Acta Polytechnica

doi:10.14311/AP.2013.53.0652
Acta Polytechnica 53(Supplement):652–658, 2013 © Czech Technical University in Prague, 2013

available online at http://ojs.cvut.cz/ojs/index.php/ap

MEASURING SUPERMASSIVE BLACK HOLE SPINS IN AGN

Laura Brenneman∗

Harvard-Smithsonian Center for Astrophysics, 60 Garden St., MS-67, Cambridge, MA 02138 USA
∗ corresponding author: lbrenneman@cfa.harvard.edu

Abstract. Measuring the spins of supermassive black holes (SMBHs) in active galactic nuclei (AGN)
can inform us about the relative role of gas accretion vs. mergers in recent epochs of the life of the host
galaxy and its AGN. Recent theoretical and observation advances have enabled spin measurements for
ten SMBHs thus far, but this science is still very much in its infancy. Herein, I discuss how we measure
black hole spin in AGN, using recent results from a long Suzaku campaign on NGC 3783 to illustrate
this process and its caveats. I then present our current knowledge of the distribution of SMBH spins in
the local universe. I also address prospects for improving the accuracy, precision and quantity of these
spin constraints in the next decade and beyond with instruments such as NuSTAR, Astro-H and future
large-area X-ray telescopes.

Keywords: black holes, active galaxies, X-rays, spectroscopy, XMM-Newton, Suzaku, NuSTAR,
NGC 3783.

1. Introduction
Measurements of the spins of supermassive black holes
(SMBHs) in active galactic nuclei (AGN) can con-
tribute to the understanding of these complex and
energetic environments in three principal ways:
• They offer a rare probe of the nature of the space-
time proximal to the event horizon of the black
hole (BH), well within the strong-field gravity
regime [12, 19];

• They can shed light on the relation of a black hole’s
angular momentum to its outflow power in the form
of winds and jets (e.g., [26, 33, 37];

• They can inform us about the relative role of gas
accretion vs. mergers in recent epochs of the life of
the host galaxy and its AGN [3].

For these reasons, developing a theoretical and obser-
vation framework in which to measure black hole spin
accurately and precisely is of critical importance to
our understanding of how galaxies form and evolve
over cosmic time.
Advances in theoretical modeling as well as

observational sensitivity in the Chandra/XMM-
Newton/Suzaku era are finally producing robust con-
straints on the spins of a handful of SMBHs. Compu-
tationally, new algorithms developed within the past
decade [2, 6, 9, 11] have made it possible to perform
fully relativistic ray-tracing of photon paths emanat-
ing from the accretion disk close to the BH, keeping
the BH spin as a variable parameter in the model.
When such models are fit to high signal-to-noise (S/N)
X-ray spectra from the innermost accretion disk, they
yield vital physical information about the BH/disk
system, including constraints on how fast – and in
what direction – the BH is rotating. If spin (formally
denoted a ≡ cJ/GM2, where c is the speed of light,

J is the BH angular momentum, G is Newton’s con-
stant and M is the mass of the BH) is known to within
Δa ≤ 10%, then meaningful correlations between spin
and other environmental variables (e.g., jet power,
history of the accretion flow) can be drawn.

In this proceeding, I discuss our current knowledge
of the distribution of SMBH spins in the local universe
and future directions of BH spin research. I begin
in §2 with an examination of the spectral modeling
techniques used to measure BH spin in AGN. I then
discuss the application of these techniques to a deep
observation of NGC 3783, and the caveats that must
be considered in §3. I describe the results of these
and other investigations of BH spin in bright, nearby
type 1 AGN in §4, examining our current knowledge
of the spin distribution of local SMBHs and its im-
plications. Conclusions and future directions for this
field of research are presented in §5.

2. Measuring black hole spin
In principle, there are at least five ways that the spin
of a single (i.e., non-merging) BH can be measured,
electromagnetically. All five are predicated on the
assumption that General Relativity provides the cor-
rect description of the spacetime near the BH, and
that there is an easily-characterized, monotonic rela-
tionship between the radius of the innermost stable
circular orbit (ISCO) of the accretion disk and the
BH spin (see Fig. 1). These five methods are listed
below.

• Thermal Continuum Fitting (e.g., McClintock
et al. [21]).

• Inner Disk Reflection Modeling (e.g., Brenne-
man & Reynolds [6]).

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vol. 53 supplement/2013 Measuring Supermassive Black Hole Spins in AGN

-1.0 -0.5 0.0 0.5 1.0
Black Hole Spin (a)

10
R

ad
iu

s
in

D
is

k
(r

Figure 1. Radius of the ISCO (solid line) and event
horizon (dotted line) as a function of BH spin. Spin
values to the left of the dashed line indicate a BH
spinning in he retrograde direction relative to the
accretion disk, while spins to the right of the dashed
line indicate prograde BH spin relative to the disk.

• High Frequency Quasi-Periodic Oscillations
(e.g., Strohmayer [34]).

• X-ray Polarimetry (e.g., Tomsick et al. [38]).
• Imaging the Event Horizon Shadow (e.g.,
Broderick et al. [7]).
There are currently limitations in applying the last

three methods listed above, and the continuum fitting
method is only viable for stellar-mass BHs, due prin-
cipally to the difficulty in finding AGN in a thermally
dominant state analagous to the high/soft state seen
in black hole X-ray binaries (e.g., Czerny et al. 2011).
We are therefore restricted to using only the reflection
modeling method for constraining the spins of SMBHs
in AGN at this time. This method assumes that the
high-energy X-ray emission (≥ 2 keV) is dominated by
thermal disk emission which has been Comptonized by
hot electrons in the “corona,” whether this structure
represents the disk atmosphere, the base of a jet or
some alternative geometry. Some of the scattered pho-
tons will depart the system and form the power-law
continuum characteristic of typical AGN in X-rays.
A certain percentage of the photons, however, will be
scattered back down (“reflected”) onto the surface of
the disk again, exciting a series of fluorescent emission
lines of various species ≤ 7 keV, along with a “Comp-
ton hump” shaped by the Fe K absorption edge at
∼ 7.1 keV and by downscattering at ∼ 20 ÷ 30 keV.
The most prominent of the fluorescent lines produced
is Fe Kα at a rest-frame energy of 6.4 keV, due largely
to its high fluorescent yield. As such, the Fe Kα line
is the most important diagnostic feature of the inner
disk reflection spectrum; its shape is altered from the
typical near-delta function expected in a laboratory,
becoming highly broadened and skewed due to the
combination of Doppler and relativistic effects close
to the BH (see Fig. 2). The energy at which the “red”
wing of this line manifests is directly linked to the

2 4 6 8

0.
5

1
1.

P
ho

to
ns

c
m

−
2

s−
1

ke
V

−
1

Energy (keV)

a = −0.998
a = 0
a = +0.998

Figure 2. Change in the shape of the Fe Kα line
as a function of BH spin. The black line represents
a = +0.998, the red line shows a = 0.0 and the blue
line shows a = −0.998.

location of the ISCO, and therefore the spin of the BH
(see [23, 31] for comprehensive reviews of the reflection
modeling technique).

3. Applying the reflection
modeling method

An AGN must satisfy three important requirements
in order to be a viable candidate for obtaining spin
constraints. Firstly, it must be bright enough in
order to be observed with the necessary S/N in X-
rays to accurately separate the reflection spectrum
from the continuum and any intrinsic absorption
within the host galaxy. Typically one must obtain
≥ 200 000 counts from 2÷10 keV [17], though in prac-
tice the required number can be substantially higher
in sources with complex absorption. Secondly, the
AGN must possess a broad Fe Kα line of sufficient
strength relative to the continuum to allow its red
wing to be successfully located; usually this corre-
sponds to a line equivalent width of hundreds of eV
(e.g., MCG–6-30-15, [6, 8, 24]). Not all type 1 AGN
have been observed to possess such features. Recent
surveys of hundreds of AGN with XMM-Newton have
concluded that broadened Fe Kα lines are only present
in ∼ 40 % of all bright, nearby type 1 AGN [10, 25]),
and some broad iron lines have been ephemeral, ap-
pearing and disappearing in the same object observed
during different epochs (e.g., NGC 5548, [5]). Thirdly,
the Fe Kα line in question must be relativistically
broad in order to be able to constrain BH spin; that
is, it must have a measured inner disk edge – assumed
to correspond to the ISCO – of rin ≤ 9 rg, where
rg ≡ GM/c2. Taking all these points into considera-
tion, the potential sample size of spin measurements
for AGN in the local universe is ∼ 30–40 sources [23].
Most of these AGN are type 1, lacking significant
obscuration by dust and gas along the line of sight to
the inner disk.

653

Laura Brenneman Acta Polytechnica

1 100.5 2 5 20

0.
5

1
1.

da
ta

/m
od

Energy (keV)

Figure 3. Suzaku XIS-FI (front-illuminated; black
crosses) and PIN (red crosses) data from the 210 ks
observation of NGC 3783 in 2009, ratioed against a
simple power-law model for the continuum affected
by Galactic photoabsorption. Black and Red solid
lines connect the data points and do not represent
a model. The green line represents a data-to-model
ratio of unity. Data from the XIS back-illuminated
CCD (XIS-BI) are not shown for clarity.

The reflection spectrum from the inner disk can
be self-consistently reproduced by models such as
reflionx [32] or xillver [14]. These models sim-
ulate not only the broad Fe Kα line, but all other
fluorescent emission species at lower energies, as well
as the Compton hump at higher energies. In order
to incorporate the effects of relativity and Doppler
shift, this static reflection spectrum must then be
convolved with a smearing kernel which computes the
photon trajectories and energies during transfer from
the accretion disk to the observer. Several free-spin
smearing algorithms are currently available for use
(see §1). The kerrconv algorithm of Brenneman and
Reynolds [6] is the only one of these models that is
currently built into xspec, though it limits BH spin to
prograde scenarios only. A more recent improvement
is the relconv model of Dauser et al. [9], which gen-
eralizes the possible spins to incorporate retrograde
BHs.

In the following Section, I describe the practicalities
of using the reflionx and relconv models to measure
the spin of the SMBH in NGC 3783 using a 210 ks
Suzaku observation.

3.1. Case study: NGC 3783
The type 1 AGN NGC 3783 (z = 0.00973) was
the subject of a deep Suzaku observation from
2009 as part of the Suzaku AGN Spin Survey Key
Project (PI: C. Reynolds, lead co-I: L. Brenneman).
The source was observed with an average flux of
FX = 6.04 × 10−11 erg cm−2 s−1 from 2 ÷ 10 keV dur-
ing the observation, yielding a total of ∼ 940 000 pho-
ton counts over this energy range in the XIS instru-
ments (S/N = 35) and ∼ 45 000 photon counts for

4 5 6 7 8

1
1
.2

1
.4

d
a
ta

/m
o
d
e
l

Energy (keV)

(b)

Figure 4. A zoomed-in view of the Fe K region in the
2009 Suzaku observation of NGC 3783, ratioed against
a simple power-law continuum. Note the prominent
narrow Fe Kα emission line at 6.4 keV and the blend
of Fe Kβ and Fe xxvi at ∼ 7 keV. XIS-FI is in black,
XIS-BI in red.

the PIN instrument from 16÷45 keV (S/N = 5), after
background subtraction [4].
The spectrum is shown in Fig. 3 as a ratio to the

power-law continuum and Galactic photoabsorbing
column in order to illustrate the various residual spec-
tral features present. The Compton hump is readily
apparent ≥ 10 keV, though its curvature is relatively
subtle compared with more prominent features of its
kind (e.g., in MCG–6-30-15). The 6 ÷ 7 keV band of
the spectrum is dominated by narrow and broad Fe K
features, including a narrow Fe Kα emission line at
6.4 keV and a blend of Fe Kβ and Fe xxvi emission
at ∼ 7 keV. The broad Fe Kα line manifests as an
elongated, asymmetrical tail extending redwards of
the narrow Fe Kα line to ∼ 4 ÷ 5 keV. The Fe K
region can be seen in more detail in Figs. 4 and 5. At
energies below ∼ 3 keV the spectrum becomes concave
due to the presence of complex, ionized absorbing gas
within the nucleus of the galaxy; the gas is ionized
enough that some contribution from this absorber is
seen at ∼ 6.7 keV in an Fe xxv absorption line. There
is a rollover back to a convex shape below ∼ 1 keV,
however, where the soft excess emission dominates.
The models described above were used by Bren-

neman [4] to fit the 0.7 ÷ 45 keV Suzaku spectrum
of NGC 3783 with a statistical quality of χ2/ν =
917/664 (1.38). Most of the residuals in the best-
fit model manifested below ∼ 3 keV in the region
dominated by the warm absorber and soft excess,
as is typical for type 1 AGN. Because the S/N of
the XIS detectors is highest at lower energies due
to the higher collecting area there, small residuals

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50
.9

0
.9

5
1

1
.0

5
1

d
a

ta
/m

o
d

e
l

Energy (keV)

(c)

Figure 5. The broad Fe Kα line at 6.4 keV becomes
more obvious when the two more prominent narrow
emission lines are modeled out, in addition to the
power-law continuum.

in the spectral modeling of this region can have an
exaggerated effect on the overall goodness-of-fit. Ex-
cluding energies below 3 keV in our fit, we achieved
χ2/ν = 499/527 (0.95). No significant residuals re-
mained.
The best-fit parameters of the BH/inner disk sys-

tem included a spin of a ≥ +0.98, a disk inclination
angle of i = 22+3−8 deg to the line of sight, a disk
iron abundance of Fe/solar = 3.7 ± 0.9 and an ion-
ization of ξ ≤ 8 erg cm s−1 (errors are quoted at 90 %
confidence for one interesting parameter). These pa-
rameters remained consistent, within errors, when
energies ≤ 3 keV were ignored in the fit, negating the
importance of the soft excess emission in driving the
fit to these parameter values.
By contrast, Patrick et al. [27] analyzed the same

data separately and reached a strikingly different con-
clusion regarding the spin of the BH in NGC 3783,
with approximately equivalent goodness-of-fit to that
obtained by Brenneman [4]: a ≤−0.04. This discrep-
ancy illustrates the importance of assumptions and
modeling choices in influencing the derived BH spin
and other physical properties of the BH/disk system.
Patrick et al. [27] made three critical assumptions that
differed from [4]:
(1.) that the iron abundance of the inner disk is fixed
to the solar value;

(2.) that the warm absorber has a high-turbu-
lence (vturb = 1000 km/s), high-ionization (ξ ∼
7400 erg cm s−1) component not reported by Bren-
neman [4];

(3.) that the soft excess originates entirely through
Comptonization, with the Comptonizing medium

having a temperature of kT ≥ 9.5 keV and an opti-
cal depth of τ = 1.9 ± 0.1.

Using a Markov Chain Monte Carlo approach,
Reynolds et al. [29] demonstrated that a solar iron
abundance is significantly detrimental to the global
goodness-of-fit (Δχ2 = +36) in NGC 3783 when com-
pared with allowing the iron abundance of the inner
disk to fit freely. Brenneman [4] found no need to
include a high-turbulence component in their fit to the
Suzaku data, and noted no evidence for such a com-
ponent in the higher-resolution 2001 Chandra/HETG
data. Finally, Reynolds et al. [29] note that there is
no physical reason to assume that the soft excess origi-
nates entirely from Comptonization, as other processes
within the AGN might contribute (e.g., photoionized
emission, scattering, thermal emission). Reynolds
et al. [29] attempted several different model fits to
the soft excess and found not only a much smaller
contribution to the overall model for the soft excess
component than Patrick et al. [27], but also no statisti-
cal difference between fits using different models (e.g.,
blackbody vs. compTT). It should be noted, however,
that modeling the soft excess with a Comptonization
component of high temperature, high optical depth
and high flux, as Patrick et al. [27] have done, re-
quires the compTT component to possess significant
curvature up into the Fe K band, reducing the need
for the relativistic reflection to account for this same
curvature seen in the data and thereby eliminating
the requirement of high BH spin. Clearly, different
modeling approaches can lead to vastly different con-
clusions regarding BH spin and careful consideration
should be given to the models used and their allowed
parameter ranges. Obtaining high S/N X-ray spec-
tra over a broad energy range (e.g., by using NuS-
TAR simultaneously with XMM-Newton or Suzaku)
will also help break the degeneracy between models
(see §5).

4. Results and implications
In the previous two sections we have noted the im-
portance of both adequate data (i.e., high S/N) and
a physically self-consistent modeling approach to con-
straining SMBH spins in AGN. We have also stressed
the importance of one very critical assumption that
must be made in order to calculate BH spin: namely,
that the inner edge of the accretion disk is at the
ISCO. If the optically-thick disk is truncated further
out, then any spin derived using this assumption and
the reflection modeling technique will be a lower limit.
If there is some emission produced inside the ISCO,
this will lead to a systematic error on the BH spin
measurement that can be ≥ 20 % above the actual
value of spin for non-spinning or retrograde BHs, but
is ≤ 2 % higher than the real spin for BHs with spins
a ≥ +0.9 [30].
The models currently used to represent both the

accretion disk and the relativistic smearing also have

655

Laura Brenneman Acta Polytechnica

AGN a WKα log M Lbol/LEdd Host

MCG–6–30–15 ≥ 0.98 305+20−20 6.65
+0.17
−0.17 0.40

+0.13
−0.13 E/S0

Fairall 9 0.52+0.19−0.15 130
+10
−10 8.41

+0.11
−0.11 0.05

+0.01
−0.01 Sc

SWIFT J2127.4+5654 0.6+0.2−0.2 220
+50
−50 7.18

+0.07
−0.07 0.18

+0.03
−0.03 —

1H0707–495 ≥ 0.98 1775+511−594 6.70
+0.40
−0.40 ∼ 1.0−0.6 —

Mrk 79 0.7+0.1−0.1 377
+47
−34 7.72

+0.14
−0.14 0.05

+0.01
−0.01 SBb

Mrk 335 0.70+0.12−0.01 146
+39
−39 7.15

+0.13
−0.13 0.25

+0.07
−0.07 S0a

NGC 7469 0.69+0.09−0.09 91
+9
−8 7.09

+0.06
−0.06 1.12

+0.13
−0.13 SAB(rs)a

NGC 3783 ≥ 0.98 263+23−23 7.47
+0.08
−0.08 0.06

+0.01
−0.01 SB(r)ab

Ark 120 0.94+0.1−0.1 105
+26
−24 8.18

+0.05
−0.05 0.04

+0.01
−0.01 Sb/pec

3C 120 ≤−0.1 48+10−10 7.74
+0.20
−0.22 0.31

+0.20
−0.19 S0

Table 1. Summary of black hole spin measurements derived from in SMBH spectra. Data are taken with Suzaku
except for 1H0707−495, which was observed with XMM-Newton, and MCG–6-30-15, in which the data from XMM
and Suzaku are consistent with each other. For references, see [4]. Spin (a) is dimensionless, as defined previously.
WKα denotes the equivalent width of the broad iron line relative to the continuum in units of eV. M is the mass of
the black hole in solar masses, and Lbol/LEdd is the Eddington ratio of its luminous output. Host denotes the galaxy
host type. Host types for 1H0707−495 and SWIFT J2127.4+5654 are unknown. The spin values of MCG–6-30-15
and NGC 3783 are disputed by Patrick et al. [27].

their inherent limitations and uncertainties. The
reflionx and xillver models both assume that the
disk has a constant density and ionization structure
throughout, which cannot be the case, physically.
There is also some question about whether a limb-
brightening vs. limb-darkening algorithm should be
used to represent the directionality of the reflected
emission from the disk when convolved with the smear-
ing kernel [35]. The nature of the disk emissivity pro-
file itself is also an active topic of research; though
the disk is thought to dissipate energy as a function of
radius (� ∝ r−q), the emissivity index (q) likely varies
as a function of radius as well [40].

Taking all these caveats into account, one can begin
to appreciate why, to date, there are only ten different
AGN with published values for their SMBH spins.
These AGN, and their properties, are listed in Tab. 1.

It is difficult to draw any robust statistical inferences
from a sample size of ten objects. There may also be
selection biases in play which make it more likely that
we measure higher spin values [4]. The only pattern
that is readily apparent in Tab. 1 is that nine out of ten
AGN have relatively high, prograde SMBH spins. The
one retrograde spin value is for 3C 120, which is the
one AGN in the sample that is radio-loud. This may
not be a coincidence; Garofalo [16] postulated that
jet power is maximized for rapidly-rotating retrograde
BHs (though this idea is not without controversy,
e.g., [37]). More work needs to be done to assess BH
spin and jet power independently in order to prove or
disprove this conjecture.
If the trend toward large prograde spins continues

to hold as our sample size increases, we might ulti-
mately infer that the growth of bright, nearby AGN in

recent epochs has been driven primarily by prolonged,
prograde accretion of gas. If the overall distribution
of SMBH spins in the local universe begins to drift
toward intermediate values, it is likely that the role of
mergers has been more significant than that of ordered
gas accretion. Similarly, if the distribution tends to-
ward low values of spin, we can infer that episodes of
randomly-oriented accretion have been the dominant
means of SMBH and galaxy growth [3].

5. Conclusions and future
directions

Measuring BH spin is painstaking work, even with the
best data from current observatories such as XMM-
Newton and Suzaku. Long observations (c. hundreds
of kiloseconds) of bright AGN are needed, and multi-
epoch, multi-instrument data should be analyzed
jointly whenever possible in order to assess the physi-
cal nature and variability of all of the components in
a given X-ray spectrum. A broad energy range is also
desirable in order to constrain the properties of the
continuum and complex absorption, particularly, and
to distinguish these components from any signatures
of inner disk reflection. Only by isolating the broad
Fe Kα line and its associated Compton hump can
we measure BH spin with the accuracy and precision
necessary to begin constructing a spin distribution
for local AGN. We can then begin to draw inferences
regarding the dominant growth mechanism of these
SMBHs over cosmic time, and to understand the role
of spin in jet production and AGN feedback.
Our current sample of ten AGN with measured,

published SMBH spins must be extended in order to
accomplish these goals. The Suzaku Spin Survey is

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vol. 53 supplement/2013 Measuring Supermassive Black Hole Spins in AGN

ongoing, and is expected to provide new spin con-
straints for 3C 120 and Mrk 841 within the next year.
Additionally, many valuable datasets from the XMM
and Suzaku archives are currently being analyzed with
an eye toward measuring spin (e.g., Walton et al., in
prep.). NuSTAR [18] will also benefit this science,
providing an invaluable high-energy (∼ 5 ÷ 80 keV)
complement to XMM-Newton and Suzaku when used
simultaneously with either observatory. Accessing this
high energy range with low background and high S/N
will enable the continuum and absorption in the spec-
trum to be more accurately modeled, allowing the
signatures of inner disk reflection to be isolated and
yielding more accurate, precise spin constraints.

In addition to NuSTAR’s role in this work,
Astro-H [36], scheduled for launch in 2014, will bring
the science of micro-calorimetry to X-ray astronomy
with a spectral resolution of ΔE ∼ 7 eV over the
0.3÷12 keV range. The calorimeter will be the unique
strength of this mission, enabling the broad and nar-
row Fe K emission and absorption features to be defini-
tively disentangled and the telltale signatures of com-
plex intrinsic absorption to be identified and modeled
correctly.

In order to achieve the order-of-magnitude increase
in sample size necessary to begin assessing the spin
distribution of SMBHs in the local universe from a sta-
tistical perspective, future large-area (≥ 1 m2) X-ray
observatories are needed. Proposed concepts such as
IXO [39], ATHENA [1] and the Extreme Physics Ex-
plorer (EPE) [15] would all offer the necessary collect-
ing area and spectral resolution to extend our sample
of measured SMBH spins to several hundred AGN us-
ing the reflection modeling method. LOFT [13] would
also bring precise timing resolution into play along
with large collecting area, allowing measurements of
spin to be made on the orbital timescale of many AGN
by tracing individual hot spots in the inner accretion
disk.
The science of determining BH spin is very much

in its infancy. Though the past decade has seen great
strides in our ability to constrain spin through long
X-ray observations coupled with detailed spectral mod-
eling, much work remains to be done in terms of im-
proving the precision and accuracy of these measure-
ments, as well as the sample size. The next decade
will see an improvement in the quality of BH spin
science, but a significant advance in the quantity of
this work in the decades beyond will depend critically
on the amount of international funding available for
large-area X-ray missions.

Acknowledgements
LB is indebted to the Vulcano conference organizers for
their kind invitation, and to NASA grant # NNX10AR44G,
which funded her travel.

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Acta Polytechnica 53(Supplement):652–658, 2013
1 Introduction
2 Measuring black hole spin
3 Applying the reflection modeling method
3.1 Case study: NGC 3783

4 Results and implications
5 Conclusions and future directions
Acknowledgements
References