fitting model for
MCG?5-23-16 is the ionized disk reflection spectrum (Ross & Fabian 2005) convolved
with kerrconv. Although we were not able to constrain the BH spin in this source, we
did achieve a fit constraint on the inner radius of the disk emission: rmin ? 16rms, which
equates to 84rg if we convert using the fit value for BH spin (a = 0.362). Given that
116
Figure 5.1: The 2.5?10.0 keV spectrum of MCG?5-23-16 fit with a two-power-law
model modified by Galactic photoabsorption. Note the prominent residual iron feature
that remains with a rest-frame energy of 6.4 keV, as well as several other emission and
absorption features and a hard energy ?tail? above 8 keV, indicating the possible presence
of ionized disk reflection.
the effective inner edge of the disk is not within the radius of marginal stability for a
Schwarzschild BH, it is not surprising that we were not able to constrain the value of the
BH spin in this source.
5.2.2 NGC 3783
NGC 3783 is a bright, nearby Sy-1 galaxy at a redshift of z = 0.0097. It was first de-
tected in X-rays with the Ariel-V all-sky survey (McHardy et al. 1981) and subsequently
in the high Galactic latitude survey conducted by HEAO-1 (Piccinotti et al. 1982). Since
these early detections, there have been many observations of NGC 3783 with higher res-
olution instruments: A ROSAT observation of the source showed evidence of an ionized
117
Model Component Parameter Value
phabs NH1 ( cm?2 ) 8?1020
phabs NH2 ( cm?2 ) 1.19+0.01?0.01?1020
po ?po 1.66+0.01?0.01
flux( ph cm?2 s?1 ) 1.98+0.04?0.13?10?2
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 4.00+0.35?0.32?10?5
EW( eV) 167.00+14.61?13.36
zgauss E( keV) 7.00
flux( ph cm?2 s?1 ) 9.80+2.98?2.87?10?6
EW( eV) 104.00+31.62?30.46
zgauss E( keV) 7.24
flux( ph cm?2 s?1 ) ?7.39+2.84?2.73?10?6
EW( eV) ?78.70+30.24?29.07
zgauss E( keV) 7.48
flux( ph cm?2 s?1 ) ?6.93+2.83?2.84?10?6
EW( eV) ?121.00+49.41?49.59
zgauss E( keV) 7.85
flux( ph cm?2 s?1 ) ?9.62+2.90?2.86?10?6
EW( eV) ?143.00+43.11?42.51
kerrconv ?1 2.45+0.59?0.61
?2 2.45+0.59?0.61
rbr (rms) 6.0
a ???
i(?) 45.88+2.34?19.42
rmin (rms) 15.66+13.40?7.33
rmax (rms) 400
reflion Fe/solar 0.61+0.08?0.05
?refl < 31.09
?refl 1.66+0.01?0.01
flux( ph cm?2 s?1 ) 1.64+0.10?0.10?10?5
?2/dof 1484/1487(1.00)
Table 5.1: Best-fitting model parameters for the 2.5?10.0 keV spectrum of MCG?5-23-
16, including components and parameter values from 0.6?1.5 keV for completeness.
The energies from 1.5?2.5 keV were not included due to the presence of absorption
edges from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. For the
zgauss lines, we required each to be intrinsically narrow, i.e., ? = 0.0. Redshifts were
frozen at the cosmological value for the source, in this case z = 0.0085. Note the absence
of warm absorption and a soft excess in this object. When no error bars are quoted, the
parameter in question is frozen at the given value.
118
Figure 5.2: The 2.5?10.0 keV best-fit model for MCG?5-23-16, including our con-
tinuum model, two narrow emission lines, and five narrow absorption lines as well as
an ionized disk reflection spectrum convolved with our kerrconv relativistic smearing
kernel. The residuals have all but disappeared. For parameter values, see Table 5.1.
absorber in the soft band (Turner et al. 1993), which was confirmed during ASCA obser-
vations (George et al. 1998a, 1995). High-resolution grating observations of NGC 3783
with Chandra and XMM-Newton followed, unveiling the soft spectrum of this source in
detail (Behar et al. 2003; Blustin et al. 2002; Kaspi et al. 2002, 2001, 2000). The higher
signal-to-noise of XMM-Newton, in particular, has also enabled the iron line to be studied
extensively in this source (Reeves et al. 2004). Using two observations from December
2001, Reeves et al. have obtained ? 240 ks of data on NGC 3783. Their global fits to the
merged EPIC-pn spectrum are currently second in length and depth only to the ? 350 ks
observation of MCG?6-30-15 (Fabian et al. 2002). In these observations, the source has
an average 2?10 keV flux of F2?10 = 6.8?10?11 erg cm?2 s?1 . The spectrum is noted to
have iron line peaks at 6.4 keV and 7.0 keV, representing neutral Fe-K? (EW ? 120 eV)
119
Figure 5.3: A ?F? plot depicting the relative flux in each of the best-fit model components
in the 2.5?10.0 keV spectrum of MCG?5-23-16.
and a blend of ionized Fe-K? and Fe-K? (EW ? 35 eV), respectively. A strong absorp-
tion line of highly ionized iron is also observed at 6.67 keV that exhibits variability in
direct correlation with that of the continuum flux. A weak red wing of the 6.4 keV line
is noted by the authors, but once warm absorption is taken into account in the system
the requirements for a broad Fe-K? component are significantly reduced (Reeves et al.
2004).
We analyzed the first of the two December 2001 XMM-Newton observations. We
chose not to merge the event files of both data sets to avoid the uncertainties inherent
in so doing, instead focusing on only one data set with an effective exposure time of
? 120 ks and a total of ? 1.8?106 photons after filtering. This number of counts is
still large enough to obtain valid statistical fits to the model parameters used. We follow
the data reduction steps of Reeves et al. , excluding the last bit of the observation due to
120
contamination from a background flare. Our analysis follows in the same spirit as these
authors, but in order to remain consistent with the method described above in ?5.1 we
do not make any assumptions about the soft spectrum and continuum emission based on
prior RGS results (Blustin et al. 2002).
We begin our analysis of the time-averaged spectrum with a simple photoabsorbed
power-law fit using the Galactic absorbing column of NH = 8.5?1020 cm?2 , and ne-
glecting the energy ranges associated with the mirror edges and the iron lines, as in ?5.1.
This fit leaves obvious residuals in all parts of the spectrum, however, and is especially
poor for the soft energies below ? 1.5 keV. Continuum curvature associated with a soft
excess and warm absorption are both clearly evident. As discussed by Reeves et al. , the fit
is much improved with the addition of a thermal blackbody component (kT ? 0.07 keV,
as compared with their value: kT ? 0.09 keV). We approach the question of the warm
absorption similarly as well, using our XSTAR table model to parameterize the column
density and ionization level of the absorbing medium, as do Reeves et al. As with these
authors, we find statistical evidence for a two-zone warm absorption structure, though
our values for the column densities and ionization parameters of these zones vary signif-
icantly from those of Reeves et al. We find NH1 = 6.84?1023 and log?1 = 0.00, with
NH2 = 1.58?1023 and log?2 = 1.40, whereas Reeves et al. find NH1 = 6.00?1020 and
log?1 = 0.30, with NH2 = 4.60?1022 and log?2 = 2.90. These differences are not sur-
prising, however, because Reeves et al. base their fits on the RGS results for this source
(Blustin et al. 2002). We do not use any a priori information to augment or guide the
EPIC-pn spectral fits due to calibration uncertainties. Finally, we allowed the value of
the neutral hydrogen absorbing column to vary in an effort to improve the goodness-
of-fit and found that the spectrum preferred a higher value than the Galactic column:
NH = 3.60?1021 cm?2 . This was also in contrast to the Reeves et al. result, where the
cold hydrogen column was held at the Galactic value and not permitted to vary.
121
Reeves et al. found two emission peaks in the spectrum at 6.4 keV (EW ?120 eV) and
7.0 keV (EW ?35 eV), representing cold Fe-K? and likely a blend of ionized Fe-K? and
Fe-K?, respectively. The latter line, in particular, showed no appreciable variance over
the observation, leading the authors to postulate a relatively distant origin for the lines
away from the central parts of the accretion disk. A 6.67 keV absorption feature of highly
ionized iron was also seen which did appear to vary with time and was strongest when
the continuum flux was highest, suggesting an origin in the region of the warm absorber
within 0.1 parsec of the nucleus. Though inclusion of the WA and this feature did lessen
the statistical case for a broad iron line in NGC 3783, Reeves et al. nonetheless identified
a residual broad feature which they fit using a diskline model with ? ? 3.3, i ? 19?,
and EW ? 58 eV.
We also detected the emission and absorption features discussed by Reeves et al. ,
though we found that the equivalent widths for the Fe-K?, Fe-K?/K? blend and ionized
iron absorption lines differed from the fits performed by these authors: EWK? = 79.0 eV,
EWK?/K? = 23.9 eV and EWabs = ?25.1 eV. We did not test the time variance of the
absorption component because such an examination is beyond the scope of this work. It
should also be noted that, contrary to the Reeves et al. analysis, we required the core of
the 6.4 keV line to be intrinsically narrow, so it is not unusual that we obtain a smaller
equivalent width than Reeves et al. When we included the broad component of the neutral
K? line, the fit improved dramatically. Our best fit to the hard spectrum of NGC 3783
convolved an ionized disk reflection spectrum with kerrconv, as can be seen in Table 5.2
below, but due to the relative narrowness of the iron line we were not able to constrain
the BH spin in this source. Not surprisingly, our constraints on the radial extent of the
disk showed that rmin < 390rms, or < 985rg, calculated using the nominal fit value of
spin (a = 0.869). A line emitted from so far out in the disk would not exhibit relativistic
signatures.
122
Model Component Parameter Value
phabs NH2 ( cm?2 ) 3.60+0.01?0.01?1021
WA 1 NWA1 ( cm?2 ) 6.84+0.42?0.20?1023
log?WA1 < 0.01
WA 2 NWA2 ( cm?2 ) 1.58+0.06?0.04?1023
log?WA2 1.40+0.04?0.02
po ?po 2.50+0.02?0.02
flux( ph cm?2 s?1 ) 4.60+0.09?0.12?10?4
bbody kT ( keV) 0.07+0.00?0.00
flux( ph cm?2 s?1 ) 4.86+0.36?0.31?10?4
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 3.07+0.45?0.46?10?7
EW( eV) 79.00+11.58?11.84
zgauss E( keV) 7.00
flux( ph cm?2 s?1 ) 8.20+2.09?2.05?10?8
EW( eV) 23.90+6.44?6.35
zgauss E( keV) 6.67
flux( ph cm?2 s?1 ) ?1.12+0.21?0.21?10?7
EW( eV) ?25.10+4.71?4.71
kerrconv ?1 ???
?2 ???
rbr (rms) 6.0
a ???
i(?) 36+11?10
rmin (rms) < 391
rmax (rms) 400
reflion Fe/solar 0.19+0.03?0.04
?refl < 40.10
?refl 2.50+0.02?0.02
flux( ph cm?2 s?1 ) 2.97+0.74?0.77?10?6
?2/dof 1526/1486(1.03)
Table 5.2: Best-fitting model parameters for the 2.5?10.0 keV spectrum of NGC 3783,
including components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. For the zgauss
lines, we required each to be intrinsically narrow, i.e., ? = 0.0. Redshifts were frozen at
the cosmological value for the source, in this case z = 0.0097. Note the two-zone warm
absorber and blackbody soft excess present in this object, similar to many other Sy-1
sources.
123
Figure 5.4: The 2.5?10.0 keV spectrum of NGC 3783 fit with a power-law model modi-
fied by Galactic photoabsorption, along with a two-zone warm absorber and a blackbody
soft excess. Note the prominent residual iron features that remain with rest-frame ener-
gies of 6.4 keV and 7.0 keV, as well as an absorption feature of ionized iron at 6.67 keV.
5.2.3 Mrk 766
Mrk 766 is designated as a classic, bright NLS1 galaxy (Sy-1.5) with a redshift of z =
0.0129 and a typical 2?10 keV flux of F2?10 ? 2.5?10?11 erg cm?2 s?1 (Pounds et al.
2003b). Previous X-ray observations of this source have provided contradictory evidence
on the detection of a broad Fe-K? feature. Although not one of the most convincing cases,
Mrk 766 was included in an ASCA spectral survey of bright Seyfert galaxies showing ev-
idence of relativistic iron lines (Nandra et al. 1997). A separate analysis of simultaneous
ROSAT and ASCA observations (Leighly et al. 1996), however, showed the X-ray spec-
trum to be described by a power-law of index increasing strongly with flux from ? ? 1.6,
but with only a narrow Fe-K? emission line (EW ? 100 eV at 6.4 keV). A later observa-
124
Figure 5.5: The 2.5?10.0 keV best-fit model for NGC 3783, including our continuum
model, two narrow emission lines and a narrow absorption line as well as an ionized
disk reflection spectrum convolved with our kerrconv relativistic smearing kernel. The
residuals have all but disappeared. For parameter values, see Table 5.2.
tion with BeppoSAX found a steeper power-law (??2.2), and evidence for an absorption
edge at ? 7.4 keV (Matt et al. 2000), implying strong reflection from intermediately ion-
ized material. Interestingly, based on XMM-Newton observations of the source, Turner
et al. found that energy-time maps of Mrk 766 reveal a periodic energy shift in an ion-
ized component of Fe-K? emission, with a period of ? 165 ks. This can be interpreted
as evidence for emission from orbiting gas within ? 100rg of the central BH. A likely
explanation is that this gas represents a hot spot on the disk illuminated by magnetic
reconnection (Turner et al. 2006).
We examine the May 2001 XMM-Newton observation of Mrk 766 taken by Mason et
al. , from which the RGS results were published in 2003 (Mason et al. 2003) and the EPIC
spectra were explored more thoroughly by other authors (Pounds et al. 2003b; Turner et al.
125
Figure 5.6: A ?F? plot depicting the relative flux in each of the best-fit model components
in the 2.5?10.0 keV spectrum of NGC 3783.
2006). In our re-analysis, the EPIC-pn data have an effective exposure time of 128 ks and
the filtered data yield ? 2.92?106 photons.
Mrk 766 bears many spectral similarities to MCG?6-30-15, showing significant com-
plexity beyond a simple photoabsorbed power-law fit. There is clear evidence for a
thermal (bbody: kT = 0.08 keV) soft excess below ? 1 keV as well as two distinct
physical zones of low (NH1 = 5.26?1022 cm?2 , log?1 = 0.21) to moderately ionized
(NH2 = 9.50?1023 cm?2 , log?2 = 3.04) intrinsic absorption. These components exist in
addition to cold absorption by the Milky Way (NH = 1.71?1020 cm?2 ). The power-law
in this source has a spectral index of ? = 2.75, comparable with the result published by
Pounds et al. Unfortunately, these authors did not probe the spectrum below 3 keV, so we
cannot compare our soft excess or warm absorption parameters to theirs. Our blackbody
component has a flux that is 1% that of the power-law component.
126
The narrow Fe-K? core of Mrk 766 has a rest-frame energy of 6.4 keV, as expected,
and an EW = 33.7 eV, again comparable with the findings of Pounds et al. Fitting this line
with a Gaussian component leaves significant residuals strongly indicative of the presence
of a broad line. This broad component is most successfully fit with a kerrconv(refl)
model, yielding comparable results to the disk reflection model employed to model the
broad iron line in Pounds et al. , though with different fit parameters. Our model also
detects no absorption features above 8 keV, as discussed by Pounds et al. , possibly due
to advances in modeling the reflection spectrum. The BH spin, to 90% confidence, is
relatively high at a > 0.85 and the inner edge of the accretion disk is constrained to
rmin < 2.25rms. The best-fit results are shown in Table 5.3. Figs. 5.7-5.9 show the iron
line residual, best fit to this residual, and relative contributions of the individual model
components, respectively.
5.2.4 3c273
3c273 is the most distant source in our sample at a redshift of z = 0.1583. Classified
as a bright variable quasar, this AGN displays a strong jet and during epochs of radio-
loudness it possesses the flat X-ray spectrum of a blazar, with highly beamed jet emission
(T?urler et al. 2006). When the jet is reduced in strength, however, this source has been
observed to exhibit Sy-1-type accretion disk signatures such as a broad iron line. This
minimum state occurred in March 1986 and allowed astronomers (Robson et al. 1986)
to identify a new near-infrared spectral component. An even better opportunity arose in
early 2004, when the sub-millimeter flux of 3c273 was observed to be almost two times
lower than in 1986. This new minimum triggered a slew of simultaneous observations
with instruments in all wavebands such as INTEGRAL, XMM-Newton and RXTE, among
several other optical, radio and sub-millimeter telescopes. The 2?10 keV flux during
this period was F2?10 = 6.7?10?11 erg cm?2 s?1 . Such a low flux in 3c273 has only
127
Model Component Parameter Value
phabs NH ( cm?2 ) 1.71+0.24?0.00?10?2
WA 1 NWA1 ( cm?2 ) 5.26+0.16?0.31?1022
log?WA1 0.21+0.01?0.03
WA 2 NWA2 ( cm?2 ) 9.50+0.05?0.02?1023
log?WA2 3.04+0.08?0.07
po ?po 2.75+0.05?0.06
flux( ph cm?2 s?1 ) 2.05+0.08?0.12?10?4
bbody kT ( keV) 0.08+0.00?0.00
flux( ph cm?2 s?1 ) 1.88+0.32?0.26?10?6
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 4.71+1.35?1.90?10?8
EW( eV) 33.70+9.66?13.59
kerrconv ?1 1.93+0.15?0.13
?2 1.93+0.15?0.13
rbr (rms) 6.0
a 0.99+0.01?0.14
i(?) 74+7?1
rmin (rms) < 2.25
rmax (rms) 400
reflion Fe/solar 1.0
?refl 579+274?134
?refl 2.75+0.05?0.06
flux( ph cm?2 s?1 ) 8.29+1.05?1.05?10?6
?2/dof 1492/1309(1.14)
Table 5.3: Best-fitting model parameters for the 2.5?10.0 keV spectrum of Mrk 766,
including components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the zgauss line representing the core of the Fe-K? feature to be intrinsically narrow,
i.e., ? = 0.0. Redshifts were frozen at the cosmological value for the source, in this case
z = 0.0130. A two-zone warm absorber and blackbody soft excess are present in this
object, as in MCG?6-30-15 and many other Sy-1 sources.
128
Figure 5.7: The 2.5?10.0 keV spectrum of Mrk 766 fit with a continuum composed
of a power-law model modified by Galactic photoabsorption, a two-zone warm absorber
model and a blackbody soft excess. Note the prominent residual iron feature that remains
with a rest-frame energy of 6.4 keV.
been measured twice in the past, by Ginga in July 1987 (Turner et al. 1990) and by
BeppoSAX on 18 July 1996 (Haardt et al. 1998), the latter of which was coincident with
the low sub-mm flux mentioned above. This X-ray/sub-mm correlation strongly supports
a synchrotron self-Compton origin for the X-ray jet emission in 3c273.
T?urler et al. obtained a 20 ks XMM-Newton observation of 3c273 during this jet-
minimum state in June 2004. We use their thin-filter EPIC-pn observation in the interest
of collecting as many photons as possible, though due to photon pile-up it is necessary
to exclude the centralmost region of the source, as detailed by the authors (T?urler et al.
2006). In our filtered data set we capture ? 7.5?105 photons.
T?urler et al. note the inadequacy of a simple photoabsorbed power-law fit to the data.
Their best fit to the continuum is achieved using two power-law components: ?hard =
129
Figure 5.8: The 2.5?10.0 keV best-fit model for Mrk 766, including our continuum
model and an ionized disk reflection spectrum convolved with our kerrconv relativistic
smearing kernel. The residuals have mostly disappeared.
1.63?0.02 and ?soft = 2.69?0.06, with the hard component flux ? 2.3 times the soft
flux. Both components were modified by Galactic photoabsorption with NH = 1.79?
1020 cm?2 . We based our initial continuum fit on theirs, with two power-law components:
?hard = 1.72+0.11?0.28 and ?soft = 3.01+1.29?0.71, both consistent with the T?urler et al. results. Our
hard/soft flux ratio is 4.18, however, significantly higher than that calculated by T?urler et
al. , and the error bars on the spectral indices led us to consider eliminating the soft com-
ponent, in particular. Our best-fitting continuum model therefore, has only one power-law
component at ? = 2.03 and exhibits the same statistical goodness-of-fit as the two power-
law model.
Evidence for excess emission from 2.5?7.0 keV was also found by T?urler et al. ,
supporting the presence of a broad Fe-K? line when 3c273 is in a jet-minimum state.
130
Figure 5.9: A ?F? plot depicting the relative flux in each of the model components in the
2.5?10.0 keV spectrum of Mrk 766.
The authors quote this excess as significant at the 6? level with an integrated flux of
2.6?0.4?10?4 ph cm?2 s?1 , corresponding to an EW = 166?26 eV. These values are
consistent with those reported from previous observations of the source in a jet-minimum
state (Kataoka et al. 2002; Page et al. 2004; Yaqoob & Serlemitsos 2000). The breadth of
the excess is not satisfactorily fitted by a Gaussian line or a diskline component from
a non-rotating BH. If the line extent is real, the only remaining explanation, according to
the authors, is that it is emitted from around a near-extreme Kerr BH. The sharp edge of
the iron line at 7 keV suggests that the angle of inclination of the accretion disk is 35?40?
(T?urler et al. 2006).
We find evidence for a similar excess around the Fe-K? line in our analysis. Inter-
estingly, we do not see a narrow emission line at 6.4 keV, but rather the narrow line core
seems to coincide with the He-like line of Fe-K? at 6.66 keV with an EW = 73.3 eV.
131
This implies that the gas in this system is highly ionized, which is not surprising in such
an active source. Visually, the residuals left over after fitting this narrow line suggest the
presence of a broad component. Modeling this component with our analysis method only
provides a marginal improvement in the global goodness-of-fit, however, so we cannot
consider the presence of a broad line robust in 3c273 in spite of the suggestive appearance
of the hard X-ray excess and residuals after adding in a narrow iron line. We are limited
in this case by the distance of the source and the paucity of the data. With a 20 ks observa-
tion we have collected < 3?105 photons from 2.5?10 keV. Given more observing time
and a larger number of (pile-up free) photons, our line analysis would be significantly
improved. Taking into account these caveats about the robustness of the broad line, our
kerrconv(refl) model provides the best fit, as shown in Table 5.4. Figs. 5.10-5.12
show the iron line residual, best fit to this residual, and relative contributions of the indi-
vidual model components in the best fit, respectively. To 90% confidence, a > 0.72 and
rmin < 2.30rms.
The question of how BH spin correlates with radio-loudness still remains unanswered.
Sikora et al. have examined the radio-loud/radio-quiet dichotomy in AGN and argue that
BH spin is a critical factor in determining the radio-loudness of an AGN. The authors
conclude that both spiral-hosted and elliptical-hosted AGN show radio-loudness increas-
ing with decreasing Eddington ratio and that the large host-morphology-related difference
between the radio-loudness reachable by AGN in disk vs. elliptical galaxies can be ex-
plained by the dual postulates that (1) the spin of a BH determines the jet outflow power,
and (2) AGN BHs can reach large spins only in early type galaxies following major merg-
ers (Sikora et al. 2007). The latter seems to conflict with the hypothesis that BHs most
likely reach near-maximal spin values through steady accretion since mergers can theoret-
ically occur with random BH spin directions (Volonteri et al. 2005). Also, the extremely
high spin observed in MCG?6-30-15, in particular, serves as evidence that high BH spins
132
Figure 5.10: The 2.5?10.0 keV spectrum of 3c273 fit with a power-law model modified
by Galactic photoabsorption. Note the subtle residual iron feature that remains with a
rest-frame energy of 6.4 keV.
can be found in AGN hosted by disk-type galaxies. If the 3c273 result is found to be
robust, we now also have an example of a radio-loud quasar with a moderately high BH
spin. These conflicts between data and theory highlight the growing need for observations
of BH spin in a large sample of AGN with varying physical characteristics (e.g., mass,
radio-loudness, etc.).
5.2.5 3c120
Like the quasar 3c273, 3c120 is also a prominent radio source that has been seen to
display broad, Sy-1-like emission lines in its optical spectrum when its jet is in a low
state. Classified as a BLRG, it is the brightest such source in the sky though it is rela-
tively distant at a redshift of z = 0.0330. Its 2?10 keV X-ray flux is quoted at F2?10 =
133
Figure 5.11: The 2.5?10.0 keV best-fit model for 3c273, including our continuum model
and an ionized disk reflection spectrum convolved with our kerrconv relativistic smear-
ing kernel. The residuals have mostly disappeared.
4.2?10?11 erg cm?2 s?1 (Sambruna et al. 1999). It is thought that perhaps the prodi-
gious activity of this source could mean that it is in the late stages of a merger. This
hypothesis is based on the residence of the AGN in a rather peculiar galaxy lacking much
in the way of spiral structure and having a randomly oriented velocity field, in addition to
showing evidence of recent starburst activity (Heckman et al. 1986). Radio observations
have shown the presence of a superluminal jet ranging from sub-parsec to nearly 100-kpc
scales. The upper limit on the inclination angle of the jet has been calculated to i ? 14?
(Eracleous & Halpern 1998), which may provide us with an independent constraint on
the accretion disk inclination angle as well (Ballantyne et al. 2004). Although a very
strong and broad Fe-K? line was originally detected with ASCA (Reynolds 1997; Sam-
bruna et al. 1999), recent X-ray observations with RXTE (Eracleous et al. 2000; Gliozzi
134
Figure 5.12: A ?F? plot depicting the relative flux in each of the model components in
the 2.5?10.0 keV spectrum of 3c273.
et al. 2003) and BeppoSAX (Zdziarski & Grandi 2001) have constrained the Fe-K? line
to be only modestly strong at EW ? 100 eV.
XMM-Newton observed 3c120 in August 2003 for 127 ks, yielding ? 2.08?106 pho-
tons in the filtered data set. The EPIC-pn data were analyzed fully and determined not
to be affected by pile-up, and the results were published the following year along with
a simultaneous RXTE observation (Ballantyne et al. 2004). We have re-analyzed this
observation, following the data reduction of Ballantyne et al.
A soft excess is clearly seen in the data below ? 1 keV, which is best fit with a
bremsstrahlung emission model (zbremss), as suggested by Ballantyne et al. This emis-
sion, with kT = 0.70, is superposed on a photoabsorbed power-law continuum with
? = 1.81 and possesses 91% of its flux. The goodness-of-fit is significantly improved
with the inclusion of cold photoabsorption from neutral hydrogen within the system
135
Model Component Parameter Value
phabs NH ( cm?2 ) 1.79+1.88?0.00?10?2
po ?po 2.03+0.30?0.12
flux( ph cm?2 s?1 ) 3.82+0.47?0.83?10?2
zgauss E( keV) 6.66
flux( ph cm?2 s?1 ) 9.30+0.76?0.75?10?5
EW( eV) 73.30+5.99?5.91
kerrconv ?1 4.22+1.78?1.48
?2 4.22+1.78?1.48
rbr (rms) 6.0
a > 0.72
i(?) < 63
rmin (rms) < 2.30
rmax (rms) 400
refl Fe/solar 1.0
?refl < 355.88
?refl 2.03+0.30?0.12
flux( ph cm?2 s?1 ) 1.70+10.12?1.37 ?10?4
?2/dof 288/265(0.86)
Table 5.4: Best-fitting model parameters for the 2.5?10.0 keV spectrum of 3c273, in-
cluding components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the zgauss line representing the core of the Fe-K? feature to be intrinsically narrow,
i.e., ? = 0.0. Interestingly, this line was found at a moderate ionization state of iron
(6.66 keV) rather than at the neutral rest-frame energy of 6.4 keV. Redshifts were frozen
at the cosmological value for the source, in this case z = 0.1583. No warm absorption or
soft excess is seen in this object.
(NH = 1.35?1021 cm?2 , total) on top of the absorption from our own Galaxy (NH =
1.11?1021 cm?2 ). Absorption from moderately ionized gas is also robustly detected with
a column density of NWA = 1.51?1022 cm?2 and an ionization parameter of log? = 2.15.
Two remaining residuals are detected around 6.4 keV and 6.9 keV, marking cold and
ionized iron emission lines. The 6.9 keV line is quite weak, with an EW = 11.9 eV.
Including another Gaussian line at 6.4 keV (with a fitted EW = 4.5 eV), we see that sig-
nificant residuals remain around the wings of the line, strongly implying a broadened
component. Running all of our broad line fits to this feature, we find that it is best mod-
136
eled with a kerrconv(refl) component, statistically, though its BH spin and the inner
edge of the accretion disk are not well constrained: a < 0.83, rmin < 332rms. Even though
we obtain 90% confidence constraints on the BH spin, given the uncertainty in rmin we
cannot claim robust evidence for a spin detection. In this case, the iron line is simply
not broad enough to allow us to place meaningful constraints on BH spin. The best-fit
parameter values for 3c120 are reported in Table 5.5. Figs. 5.13-5.15 show the iron line
residual, best fit to this residual, and relative contributions of the individual model com-
ponents in this fit. Note that we have allowed the inclination angle of the accretion disk to
fit freely, not constraining its value to i?14? as has been done in Ballantyne et al. in order
to keep our results unbiased and see if we reach the same inclination angle independently.
In our fit, we find that i = 27?36?, with 90% confidence, and that constraining i ? 14?
worsens the statistical goodness-of-fit. This provides an interesting contrast to the results
from radio observations.
5.2.6 NGC 2992
NGC 2992 is a Sy-1.9 galaxy that appears to show a broad iron line even though it is
highly obscured. This source has been the subject of intense study due to the variability
of its X-ray emission (Gilli et al. 2000). In 1997 and 1998, BeppoSAX caught NGC 2992
transitioning from a Compton-thick to a Compton-thin state, resulting in an order of mag-
nitude increase in its X-ray luminosity as well as a qualitative difference in its spectral
appearance, with more disk features (e.g., broad lines) being seen in several wavelengths.
The source has a redshift of z = 0.0077. In the two BeppoSAX pointings, NGC 2992 dis-
plays a 2?10 keV X-ray fluxes of 0.63 and 7.4?10?11 erg cm?2 s?1 (Gilli et al. 2000).
We use the May 2003 XMM-Newton observation of NGC 2992, totaling 29 ks, which
translates to ? 6.02?105 photons in the filtered data set. This observation appears to be
unpublished, so all the fit values referenced herein are our own, compiled using the re-
137
Model Component Parameter Value
phabs NH ( cm?2 ) 1.35+0.01?0.01?1021
WA NWA ( cm?2 ) 1.51+0.68?0.51?1022
log?WA 2.15+0.33?0.16
po ?po 1.81+0.01?0.01
flux( ph cm?2 s?1 ) 1.07+0.00?0.02?10?3
zbremss kT ( keV) 0.70+0.15?0.07
flux( ph cm?2 s?1 ) 9.76+1.19?1.73?10?4
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 1.70+13.16?1.54 ?10?7
EW( eV) 4.91+38.01?4.45
zgauss E( keV) 6.90
flux( ph cm?2 s?1 ) 4.16+1.99?1.91?10?7
EW( eV) 11.90+5.69?5.46
kerrconv ?1 0.24+1.15?0.24
?2 0.24+1.15?0.24
rbr (rms) 6.0
a < 0.83
i(?) 28+8?1
rmin (rms) < 332
rmax (rms) 400
reflion Fe/solar 1.0
?refl < 35.84
?refl 1.81+0.01?0.01
flux( ph cm?2 s?1 ) 4.69+0.49?0.36?10?7
?2/dof 1468/1460(1.01)
Table 5.5: Best-fitting model parameters for the 2.5?10.0 keV spectrum of 3c120, in-
cluding components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the zgauss lines to be intrinsically narrow, i.e., ? = 0.0. Redshifts were frozen at
the cosmological value for the source, in this case z = 0.0330. A warm absorber and
bremsstrahlung soft excess are present in this object, as in many other Sy-1 sources.
138
Figure 5.13: The 2.5?10.0 keV spectrum of 3c120 fit with a continuum composed of a
power-law model modified by Galactic photoabsorption, a warm absorber model and a
bremsstrahlung soft excess. Note the prominent residual iron features that remain with
rest-frame energies of 6.4 keV and 6.9 keV.
duction and analysis methods detailed in the first portion of this Chapter and in particular
in ?5.1.
Upon first inspection, it is immediately clear that NGC 2992 is heavily absorbed be-
low ? 2 keV. Though statistical evidence exists for a soft excess, none of the telltale
signatures of intrinsic warm absorption are present, and the flux decreases precipitously
at soft energies. When a simple photoabsorbed power-law model plus blackbody emis-
sion is applied to the continuum, the remaining residuals on the soft end indicate that some
absorption remains unaccounted for, but allowing the column density of hydrogen to fit
freely above the Galactic value of NH = 5.26?1020 cm?2 neatly corrects the discrepancy.
The final continuum parameters are NH = 5.11?1021 cm?2 , ? = 1.69 and kT = 0.05 keV
with the power-law flux 1.4 times greater than that of the blackbody component.
139
Figure 5.14: The 2.5?10.0 keV best-fit model for 3c120, including our continuum model
and an ionized disk reflection spectrum convolved with our kerrconv relativistic smear-
ing kernel. The residuals have all but disappeared.
The Fe-K? line is present with a narrow core at 6.4 keV and EW = 38.8 eV. Sig-
nificant residuals remain surrounding the core, however, and the best statistical fit is
achieved with a kerrconv(refl) model. See Table 5.6 for model parameters and er-
ror bars. Figs. 5.16-5.18 show the iron line residual, best fit to this residual, and rel-
ative contributions of the individual model components for the best fit. Note that the
BH spin cannot be constrained. Constraints are also difficult to achieve on the disk
emissivity index ?, especially, though we have constrained the effective inner disk ra-
dius to rmin < 11.78rms. These large error bars are seen due to the paucity of pho-
tons in the hard band (2.5?10 keV) in this observation: with only 29 ks and a flux of
F2.5?10 = 8.06?10?11 erg cm?2 s?1 , we have < 2?105 photons to use in spectral fitting.
This is only a small fraction (< 20%) of the number of counts we have at our disposal for
140
Figure 5.15: A ?F? plot depicting the relative flux in each of the model components in
the 2.5?10.0 keV spectrum of 3c120.
the same energy range in MCG?6-30-15, so it is not surprising that our statistics are not
as sound in this case.
5.2.7 NGC 4051
NGC 4051, like NGC 2992, is a heavily absorbed Seyfert AGN (Sy-1.5; NLS1) seen to
vary significantly in flux over the course of several observations (Guainazzi et al. 1996;
Lamer et al. 2003). The source is at a redshift of z = 0.0023 and has a typical flux
on the order of a few times 10?11 erg cm?2 s?1 , though as stated above, this flux can
vary significantly on a variety of time scales, along with the spectral characteristics of the
source. Unusually low flux states in this object can last for weeks to months, during which
time the X-ray spectrum shows a hard continuum power-law of spectral slope ? ? 1, but
is dominated by a softer component at lower energies with ? ? 3 (Uttley et al. 2004).
141
Figure 5.16: The 2.5?10.0 keV spectrum of NGC 2992 fit with a continuum composed
of a power-law model modified by Galactic photoabsorption as well as a blackbody soft
excess. Note the prominent residual iron feature that remains with a rest-frame energy of
6.4 keV.
A highly broadened and redshifted iron line has also been noted in the low flux state of
NGC 4051 with RXTE, suggesting that reflection features from the accretion disk close
to the BH may remain constant in this source in spite of the large variations in continuum
properties (Uttley et al. 2003).
NGC 4051 was observed with XMM-Newton in May 2001 for a duration of 117 ks,
yielding ? 3.27?106 photons in the filtered data set. The EPIC-pn results were first
reported by Mason et al. , and suggested a continuum described by a power-law ?piv-
oting? around 100 keV, according to a simultaneous observation with RXTE. Ultraviolet
emission from the Optical Monitor on XMM-Newton was found to lag the X-ray emis-
sion by ? 0.2 days, indicating that it is likely reprocessed X-ray emission. The X-ray
emission itself showed variability on time scales as small as 1?2 hours (Mason et al.
142
Figure 5.17: The 2.5?10.0 keV best-fit model for NGC 2992, including our continuum
model and an ionized disk reflection spectrum convolved with our kerrconv relativistic
smearing kernel. The residuals have all but disappeared.
2002). These results were expanded upon by Pounds et al. , who noted the intermediate
flux of the source at this time and validated the presence of both an iron line and a thermal
soft excess during the May 2001 observation (Pounds et al. 2004). Ponti et al. recently
re-analyzed this observation as well as a lower-flux pointing from November 2002 and
reinforced the veracity of this model, while also considering the comparable efficacy of a
model dominated by ionized reflection from radii quite close to the BH (Ponti et al. 2006).
We have also focused on the May 2001 observation of NGC 4051, following the
reduction and analysis of Mason et al. and Ponti et al. but using modern calibration files.
A two power-law model parameterized the continuum with much greater accuracy than
either a single power-law, a broken power-law or a ?pivoting? power-law of the type
employed in previous X-ray spectral analyses. Hard and soft components were detected:
143
Figure 5.18: A ?F? plot depicting the relative flux in each of the model components in
the 2.5?10.0 keV spectrum of NGC 2992.
?hard = 2.01 and ?soft = 5.20. The hard/soft flux ratio for these components is 1.21, and
each is modified by photoabsorption from neutral hydrogen with NH = 7.63?1020 cm?2 .
This column density is greater than the Galactic value by a factor of ? 6, indicating the
presence of cold absorption within the NGC 4051 system. Additionally, there is statistical
evidence to support the presence of a warm absorber within the AGN as well: a significant
improvement in the global goodness-of-fit is seen with the inclusion of one of our XSTAR
multiplicative table models with a hydrogen column density of NWA = 5.08?1022 cm?2
and log?WA = 0.06. Note that this warm absorber is essentially neutral, implying that
it does not experience significant heating from the central engine and may exist at some
distance from the source of the X-ray emission in NGC 4051. Finally, a soft excess is
also seen below ? 1 keV, as in so many other Seyfert galaxies. The best fit to this feature
is achieved with a thermal blackbody component, with kT = 0.27 and a flux ? 120 times
144
Model Component Parameter Value
phabs NH ( cm?2 ) 5.12+0.09?0.10?1021
po ?po 1.69+0.02?0.03
flux( ph cm?2 s?1 ) 2.14+0.08?0.07?10?2
bbody kT ( keV) 0.05+0.01?0.01
flux( ph cm?2 s?1 ) 1.53+5.01?0.93?10?2
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 1.85+2.32?1.54?10?5
EW( eV) 38.80+48.66?32.30
kerrconv ?1 7.36+2.64?6.12
?2 7.36+2.64?6.12
rbr (rms) 6.0
a ???
i(?) 41+7?21
rmin (rms) 2.50+9.28?1.50
rmax (rms) 400
reflion Fe/solar 1.0
?refl 30.0
?refl 1.69+0.02?0.03
flux( ph cm?2 s?1 ) 2.49+0.85?0.77?10?5
?2/dof 1402/1312(1.07)
Table 5.6: Best-fitting model parameters for the 2.5?10.0 keV spectrum of NGC 2992,
including components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the 6.4 keV zgauss line core to be intrinsically narrow, i.e., ? = 0.0. Redshifts were
frozen at the cosmological value for the source, in this case z = 0.0077. No evidence
for warm absorption is detected, though a soft excess is found in this object, as in many
other Sy-1 sources.
smaller than the hard power-law component.
A narrow 6.4 keV Gaussian was successfully fit to the core of the Fe-K? line in this
source, though by forcing the line to be narrow (i.e., freezing ? = 0.0) we note significant
residuals marking the red and blue wings of the broadened line. The narrow core has an
EW = 57.8 eV. The remaining broad line is best fit with a kerrconv(refl) model hav-
ing a BH spin of a > 0.67 and an rmin = 2.25?4.62rms. Full parameter values and 90%
confidence error bars are listed in Table 5.7. Figs. 5.19-5.21 show the iron line residual,
145
Figure 5.19: The 2.5?10.0 keV spectrum of NGC 4051 fit with a continuum composed
of two power-law models modified by Galactic photoabsorption, a warm absorber model
and a blackbody soft excess. Note the prominent residual iron feature that remains with
a rest-frame energy of 6.4 keV.
best fit to this residual, and relative contributions of the individual model components,
respectively.
5.2.8 Ark 120
Ark 120 is a bright Sy-1 AGN with an estimated BH mass of ?2?108 Mcircledot (Wandel et al.
1999) and a bolometric luminosity of Lbol ? 1045 erg s?1 (Edelson & Malkan 1986). At
a redshift of z = 0.0327, this source has a relatively constant 2?10 keV X-ray flux of
F2?10 ? 2.50?10?11 erg cm?2 s?1 (Vaughan et al. 2004). The source is radio-quiet, and
due to a lack of observed evidence for intrinsic absorption, Ark 120 has been labeled a
?bare? Sy-1 nucleus (Ward et al. 1987). Its host galaxy is an early-type spiral of Hubble
146
Model Component Parameter Value
phabs NH ( cm?2 ) 7.63+1.97?3.29?1020
WA NWA ( cm?2 ) 5.08+0.83?0.72?1022
log?WA < 0.06
po ?po 5.20+0.12?0.35
flux( ph cm?2 s?1 ) 6.13+0.61?0.58?10?4
po ?po 2.01+0.08?0.06
flux( ph cm?2 s?1 ) 7.43+0.51?0.47?10?4
bbody kT ( keV) 0.27+0.02?0.01
flux( ph cm?2 s?1 ) 6.31+1.29?1.14?10?6
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 1.05+0.33?0.31?10?6
EW( eV) 57.80+18.17?17.06
kerrconv ?1 6.78+3.22?2.55
?2 6.78+3.22?2.55
rbr (rms) 6.0
a 0.98+0.01?0.31
i(?) 38+3?3
rmin (rms) 3.37+1.25?1.13
rmax (rms) 400
reflion Fe/solar 1.89+3.80?0.64
?refl < 107.77
?refl 2.01+0.08?0.06
flux( ph cm?2 s?1 ) 7.55+6.28?5.56?10?7
?2/dof 1475/1394(1.06)
Table 5.7: Best-fitting model parameters for the 2.5?10.0 keV spectrum of NGC 4051,
including components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the 6.4 keV zgauss line to be intrinsically narrow, i.e., ? = 0.0. Redshifts were frozen
at the cosmological value for the source, in this case z = 0.0023. A warm absorber and
blackbody soft excess are present in this object, as in many other Sy-1 sources.
147
Figure 5.20: The 2.5?10.0 keV best-fit model for NGC 4051, including our continuum
model and an ionized disk reflection spectrum convolved with our kerrconv relativistic
smearing kernel. The residuals have all but disappeared.
type S0/a with an inclination angle of i ? 26? (Nordgren et al. 1995). Ark 120 has been
observed by most of the major X-ray observatories. An EXOSAT observation showed the
source to have a steep soft X-ray spectrum (Turner & Pounds 1989), as did a subsequent
ROSAT observation (Brandt et al. 1993). Furthermore, as mentioned above, these X-ray
observations showed no indication of any warm absorption features. Similar findings
were seen in ultraviolet observations (Crenshaw & Kraemer 2001; Crenshaw et al. 1999).
The source was observed by XMM-Newton in August 2003 for an effective duration of
100 ks (?2.74?106 photons) by Vaughan et al. , whose results on the EPIC-pn spectrum
were reported the following year. We follow the data reduction and analysis of these au-
thors, though we restrict our attention to the EPIC-pn camera data. Vaughan et al. find that
the continuum emission is well described by a simple photoabsorbed power-law model
148
Figure 5.21: A ?F? plot depicting the relative flux in each of the model components in
the 2.5?10.0 keV spectrum of NGC 4051.
with no evidence for complex absorption intrinsic to the system. A multiple blackbody
component for the soft excess is used to reduce residuals left over from the power-law fit
below ?1 keV, and a slight curvature of the continuum is noted that is thought to indicate
the presence of disk reflection in this source (Vaughan et al. 2004).
Our continuum fit differs from that of Vaughan et al. , most notably over whether or not
a warm absorber is present. These authors relied heavily upon the RGS data to draw their
conclusions about the X-ray spectrum of Ark 120 below?3 keV, whereas we use only the
EPIC-pn spectrum to produce our global fits to avoid dealing with the calibration prob-
lems that exist between the two instruments, as discussed in previous Chapters. We do
find a similar photoabsorbed power-law, however: ? = 2.25 and NH = 1.26?1021 cm?2
(the Galactic value, with no evidence for intrinsic cold absorption in the AGN). We detect
the presence of a two-zone warm absorber in the system with hydrogen column den-
149
sities of N1 = 1.51?1023 cm?2 , N2 = 2.90?1022 cm?2 and ionization parameters of
log?1 = 2.97 and log?2 = 1.24. Our best fit to the soft excess required one blackbody
component of kT = 0.13 keV and a flux of Fbb = 1.95?10?6 ph cm?2 s?1 , a factor of
60 below the flux of the power-law component. It should be noted that adding in the
first WA table resulted in a ??2/dof = ?838/+ 2, and adding in the second table fur-
ther improved the fit by ??2/dof = ?1163/+2. The blackbody component resulted in
??2/dof =?4416/+2. All of these additions to the global fit are therefore statistically
warranted.
Vaughan et al. detected the presence of broad and narrow components to the 6.4 keV
Fe-K? line (EWbroad ? 100 eV, EWnarrow ? 40 eV). The narrow component could easily
be fit with a 6.4 keV Gaussian profile, as was our Fe-K? narrow core, but Vaughan et
al. found that a diskline model worked best for their broad component (rmin ? 144rg).
Interestingly, this broad component fit to a rest-frame energy of 6.56 keV rather than
6.4 keV, with the latter yielding a substantially worse global fit (??2 = +21.5) (Vaughan
et al. 2004). This energy corresponds to the line emission being dominated by mildly
ionized iron (Fe XX-XXII), meaning that resonant trapping and the Auger effect should
destroy the line (Ross et al. 1996).
In an effort to solve this puzzle we have fit our iron line profile with two narrow Gaus-
sian components, one at 6.4 keV and one at 6.97 keV, representing neutral and highly
ionized iron. The lines have EWcold = 54.4 eV and EWionized = 19.9 eV. This fit leaves
a residual broad feature nicely centered at 6.4 keV, which renders this scenario physi-
cally consistent with other systems and removes the need to explain the presence of the
broad line of iron in an intermediate state of ionization. We then achieve a best fit to the
broad component using a kerrconv(refl) model, which also nicely accounts for the
additional curvature noted in the spectrum by Vaughan et al. From this fit, we have con-
strained the spin of the BH to be a = 0.63?0.68 and rmin = 1.00?1.09rms. The best-fit
150
parameter values and error bars are presented in Table 5.8. Figs. 5.22-5.24 show the iron
line residual, best fit to this residual, and relative contributions of the individual model
components for the best fit.
Though this result is intriguing for its intermediate BH spin value, one must interpret
it with caution. This source, in particular, seems to have a weak emission feature present
in the spectrum just below the neutral iron line in energy that sticks out as a ?bump? in the
spectrum. It is unclear what this feature may represent, and left unmodeled, the spectral
fit seems to smooth over it rather than fit it properly. This may affect the parameter
values and error bars we obtain for the kerrconv(refl) model. More detailed, longer
observations with higher spectral resolution will be required to solve this puzzle and more
reliably determine the BH spin in Ark 120.
5.2.9 Fairall 9
Fairall 9 is a radio-quiet Sy-1 type galaxy with an elliptical companion, both at a moderate
redshift of z = 0.047. This source has not been observed to undergo very large changes
in X-ray flux over the time it has been observed: the typical 2?10 keV flux of Fairall 9 is
F2?10 ? 1.5?5.0?10?11 erg cm?2 s?1 (Gondoin et al. 2001; Reynolds 1997). Previous
X-ray observations with ASCA show that the source has a continuum well-described by a
photoabsorbed power-law with a fluorescent Fe-K? line and a high-energy tail (a common
signature of disk reflection, as has been discussed previously with respect to a number of
other sources in this Section) (Nandra et al. 1997; Reynolds 1997). A soft excess has also
been detected below ? 2 keV (Pounds et al. 1994), though no strong evidence of warm
absorption has been observed in the soft spectrum (Gondoin et al. 2001).
The source was observed with XMM-Newton by Jansen et al. in July 2000 for an ef-
fective duration of ? 29 ks (? 3.95?105 photons) (Jansen et al. 2001), and the EPIC-pn
data were presented in full by Gondoin et al. the following year (Gondoin et al. 2001).
151
Model Component Parameter Value
phabs NH ( cm?2 ) 1.26?1021
WA 1 NWA1 ( cm?2 ) 1.51+0.37?0.12?1023
log?WA1 2.97+0.26?0.04
WA 2 NWA2 ( cm?2 ) 2.90+0.30?0.22?1022
log?WA2 1.24+0.05?0.02
po ?po 2.25+0.05?0.05
flux( ph cm?2 s?1 ) 1.27+0.04?0.01?10?4
bbody kT ( keV) 0.14+0.01?0.01
flux( ph cm?2 s?1 ) 1.95+0.04?0.06?10?6
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 1.15+0.23?0.14?10?7
EW( eV) 54.40+10.88?6.62
zgauss E( keV) 6.97
flux( ph cm?2 s?1 ) 5.40+1.69?1.64?10?8
EW( eV) 19.90+6.23?6.04
kerrconv ?1 2.34+0.11?0.05
?2 2.34+0.11?0.05
rbr (rms) 6.0
a 0.65+0.03?0.02
i(?) 79+1?0
rmin (rms) < 1.09
rmax (rms) 400
reflion Fe/solar 1.0
?refl 30.0
?refl 2.25+0.05?0.05
flux( ph cm?2 s?1 ) 4.03+1.96?0.10?10?7
?2/dof 1543/1421(1.09)
Table 5.8: Best-fitting model parameters for the 2.5?10.0 keV spectrum of Ark 120,
including components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the zgauss lines to be intrinsically narrow, i.e., ? = 0.0. Redshifts were frozen at the
cosmological value for the source, in this case z = 0.0327. A two-zone warm absorber
and blackbody soft excess are present in this object, as in many other Sy-1 sources.
152
Figure 5.22: The 2.5?10.0 keV spectrum of Ark 120 fit with a continuum composed
of a power-law model modified by Galactic photoabsorption, a two-zone warm absorber
model and a blackbody soft excess. Note the prominent residual iron features that remain
with rest-frame energies of 6.4 keV and 6.97 keV.
We have followed the general procedures for data reduction and analysis discussed by
Gondoin et al. , using the most up-to-date calibration files and software as we have for all
other sources analyzed in this work.
Gondoin et al. find that continuum of Fairall 9 is best modeled with a photoabsorbed
power-law (NH = 3?1020 cm?2 , ? = 1.80), in which the absorbing column density of
neutral hydrogen gas is approximately equal to its Galactic value along the line of sight
to this source (NH = 3.19?1020 cm?2 ). A soft excess is noted below ? 2 keV, and an
RGS analysis yielded a best-fitting blackbody model for this component: kT = 0.17 keV.
Incorporating reflection from an ionized disk with solar abundances and a reflection frac-
tion of frefl = 1.0, the authors find that the high-energy tail is quite well modeled by a disk
at an inclination angle of i = 26? (Gondoin et al. 2001). We have performed a similar fit
153
Figure 5.23: The 2.5?10.0 keV best-fit model for Ark 120, including our continuum
model and an ionized disk reflection spectrum convolved with our kerrconv relativistic
smearing kernel. The residuals have all but disappeared.
using only the EPIC-pn data, and find some similar parameters describing the power-law,
blackbody soft excess and reflection components (the column density of neutral hydrogen
absorption was frozen at the Galactic value): ? = 2.04, kT = 0.20 keV with a flux ?0.5%
that of the power-law component, and the disk inclination angle is i = 57? for solar abun-
dance and assumed near-neutrality. Unfortunately, due to the relatively small number of
photons, the disk ionization and metallicity were not able to be adequately constrained,
hence the assumptions of solar metallicity and near-neutrality. In contrast to the Gon-
doin et al. analysis, we do detect evidence for a warm absorber within the system with
NWA = 1.21?1023 cm?2 and log?WA = 2.85. Inclusion of this component improves the
global goodness-of-fit by ??2/dof =?13/+2, making it statistically significant accord-
ing to the f-test. The presence of the warm absorber also eliminates some of the residual
154
Figure 5.24: A ?F? plot depicting the relative flux in each of the model components in
the 2.5?10.0 keV spectrum of Ark 120.
continuum curvature in the soft spectrum.
Gondoin et al. also note the presence of a 6.4 keV Fe-K? line in the spectrum with
EW ? 120 eV, which they modeled with a Gaussian component. Due to its relatively
narrow profile, the line is suggested to originate from low-ionization material orbiting
relatively far out in the disk. Additionally, an Fe-K absorption edge is also noted at
7.64 keV with ? = 0.18, consistent with reflection from cold, optically thick material.
We find that the inclusion of such an edge is not statistically robust in our model once
reflection is included, but we do find the 6.4 keV line in emission and model it first with
a narrow Gaussian feature representing the core of the Fe-K? line. This feature has an
EW = 133 eV, but even after its inclusion residual features remain indicating the presence
of a broader iron line component. The best fit for this line, which is physically consistent
with our disk reflection model, is achieved using a kerrconv(refl) component with an
155
Figure 5.25: The 2.5?10.0 keV spectrum of Fairall 9 fit with a continuum composed of
a power-law model modified by Galactic photoabsorption, a warm absorber model and
a blackbody soft excess. Note the prominent residual iron feature that remains with a
rest-frame energy of 6.4 keV.
inner radius of emission of rmin < 6.27rms, or < 10.75rg, calculated using the fit value of
BH spin (a = 0.972). The BH spin itself, however, was unable to be constrained. Best-fit
values and error bars for all the parameters in our model are listed in Table 5.9. Figs. 5.25-
5.27 show the iron line residual, best fit to this residual, and relative contributions of the
individual model components, respectively.
5.3 Comparison of Sample Results
We have compiled the relevant parameter constraints from all of our spectral fits to ten
Sy-1 sources: MCG?6-30-15, MCG?5-23-16, Mrk 766, NGC 3783, NGC 4051, Ark 120,
Fairall 9, NGC 2992, 3c273 and 3c120. The constraints on the relativistic disk parameters
156
Figure 5.26: The 2.5?10.0 keV best-fit model for Fairall 9, including our continuum
model and an ionized disk reflection spectrum convolved with our kerrconv relativistic
smearing kernel. The residuals have all but disappeared.
for each object are presented in Tables 5.10-5.12. Note that in each case a model including
reflection from an ionized disk convolved with a relativistic smearing kernel provides the
best statistical fit, and that in almost every case the kerrconv model (with arbitrary spin)
provides a better fit than the kdblur model (spin fixed at a = 0.998).
To assess whether evidence exists for a relativistically broadened iron line, we first
considered the laor fits in which BH spin is fixed at a = 0.998. While each source
demonstrated a significant improvement in its global fit as compared to a model fitting
only a narrow iron line core with a Gaussian component, the important parameter to eval-
uate in this case is the inner radius of disk emission. Roughly speaking, as stated in ?5.1,
if rmin lessorsimilar20rg we can say with some confidence that there is substantial emission from the
inner part of the accretion disk where relativistic effects (such as BH spin) become impor-
157
Figure 5.27: A ?F? plot depicting the relative flux in each of the model components in
the 2.5?10.0 keV spectrum of Fairall 9.
tant in shaping the overall iron line profile. Out of our ten sources, five did not meet this
criterion outright (MCG?5-23-16, NGC 3783, Ark 120, Fairall 9 and 3c120) while one
source spectrum possesses so few photons that it is difficult to quote parameter values and
error bars with confidence (3c273). Allowing for arbitrary BH spin via kerrdisk instead
of laor does help the situation somewhat: only 3c120 and NGC 3783 did not meet the
rmin criterion in this fit, though for none of the sources is the global fit greatly improved
over its laor value. Fairall 9 and 3c273 have spins that cannot be constrained with the
kerrdisk model.
We have also examined the question of how robust the presence of a broad line is in
the spectrum when reflection is included. Beginning with a base continuum model in-
cluding an ionized disk reflection spectrum (Ross & Fabian 2005), we noted the overall
goodness-of-fit and the residual features remaining, especially around the iron line region.
158
Model Component Parameter Value
phabs NH ( cm?2 ) 3.19+0.42?0.00?1020
WA NWA ( cm?2 ) 1.21+1.60?0.97?1023
log?WA 2.85+0.89?0.79
po ?po 2.04+0.14?0.10
flux( ph cm?2 s?1 ) 3.28+0.47?0.30?10?4
bbody kT ( keV) 0.20+0.01?0.02
flux( ph cm?2 s?1 ) 1.57+0.40?0.35?10?6
zgauss E( keV) 6.40
flux( ph cm?2 s?1 ) 1.16+0.42?0.27?10?6
EW( eV) 133+48?31
kerrconv ?1 5.17+4.83?3.31
?2 5.17+4.83?3.31
rbr (rms) 6.0
a ???
i(?) 57+7?5
rmin (rms) < 6.27
rmax (rms) 400
reflion Fe/solar 1.0
?refl 30.0
?refl 2.04+0.14?0.10
flux( ph cm?2 s?1 ) 8.10+4.21?2.66?10?7
?2/dof 665/691(0.96)
Table 5.9: Best-fitting model parameters for the 2.5?10.0 keV spectrum of Fairall 9,
including components and parameter values from 0.6?1.5 keV for completeness. The
energies from 1.5?2.5 keV were not included due to the presence of absorption edges
from the XMM-Newton mirrors. Error bars are quoted at 90% confidence. We required
the 6.4 keV zgauss line to be intrinsically narrow, i.e., ? = 0.0. Redshifts were frozen
at the cosmological value for the source, in this case z = 0.0470. A warm absorber and
blackbody soft excess are present in this object, as in many other Sy-1 sources.
We then convolved this model with relativistic effects, first using the kdblur smearing
kernel, then substituting in kerrconv. A significant improvement in the global fit with
kdblur indicates that relativistic smearing is important in the system, and further signif-
icant improvement with kerrconv instead of kdblur indicates that although relativity is
important, in the best fit scenario the BH spin deviates from its maximal value. When-
ever possible we allowed the iron abundance and ionization parameter to fit freely in the
159
ionized disk model, though in some cases these additional degrees of freedom prevented
us from obtaining a reliable fit. For these sources it was necessary to assume a neutral
disk (? = 30) and solar iron abundance (Fe/solar=1): Ark 120, Fairall 9 and 3c273. The
kdblur and kerrconv fits returned similar results in terms of parameter constraints and
overall fit to the iron line profile in each source, and in nearly all cases also produced a sta-
tistically significant improvement in the overall goodness-of-fit, with the exception being
NGC 3783, in which only a marginal improvement in the goodness-of-fit was seen. The
kerrconv model fit was clearly superior to the kdblur fit in two cases: MCG?6-30-15
and Ark 120.
We have obtained formal constraints on BH spin in four of the ten cases: MCG?6-30-
15 (a > 0.96 from 2.5?10.0 keV, a > 0.987 based on our 0.6?10.0 keV fit discussed in
Chapter 4); Ark 120 (a = 0.63?0.68), Mrk 766 (a > 0.85) and NGC 4051 (a > 0.67).
We fit a BH spin of a > 0.72 to 3c273, but as mentioned previously, this result must
be considered questionable due to the paucity of photons in our data set. Interestingly,
we also were able to constrain the BH spin of 3c120 with kerrconv to a < 0.83, but
given the poor constraints on many of the other parameters of this source (e.g., rmin <
332rms), this value lacks credibility. We were unable to constrain BH spin in MCG?5-
23-16, NGC 3783, Fairall 9 and NGC 2992 in the kerrconv fits.
There are several potential reasons why one might not be able to obtain a good spin
constraint for a given source. Firstly, a lack of sufficient photons in the data set is a severe
limitation for obvious reasons. This is certainly the case in 3c273, for example, and also
plays a role in the spectra of NGC 2992 and Fairall 9. Generally speaking, the more
photons one has to work with, the better the fit constraints will be.
Secondly, if the iron line is not sufficiently broad, then the fit will be more likely to
have difficulty picking out the role of relativistic contributors like BH spin to the over-
all line shape. A narrow iron line could originate from far out in the disk, away from
160
the spacetime where relativistic effects become important. This scenario would make it
impossible to know the spin of the BH. Even iron lines from the inner regions of non-
spinning BHs show the spectral signatures of relativity, as shown in Chapter 3, so even if
the line originates from fairly close range in the disk around a non-spinning BH, we should
be able to constrain its spin. Therefore, we should not be surprised that the sources for
which we are unable to get spin constraints all share a common characteristic: constraints
on rmin that fall outside the inner portion of the disk, i.e., well outside of 6rg.
161
AGN
?
a
i(?
)
rmin
(rg
)
?2
/dof
MCG?6-30-15
2.84
?
2.95
0.998
30
?
32
1.71
?
2.11
940
/1002
(0.
94
)
5.93
?
6.37,
2.27
?
2.46,
10
.28
?
13
.99
0.97
?
0.98
30
?
31
1.68
?
2.67
907
/999
(0.
91
)
MCG?5-23-16
1.98
?
4.30
0.998
21
?
37
18
?
44
1509
/1490
(1.
01
)
2.27
?
2.82
<
0.71
38
?
39
32
?
65
1514
/1489
(1.
03
)
Mrk
766
1.78
?
2.05
0.998
85
?
86
1.24
?
1.82
1542
/1311
(1.
18
)
2.14
?
2.33
0.39
?
0.62
77
?
78
4.41
?
4.67
1539
/1310
(1.
17
)
NGC
3783
9.23
?
10
.00
0.998
<
18
1.24
?
1.80
1741
/1489
(1.
17
)
?
?
?
>
0.89
17
?
18
315
?
388
1732
/1488
(1.
16
)
NGC
4051
2.45
?
3.63
0.998
30
?
39
3.96
?
6.98
1480
/1397
(1.
06
)
4.24
?
10
.00
<
0.87
32
?
41
3.63
?
5.67
1479
/1396
(1.
06
)
Fairall
9
1.40
?
2.70
0.998
>
50
1.24
?
25
672
/692
(0.
97
)
1.79
?
3.50
?
?
?
52
?
69
3.86
?
59
671
/691
(0.
97
)
Ark
120
?
?
?
0.998
52
?
69
>
150
.00
1639
/1422
(1.
15
)
1.65
?
1.98
<
0.69
67
?
69
3.94
?
6.43
1620
/1421
(1.
14
)
NGC
2992
1.31
?
3.15
0.998
37
?
55
3.07
?
4.27
1399
/1310
(1.
07
)
3.90
?
10
.00
>
0.97
38
?
49
1.67
?
6.22
1399
/1309
(1.
07
)
3c273
2.83
?
6.37
0.998
<
67
1.24
?
3.18
228
/267
(0.
854
)
?
?
?
?
?
?
<
35
1.64
?
3.99
229
/266
(0.
86
)
3c120
?
?
?
0.998
>
72
>
253
1474
/1462
(1.
01
)
1.74
?
10
.00
?
?
?
13
?
14
44
?
47
1482
/1461
(1.
01
)
Table
5.10:
Comparison
of
the
spectral
fitting
results
for
the
2.5
?10
.0
keV
spectra
using
the
laor
and
kerrdisk
models.
All
AGN
in
our
sample
that
are
thought
to
possess
broad
iron
lines
are
presented.
For
each
source
the
top
row
represents
the
laor
range
in
parameter
value
while
the
bottom
row
represents
the
kerrdisk
range
in
parameter
value.
Ranges
are
giv
en
at
90%
confidence.
Note
that
MCG?6-30-15
is
able
to
be
fit
with
abrok
en
po
wer
-la
w
emissi
vity
inde
x,
which
islisted
under
?
as
?1
,?
2,
rbr
(rg
).
For
all
other
sources,
?1
=
?2
and
rbr
=
6.0
rg.
162
AGN
Fe/solar
?
?
i(?
)
rmin
(rg
)
?2
/dof
MCG?6-30-15
9.57
?
10
.00
249
?
273
1296
/1003
(1.
29
)
5.97
?
10
.00
<
39
8.89
?
10
.00
39
?
40
4.47
?
4.94
887
/1000
(0.
87
)
MCG?5-23-16
0.53
?
0.83
<
34
1555
/1492
(1.
04
)
0.48
?
0.72
<
31
1.05
?
4.40
22
?
37
1.24
?
64
1485
/1488
(1.
00
)
Mrk
766
1.00
1742
?
3886
1534
/1313
(1.
17
)
1.00
413
?
672
1.71
?
2.04
73
?
81
1.24
?
2.96
1495
/1310
(1.
14
)
NGC
3783
0.18
?
0.34
<
53
1534
/1490
(1.
03
)
0.14
?
0.23
<
46
?
?
?
<
35
>
102
1525
/1487
(1.
03
)
NGC
4051
1.21
?
4.27
<
57
1506
/1398
(1.
08
)
1.29
?
10
.00
<
122
3.08
?
4.29
32
?
38
1.24
?
7.36
1476
/1395
(1.
06
)
Fairall
9
1.00
30
.00
680
/695
(0.
98
)
1.00
30
.00
2.47
?
10
.00
50
?
87
1.24
?
8.25
665
/692
(0.
96
)
Ark
120
1.00
30
.00
1717
/1425
(1.
20
)
1.00
30
.00
1.59
?
1.83
82
?
86
1.24
?
2.02
1576
/1422
(1.
11
)
NGC
2992
1.00
30
.00
1414
/1313
(1.
08
)
1.00
30
.00
1.50
?
4.17
17
?
42
?
?
?
1405
/1310
(1.
07
)
3c273
1.00
30
.00
235
/269
(0.
87
)
1.00
30
.00
2.45
?
10
.00
<
60
1.24
?
11
228
/266
(0.
86
)
3c120
1.44
?
10
.00
47
?
186
1485
/1463
(1.
02
)
0.92
?
10
.00
<
160
?
?
?
17
?
39
>
71
1471
/1460
(1.
01
)
Table
5.11:
Comparison
of
the
spectral
fitting
results
for
the
2.5
?10
.0
keV
spectra
using
the
ionized
reflection
model
reflion
and
kdblur(refl)
,which
con
volv
es
the
reflec-
tion
spectrum
with
asmearing
kernel
from
amaximally-spinning
BH.
All
AGN
in
our
sample
that
are
thought
to
possess
broad
iron
lines
are
presented.
For
each
column
of
data,
the
top
row
represents
the
reflion
range
in
parameter
values
while
the
bottom
row
represents
the
kdblur(refl)
range
in
parameter
values.
For
the
reflion
component,
the
value
of
the
incident
po
wer
-la
w
spectral
inde
xis
set
equal
to
that
of
the
continuum.
Ranges
are
giv
en
at
90%
confidence.
163
AGN
Fe/solar
?
?
a
i(?
)
rmin
(rg
)
?2
/dof
MCG?6-30-15
4.75
?
10
.00
<
83
5.46
?
6.95
,2.
34
?
2.66
,7
?
11
>
0.96
30
?
32
1.43
?
2.22
834
/997
(0.
84
)
MCG?5-23-16
0.55
?
0.69
<
31
1.84
?
3.04
?
?
?
26
?
48
44
?
152
1483
/1487
(1.
00
)
Mrk
766
1.00
444
?
852
1.80
?
2.08
>
0.85
73
?
81
<
2.78
1492
/1309
(1.
14
)
NGC
3783
0.15
?
0.22
<
40
?
?
?
?
?
?
26
?
46
<
983
1526
/1486
(1.
03
)
NGC
4051
1.25
?
5.69
<
108
4.23
?
10
.00
>
0.67
36
?
40
3.50
?
7.19
1475
/1394
(1.
06
)
Fairall
9
1.00
30
.00
1.86
?
10
.00
?
?
?
52
?
64
?
?
?
665
/691
(0.
96
)
Ark
120
1.00
30
.00
2.29
?
2.44
0.63
?
0.68
79
?
80
3.62
?
3.95
1543
/1421
(1.
09
)
NGC
2992
1.00
30
.00
1.24
?
10
.00
?
?
?
20
?
48
5.57
?
12
.00
1402
/1312
(1.
07
)
3c273
1.00
<
356
2.74
?
10
.00
>
0.72
<
63
1.24
?
2.84
228
/265
(0.
86
)
3c120
1.00
<
36
<
1.39
<
0.83
27
?
36
2.76
?
915
.00
1468
/1460
(1.
01
)
Table
5.12:
Comparison
of
the
spectral
fitting
results
for
the
2.5
?10
.0
keV
spectra
using
the
ionized
reflection
model
reflion
con
volv
ed
with
asmearing
kernel
from
aBH
of
arbitrary
spin
kerrconv
.All
AGN
in
our
sample
are
presented,
based
on
the
fits
sho
wn
abo
ve
in
Tables
5.10
-5.11
.F
or
the
reflion
component,
the
value
of
the
incident
po
wer
-
law
spectral
inde
xis
set
equal
to
that
of
the
continuum.
Parameter
value
ranges
are
giv
en
at
90%
confidence.
Note
that
MCG?6-30-15
is
able
to
be
fit
with
abrok
en
po
wer
-la
w
emissi
vity
inde
x,
which
islisted
under
?
as
?1
,?
2,
rbr
(rg
).
For
all
other
sources,
?1
=
?2
and
rbr
=
6.0
rg.
164
Chapter 6
Conclusions
This thesis explores the use of broad iron emission lines to constrain black hole spin, and
makes the first steps toward estimating the spins in a small and relatively homogeneous
sample of AGN. Our study of ten prominent Sy-1 AGN observed to have prominent iron
lines has provided us with some intriguing data on this subject and has also put us in an
excellent position to apply our spectral fitting techniques to many other sources in the
future.
6.1 Summary of Results
We began this work by discussing the importance of BH spin, both as a fundamental
property of the BH itself as well as a means of extending the physical influence of the
BH to its surroundings, both near (gravitationally and magnetically on the accretion disk)
and far (AGN jets can extend up to kpc or even Mpc scales, providing feedback in galaxy
clusters and perhaps solving the so-called ?cooling flow? problem). We then presented the
strengths of the iron line spectral fitting method we use to constrain BH spin in Chapter 1,
and stressed the importance of X-ray observations of AGN in this vein. We reviewed the
history of X-ray astronomy in order to place our current work in context, and to emphasize
165
the unprecedented spectral resolution and throughput of modern detectors such as XMM-
Newton, Chandra and Suzaku.
Chapter 1 provides an overview of the complex interaction between a BH and its
accretion disk, as well as its other surroundings, and discusses the use and efficacy of the
iron line spectral fitting method as a BH spin diagnostic. In Chapter 2 we expand upon
the caveats one must take into account when using spectral modeling to assess spin, most
notably the complication of absorption. In order to isolate the effects of spin on the shape
of the iron line profile it is imperative to first model the continuum accurately, including
any absorption features present. These lines and edges, whether Galactic in origin or
intrinsic to the AGN system as either cold or ionized ?warm? absorption, can alter the
curvature of the continuum and, if not properly accounted for, can give the misleading
impression of a broad red wing to an iron line profile. To illustrate the complexities
inherent in properly modeling the spectral continuum we present an analysis of the Sy-1
AGN NGC 4593. While this source does not appear to harbor a broad iron line or show
any other features indicative of reflection from the inner portions of an ionized accretion
disk, it is an excellent example of a spectrum complicated by absorption and a soft excess,
and provided an important test case for us to use in developing our systematic approach
to modeling the continuum in an AGN.
With the aforementioned new detectors currently in orbit and sending back spectra of
unprecedented quality, we are now in a position to start extracting meaningful constraints
on BH spin for the first time. To do so, however, requires a fully relativistic iron line
model that allows the BH spin to be a free parameter in the spectral fit. Chapter 3 presents
our version of this model, called kerrdisk, as well as its incorporation into a convolu-
tion model that can be applied to a full ionized disk reflection spectrum, kerrconv. We
discuss the construction of this model in detail and compare its results to those of the
publicly available models within the XSPEC X-ray spectral modeling package, as well as
166
similar models with free BH spin that are currently being developed by other groups. We
find that our model outperforms both the public diskline (a = 0) and laor (a = 0.998)
models in terms of accuracy and noise reduction. Though we do not yet include emission
from within the marginally stable orbit of the accretion disk, our results from outside the
plunging region mimic the precision and accuracy of the other groups with free-spin mod-
els. Whereas these other groups rely on large, heavily sampled pre-computed tables of
the photon transfer function, however, we sample the transfer function more sparsely and
linearly interpolate between tabulated points. This works because the transfer function is
a slowly-varying function over radius, relative redshift, spin and inclination angle. While
this method is more computationally intensive, it produces the same spectral line profile
and the table takes up only ? 40 MB of disk space as opposed to the multi-GB required
for the tables of similar codes being developed. This makes our code much more portable
without sacrificing quality.
Chapter 4 discusses our application of these new models to the spectrum of MCG?6-
30-15, a Sy-1 AGN with the broadest iron line yet observed. Using a 350 ks XMM-Newton
EPIC-pn observation with over 4?106 photons, we were able to accurately model the
continuum with a power-law modified by both Galactic and intrinsic warm absorption and
a thermal soft excess below 2 keV. Above 3 keV the red wing of the iron line becomes
evident, and though this feature is well fit by a narrow Gaussian core at 6.4 keV and a
broad kerrdisk component at the same energy (as well as an ionized line of iron at
6.9 keV), the best fit is achieved by convolving an ionized disk reflection spectrum with
the kerrconv model. This model has the physical appeal of simultaneously accounting
for the soft excess (thought to be thermal emission from the disk) and the broad iron
line, as well as the so-called ?hard tail? of excess emission seen above 8 keV. The model
fit yields a formal 90% confidence constraint on the BH spin of a > 0.987, with rmin =
1.62rg, and statistically rules out the possibility of a Schwarzschild BH in this source.
167
More detailed observations may statistically constrain the BH spin in MCG?6-30-15 at
a slightly lower value, but the goodness-of-fit of our model to the data strongly indicates
that this is a rapidly spinning BH. Additionally, due to an enhancement of emission seen
in the innermost portion of the disk (?1 ?6 within r = 5.56rg), we may be witnessing the
extraction of rotational energy from the BH by the accretion disk via magnetic torquing at
the ISCO in MCG?6-30-15. Though this excess inner emission could also be explained
by gravitational light bending acting on a centrally-concentrated X-ray continuum source
located just above the BH/disk, we are undoubtedly seeing strong relativistic effects in
this source, which will continue to remain an object of intense study in the future as we
pursue answers to these questions, among others.
We extend the application of our new models to other Sy-1 AGN thought to harbor
broad iron lines in Chapter 5. All data were obtained from the XMM-Newton public
archive, and only the EPIC-pn spectra were examined. Using our work on NGC 4593 and
MCG?6-30-15 as templates for establishing our spectral fitting method, we first model
the continuum of each source, taking the effects of absorption into account as well as any
soft excess that might be present. We then restrict our attention to the hard spectrum from
2.5?10.0 keV and focus on fitting the iron line in each source using a systematic approach
designed to assess the presence of a broad component, determine if disk reflection is a
factor, and parameterize the line as accurately as possible in order to extract the best
statistical constraints we can on the BH spin for each object. The hard spectrum of MCG?
6-30-15 is revisited, as well as nine other AGN identified through the prominence of
their iron lines. Of these nine, we were able to get reliable spin constraints for three:
Ark 120 (a = 0.63?0.68), Mrk 766 (a = 0.59?0.84), and NGC 4051 (a > 0.67). In
each of the nine cases the best fit was given by a kerrconv model including reflection,
and the three cases with reliable spin constraints each showed a significant improvement
in their overall goodness-of-fit using a kerrconv component as opposed to a kdblur
168
component, where the spin is hardwired at a = 0.998. A fourth source, 3c273, was able
to have its spin constrained in our fits to a > 0.72, but due to the paucity of photons in
the observation this constraint cannot be considered robust. If future observations support
this spin constraint, however, it will be an interesting result because 3c273 is ordinarily
radio-loud and was observed by XMM-Newton in a rare quiescent state when the broad
line could be detected. The other radio-loud source in our sample, 3c120, was not able to
have its spin constrained.
6.2 Discussion
The demographics of BH spin are unknown, and, until recently, unknowable. The advent
of high-resolution X-ray spectroscopy and the promising development of gravitational
wave detectors are now making this field of research accessible. For the first time in the
history of astronomy we are now in a position of being able to calculate a BH?s mass and
spin, thus completely defining it in a mathematical sense.
This thesis represents the first-ever survey to quantify the angular momenta of BHs in
AGN using relativistically broadened iron lines as spin diagnostics. Because this method
is mass-independent and because the Fe-K? line is prevalent in BH/accretion disk sys-
tems, we anticipate that this work will serve as a stepping stone for guiding future spin
surveys across a wide range of environments, including AGN of varying host galaxy mor-
phology, and supermassive BHs vs. stellar-mass BHs, to name two interesting population
comparisons.
Though our sample of ten Sy-1 AGN is far too small to allow us to draw any robust
conclusions about the distribution of BH spins in this group of objects as a whole, this
work has allowed us to design a viable method for evaluating the presence of a broad
iron line in the data and using it to place constraints on the BH spin with our new models,
169
kerrdisk and kerrconv. Based on our data analysis we have arrived at several important
conclusions that we hope will inform subsequent BH spin surveys:
1. It is necessary to have a certain minimum number of photons in order to have a
spectrum of the quality needed to extract spin information. Based on our results,
this number is greaterorsimilar 106 photons. This makes sense, given that spectral line fitting of
any kind is a statistical process and without enough data points one cannot expect
to model a line with any statistical certainty.
2. A broad iron line is needed in order to constrain spin. Simply put, a narrow line
cannot represent emission from the inner part of the disk because it would show
signatures of Doppler shifting and relativistic effects that combine to give good
diagnostic disk lines their characteristic shapes. If a line does not originate in the
inner disk, then relativity is not important to its morphology, and it cannot be used
as a spin diagnostic because spin is a relativistic effect.
3. We are seeing broad lines in many Sy-1 sources, robustly. Five out of ten sources
showed a significant improvement in their global goodness-of-fit when relativistic
smearing was added to a static ionized disk reflection spectrum. Granted, these
sources were selected based on prior observations of a broadened iron line in their
spectra, but it is thought that broad iron lines may inhabit the spectra of a significant
portion of AGN.
4. Across our sample of radio-quiet Sy-1 sources, we see a mix of spin constraints
from moderate to very high, though interestingly we do not see any non-spinning
sources. This shows that radio-loudness is not dependent on spin alone: it must be
determined by at least one other parameter. Magnetic fields and/or thick disks are
likely candidates: the Blandford-Znajek process is thought to be critical in jet for-
mation, and most sources with radio jets are hypothesized to emanate from systems
170
with truncated thin disks (perhaps ADAFs).
5. Unfortunately, nature may be working against us in terms of measuring BH spin in
radio-loud sources using the iron line method. Jet activity tends to overwhelm the
spectrum along lines of sight to the broad line region, effectively burying the broad
line and other disk signatures. For such radio-loud sources it may be necessary
to rely on other methods of diagnosing spin such as thermal continuum fitting and
polarimetry.
6.3 Future Work
Because we know so little about the spin distributions of black holes, much work remains
to be done in this field. While the development of free-spin models such as kerrdisk
and kerrconv has allowed us to begin attacking this question quantitatively and robustly
for the first time among AGN sources, our survey represents only a first step in a much
larger picture. Clearly, we need more sources with broad iron lines to form a larger
statistical sample. We need better quality data with more photons and higher spectral
resolution in order to better constrain the BH/disk parameters in broad iron line sources.
We can get this through longer observations with active observatories such as XMM-
Newton, Chandra and Suzaku, as well as coordinated observations in other wavebands
(e.g., radio and optical) which can help us form a more complete picture of the physics
at work in these systems. The upcoming GLAST mission (2008) will give us a tool with
which to better investigate the nature of jets and other relativistic outflows from these
systems which may depend in part on BH spin. In the coming decade X-ray astronomers
will hopefully have an even more powerful instrument if Constellation-X receives the
funding it needs. The calorimeters on board this mission promise unprecedented spectral
resolution that will be invaluable to iron line studies.
171
We also need to expand our search radius to include stellar-mass BHs. These objects
are thought to have their natal spins intact, so it will be interesting to see how the spin
distribution in this population compares to that of AGN, especially given the physical
similarities between AGN and GBHs in so many other areas. The advantage of the iron
line method is its lack of dependence on BH mass, so this is an ideal technique to employ
for such a comparison. Given the presence of other methods to diagnose BH spin, it
will also be important to see how our results compare to those obtained using thermal
continuum fitting, polarimetry and QPOs. Ideally, the spin constraints calculated using
each different method should be consistent.
Finally, we can improve the accuracy of the kerrdisk and kerrconv models by
including the effects of relativity on emission produced from within the ISCO of the disk.
In so doing, however, it is crucial to properly account for the ionization level and optical
depth of the material in the plunging region. Because this gas is subject to greater tidal
forces and incident blueshifted radiation than the gas outside the ISCO, it is likely to be
quite rarefied, optically thin and highly ionized. Proper modeling of the gas physics in
this region is necessary in order to evaluate the overall contribution of emission from this
region to the broad iron line.
The pace of discovery in this field is ever-increasing. With access to new X-ray data
each day and detectors such as Constellation-X and LISA on the horizon, it is an exciting
time to explore the nature of black holes and what they can tell us about the accuracy of
General Relativity in the strong-field limit. We are poised to answer some of science?s
most fundamental questions in the new millennium.
172
Appendix A
Computing kerrdisk Line Profiles
We include here the FORTRAN driver program for computing line profiles with kerrdisk.
This program is called as a subroutine in the XSPEC spectral modeling package. The basic
principles of the code are expanded upon in detail in Chapter 3. This program creates a
simulated emission line profile from matter orbiting an accretion disk around a black hole.
It uses photon ray-tracing and fully relativistic calculations to compute the energies and
trajectories of each photon leaving the system (Cunningham 1975; Speith et al. 1995),
storing this information in a table that is accessed by the driver code each time it is run.
Several parameters are input by the user, among them BH spin (a) and disk inclination
angle (i). Because the photon transfer function varies slowly over these two parameters,
we use linear interpolation to calculate the value of the transfer function between tabulated
points. This technique produces a very accurate line profile without having to reference a
table that is hundreds of GB in size, as must be done in many similar line emission codes
that allow BH spin to be a free parameter in the model fit.
Parameters that must be input by the user are given below:
1. Rest-frame line energy (E) in keV.
2. The emissivity index of the inner disk (?1); the disk radiates as r?? at a given
173
radius. Parameter range is ? = 0?10.
3. The emissivity index of the outer disk (?2). Same parameter range as above.
4. The break radius (rbr) at which the disk switches from the inner to outer emissivity
index, in units of the radius of marginal stability (rms). Possible values range from
1?400rms.
5. The dimensionless spin of the BH (a), which can range from a = 0?0.998.
6. The inclination angle of the accretion disk to our line of sight (i), ranging from
0?90?.
7. The inner emitting radius of the accretion disk (rmin) in units of rms. We do not
include emission from within rms at this time, so the possible values range from
1?400rms.
8. The outer emitting radius of the accretion disk (rmax) in units of rms. The maximum
possible value is 400rms.
The code is presented in full below:
subroutine spin(EAR,NE,PARAM,IFL,PHOTAR,PHOTER)
c
c XSPECv11 subroutine to produce an emission line profile from a thin
c Keplerian disk around a Kerr black hole with arbitrary spin
c parameter. Method relies on the transfer function approach
c of Cunningham (1975); the line profile can be computed via a
c simple integral with an analytic integrand apart from the
c effects of gravitational light bending/lensing. These are
c incorporated into a slowly varying transfer function computed
c via the code of Speith et al. (1995) and sparsely tabulated in the
c accompanying table "kerrtable.dat". High quality results are
c obtained despite the sparse sampling of the TF through
c linear interpolation of this slowly varying function.
c
174
c This code also generates the basic relativistic disk kernel
c used for the convolution model kerrconv.
c
c Two features have been hardwired into this code but are simple
c to change. First, we assume that the line emissivity is described
c with a broken powerlaw (see comment starting "EMISSIVITY PROFILE").
c It is trivial to include any functional form. Second, we have
c used the same limb-darkening rule as used in Laor (1991; see
c comment starting "LIMB DARKENING"). This is readily changed to any
c functional form.
c
c For other details of this code see Brenneman & Reynolds (2006).
c Please reference this paper if you publish results derived from this
c model.
c
c Developed by Laura Brenneman and Chris Reynolds
c Dept. of Astronomy, University of Maryland, College Park.
c
c
IMPLICIT NONE
INTEGER IFL, NE
REAL*4 EAR(0:NE), PARAM(9), PHOTAR(NE), PHOTER(NE)
c
c---------Initialization--------------
c
real*8 rplus,sumspec
integer nradii,ng,readflag,ia,imu0,abins,mu0bins
parameter(nradii=50,ng=20,abins=20,mu0bins=20)
real*8 a,theta0,mu0,gstar(ng),g(nradii,ng),cosneh(2)
real*8 a_tab(abins),mu0_tab(mu0bins),temp
real*8 aintfac,mu0intfac
real*8 trff_tab(nradii,ng,2,abins,mu0bins)
real*8 cosne_tab(nradii,ng,2,abins,mu0bins)
real*8 gmin_tab(nradii,abins,mu0bins)
real*8 gmax_tab(nradii,abins,mu0bins)
real*8 trffh(2),re(nradii),gmin(nradii)
real*8 gmax(nradii),trff(nradii,ng,2),cosne(nradii,ng,2)
real*8 ispec,lspec(ne),normspec(ne),eeo(0:ne)
real*8 lspecfine(4*ne),eeofine(4*ne)
real*8 intgmin,intgmax,inttf(ng,2),intmu(ng,2),rad,lgrad,intfac
real*8 intgs
real*8 rms,marginal,gee,gstar2,trf,mu,eem1,eem2
real*8 rmin,rmax,alp1,alp2,rbreak,lineE,z
175
real*8 rmin_grid,rmax_grid
real*8 pi,r1,r2,r(nradii),wr(nradii),g1,g2,wg(ng)
integer energy(10000)
integer i,j,k,ii,jj,ii1,ii2,igstar2,irad
external gauleg
save a_tab,trff_tab,cosne_tab,gmin_tab,gmax_tab,mu0_tab
c
c Get parameters of model from xspec.
c
lineE=param(1)
alp1=param(2)
alp2=param(3)
rbreak=param(4)
a=param(5)
theta0=param(6)
rmin=param(7)
rmax=param(8)
z=param(9)
rms=marginal(a)
rmin=rmin*rms
rmax=rmax*rms
c
c Set pi and convert angle variables.
c
pi = 4.d0*atan(1.d0)
theta0=theta0*pi/180.d0
mu0=cos(theta0)
c
c Read in transfer function from the kerrtable.dat file. We use
c the value of a_tab(1) to determine whether this is the first call
c to the code in a given xspec session. On subsequent calls, we
c do not need to read the file.
c
if ( dabs(a_tab(1) - 1.0e-2) .gt. 1.0e-3) then
c
c USER MUST SPECIFY FULL PATH TO KERRTABLE.DAT HERE
c
open (8,file=
&?/n/artemis/lwb/software/xspec_local_models/kerrtableb.dat?
& ,status=?unknown?)
read(8,*),ii,jj
read(8,*),a_tab
176
read(8,*),mu0_tab
do i=1,abins
do j=1,mu0bins
read(8,*),gmin
read(8,*),gmax
read(8,*),trff
read(8,*),cosne
do ii=1,nradii
gmin_tab(ii,i,j)=gmin(ii)
gmax_tab(ii,i,j)=gmax(ii)
do jj=1,ng
do k=1,2
trff_tab(ii,jj,k,i,j)=trff(ii,jj,k)
cosne_tab(ii,jj,k,i,j)=cosne(ii,jj,k)
enddo
enddo
enddo
enddo
enddo
close(8)
endif
c
c Work out interpolation factors in spin and mu0 directions.
c
ia=1
do i=1,abins
if (a_tab(i) .lt. a) ia=i
enddo
aintfac=(a-a_tab(ia))/(a_tab(ia+1)-a_tab(ia))
imu0=1
do i=1,mu0bins
if (mu0_tab(i) .lt. mu0) imu0=i
enddo
mu0intfac=(mu0-mu0_tab(imu0))/(mu0_tab(imu0+1)-mu0_tab(imu0))
c
c Attempt to fix low-inclination problem
c
if (mu0_tab(mu0bins) .lt. mu0) then
imu0=mu0bins-1
mu0intfac=1
endif
c
c Interpolate transfer function in a and mu0 plane.
c
177
do i=1,nradii
gmin(i)=(1.0-aintfac)*(1.0-mu0intfac) *
$ gmin_tab(i,ia,imu0)
$ +aintfac*(1.0-mu0intfac)*
$ gmin_tab(i,ia+1,imu0)
$ +(1.0-aintfac)*mu0intfac*
$ gmin_tab(i,ia,imu0+1)
$ +aintfac*mu0intfac*
$ gmin_tab(i,ia+1,imu0+1)
gmax(i)=(1.0-aintfac)*(1.0-mu0intfac) *
$ gmax_tab(i,ia,imu0)
$ +aintfac*(1.0-mu0intfac)*
$ gmax_tab(i,ia+1,imu0)
$ +(1.0-aintfac)*mu0intfac*
$ gmax_tab(i,ia,imu0+1)
$ +aintfac*mu0intfac*
$ gmax_tab(i,ia+1,imu0+1)
do j=1,ng
do k=1,2
trff(i,j,k)=(1.0-aintfac)*(1.0-mu0intfac) *
$ trff_tab(i,j,k,ia,imu0)
$ +aintfac*(1.0-mu0intfac)*
$ trff_tab(i,j,k,ia+1,imu0)
$ +(1.0-aintfac)*mu0intfac*
$ trff_tab(i,j,k,ia,imu0+1)
$ +aintfac*mu0intfac*
$ trff_tab(i,j,k,ia+1,imu0+1)
cosne(i,j,k)=(1.0-aintfac)*(1.0-mu0intfac) *
$ cosne_tab(i,j,k,ia,imu0)
$ +aintfac*(1.0-mu0intfac)*
$ cosne_tab(i,j,k,ia+1,imu0)
$ +(1.0-aintfac)*mu0intfac*
$ cosne_tab(i,j,k,ia,imu0+1)
$ +aintfac*mu0intfac*
$ cosne_tab(i,j,k,ia+1,imu0+1)
enddo
enddo
enddo
c
c Set up a radial grid: inversely spaced, and define integration values
c for g* via gauleg as in radial case.
c
rmin_grid=rms
rmax_grid=2500*rms
178
r1=1.d0/sqrt(rmax_grid)
r2=1.d0/sqrt(rmin_grid)
call gauleg(r1,r2,r,wr,nradii)
do i=1,nradii
re(i)=1.d0/(r(i)**2.0)
enddo
g1=0.d0
g2=1.d0
call gauleg(g1,g2,gstar,wg,ng)
c
c---------Integrate the line profile-------------------------
c
c
c Generate energy grid and finer grid within it (4 x finer)
c to effectively get greater resolution than before without
c smoothing. We will linearly interpolate between grid point
c values later.
c
do ii=0,ne
lspec(ii)=0.d0
eeo(ii)=dble(ear(ii))
enddo
do ii=1,ne
do j=1,4
lspecfine((ii-1)*4+j)=0.d0
intfac=float(j)/4.0
eeofine((ii-1)*4+j) =
& intfac*eeo(ii)+(1.0-intfac)*eeo(ii-1)
enddo
enddo
c
c Latest generation of line integration. Integrates over a
c large number of radii, using linear radial interpolation
c of the TF as well as gmin and gmax.
c
irad=nradii-1
do ii=1,nradii
if (rmin .lt. re(ii)) irad=ii
enddo
do lgrad=dlog10(re(nradii)),dlog10(re(1)),0.2/float(ne)
rad=10.0**(lgrad)
if ((rad .gt. rmin) .and. (rad .lt. rmax)) then
if (rad .gt. re(irad)) irad=irad-1
179
intfac=(rad-re(irad+1))/(re(irad)-re(irad+1))
do j=1,ng
do k=1,2
inttf(j,k)=intfac*trff(irad,j,k) +
& (1.0-intfac)*trff(irad+1,j,k)
intmu(j,k)=intfac*cosne(irad,j,k) +
& (1.0-intfac)*cosne(irad+1,j,k)
enddo
enddo
intgmin=intfac*gmin(irad)+(1.0-intfac)*gmin(irad+1)
intgmax=intfac*gmax(irad)+(1.0-intfac)*gmax(irad+1)
c
c Emissivity profile is hardwired in here. Currently a broken
c powerlaw.
c
if (rad .lt. rbreak) then
ispec=(rad/rbreak)**(-alp1)
else
ispec=(rad/rbreak)**(-alp2)
endif
c
eem1=lineE*intgmin/(1.0d0+z)
eem2=lineE*intgmax/(1.0d0+z)
ii1=1
ii2=1
do ii=1,4*ne
if (eeofine(ii) .lt. eem1) ii1=ii
enddo
do ii=ii1-1,4*ne
if (eeofine(ii) .lt. eem2) ii2=ii
enddo
if ((ii1 .gt. 1) .and. (ii2 .gt. 1)) then
2005 do ii=ii1+1,ii2
gee=eeofine(ii)/(lineE/(1.0d0+z))
gstar2=(gee-intgmin)/(intgmax-intgmin)
do k=1,2
if (gstar2 .le. gstar(1)) then
trf=inttf(1,k)
mu=intmu(1,k)
endif
if (gstar2 .ge. gstar(ng)) then
trf=inttf(ng,k)
180
mu=intmu(ng,k)
endif
if ((gstar2 .lt. gstar(ng)) .and.
& (gstar2 .gt. gstar(1))) then
do j=1,ng-1
if (gstar(j) .lt. gstar2) igstar2=j
enddo
intgs=(gstar2-gstar(igstar2))/
& (gstar(igstar2+1)-gstar(igstar2))
trf=intgs*inttf(igstar2,k) +
& (1.0-intgs)*inttf(igstar2+1,k)
mu=intgs*intmu(igstar2,k) +
& (1.0-intgs)*intmu(igstar2+1,k)
endif
c
c Next line actually is the guts of the integral. The
c LIMB DARKENING is hardwired in here. It is currently set to
c mu*(1+2.06*mu), as per Laor (1991).
c
lspecfine(ii)=lspecfine(ii) +
& rad*gee*(2.0*pi*gee)**2.0
& *trf*ispec*(1.0+2.06*mu)*rad/
& (sqrt(gstar2-gstar2**2.0)*(intgmax-intgmin))
enddo
enddo
endif
endif
enddo
c
c Bin up lspecfine to give to lspec.
c
do i=1,ne
do j=1,4
lspec(i)=lspec(i)+lspecfine((i-1)*4+j)
enddo
enddo
c
c---------Output of spectral luminosity-----------------
c
c Divide each lspec(ii) by the observed energy of that
c gridpoint --> ph/cm^2/s units.
c
do ii=1,ne
181
lspec(ii)=lspec(ii)/eeo(ii)
enddo
sumspec=0.d0
do ii=1,ne
if (lspec(ii) .gt. 0.d0) then
c
c Sumspec weighted by the energy bin size.
c
sumspec=sumspec+lspec(ii)*(eeo(ii)-eeo(ii-1))
endif
enddo
c open(7,file=?lspec.dat?,status=?unknown?)
do ii=1,ne
if (lspec(ii) .gt. 0.d0) then
c
c Normspec weighted by the energy bin size.
c
normspec(ii)=lspec(ii)*(eeo(ii)-eeo(ii-1))/sumspec
else
normspec(ii)=0.d0
endif
photar(ii)=normspec(ii)
c write(7,*) eeo(ii),normspec(ii)
enddo
c close(unit=7)
end
c
c---------Subroutines------------------------
c
c
c Subroutine to calculate rms for a given spin (a). Assumes only prograde BHs.
c
function marginal(a)
implicit none
real*8 marginal,a,Z1,Z2
Z1=1.0+(1.0-a**2.0)**0.33*((1.0+a)**0.33+(1.0-a)**0.33)
Z2=((3.0*a**2.0)+(Z1**2.0))**0.5
marginal=3.0+Z2-((3.0-Z1)*(3.0+Z1+(2*Z2)))**0.5
return
end
182
C========================================================================
C Subroutine to calculate the abscissas and weights for the Gauss-Legendre-
C Quadrature. The routine is based on the NUMERICAL RECIPES and uses an
C algorithem of G.B. Rybicki.
C Input: x1 ,x2: range of integration.
C n: order of the orthogonal polynomials and the quadrature formula.
C Output: x = x(n): array of the abscissas.
C w = w(n): array of the weights.
SUBROUTINE GAULEG(X1,X2,X,W,N)
INTEGER N,M,I,J
REAL*8 X1,X2,X(N),W(N)
REAL*8 PI,XM,XL,Z,P1,P2,P3,Z1,PP,EPS
PARAMETER (PI = 3.14159265358979323846D0)
PARAMETER (EPS=3.D-14)
M=(N+1)/2
XM=0.5D0*(X2+X1)
XL=0.5D0*(X2-X1)
DO 12 I=1,M
Z=COS(PI*(I-.25D0)/(N+.5D0))
1 CONTINUE
P1=1.D0
P2=0.D0
DO 11 J=1,N
P3=P2
P2=P1
P1=((2.D0*J-1.D0)*Z*P2-(J-1.D0)*P3)/J
11 CONTINUE
PP=N*(Z*P1-P2)/(Z*Z-1.D0)
Z1=Z
Z=Z1-P1/PP
IF(ABS(Z-Z1).GT.EPS) GOTO 1
X(I)=XM-XL*Z
X(N+1-I)=XM+XL*Z
W(I)=2.D0*XL/((1.D0-Z*Z)*PP*PP)
W(N+1-I)=W(I)
12 CONTINUE
RETURN
END
183
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