This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

This content was downloaded by: chrissr

IP Address: 68.238.161.172

This content was downloaded on 29/11/2013 at 14:14

Please note that terms and conditions apply.

The spin of supermassive black holes

View the table of contents for this issue, or go to the journal homepage for more

2013 Class. Quantum Grav. 30 244004

(http://iopscience.iop.org/0264-9381/30/24/244004)

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING CLASSICAL AND QUANTUM GRAVITY

Class. Quantum Grav. 30 (2013) 244004 (17pp) doi:10.1088/0264-9381/30/24/244004

The spin of supermassive black holes

Christopher S Reynolds

Department of Astronomy and the Joint Space Science Institute, University of Maryland,College Park, MD 20901, USA

E-mail: chris@astro.umd.edu

Received 2 July 2013, in final form 29 August 2013Published 29 November 2013Online at stacks.iop.org/CQG/30/244004

AbstractBlack hole spin is a quantity of great interest to both physicists andastrophysicists. We review the current status of spin measurements insupermassive black holes (SMBH). To date, every robust SMBH spinmeasurement uses x-ray reflection spectroscopy, so we focus almost exclusivelyon this technique as applied to moderately-luminous active galactic nuclei(AGN). After describing the foundations and uncertainties of the method, wesummarize the current status of the field. At the time of writing, observationsby XMM-Newton, Suzaku and NuSTAR have given robust spin constraints on22 SMBHs. We find a significant number of rapidly rotating SMBHs (withdimensionless spin parameters a > 0.9) although, especially at the highermasses (M > 4 × 107M�), there are also some SMBHs with intermediatespin parameters. This may be giving us our first hint at a mass-dependent spindistribution which would, in turn, provide interesting constraints on modelsfor SMBH growth. We also discuss the recent discovery of relativistic x-rayreverberation which we can use to ‘echo map’ the innermost regions of theaccretion disc. The ultimate development of these reverberation techniques,when applied to data from future high-throughput x-ray observatories such asLOFT, ATHENA+, and AXSIO, will permit the measurement of black holespin by a characterization of strong-field Shapiro delays. We conclude with abrief discussion of other electromagnetic methods that have been attempted orare being developed to constrain SMBH spin.

PACS number: 98.62.Js

(Some figures may appear in colour only in the online journal)

1. Introduction

Supermassive black holes (SMBHs) are commonplace in today’s Universe, being found atthe center of essentially every galaxy [1]. As such, they have attracted the attention ofastrophysicists and physicists alike. Astrophysicists have long been fascinated by the extremely

0264-9381/13/244004+17$33.00 © 2013 IOP Publishing Ltd Printed in the UK & the USA 1

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

energetic phenomena powered by the accretion of matter onto black holes (BHs) [2]. Beyondthe natural draw of studying ‘cosmic fireworks’, it is now believed that the energy released bygrowing SMBHs is important in shaping the properties of today’s galaxies and galaxy clusters[3, 4]. Thus, SMBHs are important players in the larger story of galactic-scale structureformation. To the gravitational physicist, SMBHs provide the ultimate laboratory in which totest the prediction of General Relativity (GR) and its extensions [5].

This paper discusses recent progress in observational studies of strong gravitationalphysics close to SMBHs and, in particular, the characterization of BH spin. In order tobring focus to this discussion, we shall address exclusively studies of SMBHs. A large bodyof parallel work exists directed towards stellar-mass BHs; we direct the interested reader tosome excellent reviews [6, 7]. Before beginning our discussion, it is worth reiterating whySMBH spin is an interesting quantity to pursue. Assuming that standard GR describes themacroscopic physics, spin provides a powerful way to probe the growth history of SMBHsand, ultimately, their formation pathways (an issue that remains mysterious). In essence,scenarios in which SMBH growth is dominated by BH–BH mergers predict a population ofmodestly spinning SMBHs, whereas growth via gas accretion can lead to a rapidly spinningor a very slowly spinning population depending upon whether the accreting matter maintainsa coherent angular momentum vector over the time it takes to double the BH mass [8, 9].SMBH spin can also be a potent energy source, and may well drive the powerful relativisticjets that are seen from many BH systems [10, 11]. On more fundamental issues, genericdeviations from or extensions to GR tend to show up at the same order as spin effects (e.g.[12])—thus observational probes capable of diagnosing spin are also sensitive to physicsbeyond GR. In addition, spinning BHs have recently been shown to be unstable in extensionsof GR with massive gravitons; for sufficiently massive gravitons, SMBHs should spin down onastrophysically-relevant timescales [5, 13] (although see [14]). Thus, observations of spinningSMBHs can set upper limits on the graviton mass.

We structure this paper as follows. In section 2, we briefly review the basic physicsrelevant to the discussion of accreting SMBHs. In section 3, we describe the basic anatomyof an accreting SMBH (section 3.1), and then present the main tool employed to measure BHspin, namely x-ray reflection spectroscopy (sections 3.2 and 3.3). We illustrate the methodwith a detailed discussion of the SMBH in the galaxy NGC 3783 (section 3.4), discuss theuncertainties and caveats that should be attached to these spin measurements (section 3.5), andthen summarize recent attempts to map out the distribution of BH spins (section 3.6). Whilethe long-term future of precision SMBH spin measurements will likely be dominated by space-based gravitational wave astronomy [15] (GWA), section 4 concludes with a brief discussionof other electromagnetic probes of spin that are complementary to x-ray spectroscopy and canbe developed in the pre-GWA era.

In what follows, the mass of the SMBH shall be denoted M. Following the usualconvection, we shall mostly use units in which G = c = 1; thus, length and time are measuredin units of M with 1M� ≡ 1.48 km ≡ 4.93 μs

2. Review of the basic physics

We begin by stating two basic but important facts about a SMBH at the center of a galaxy.Firstly, the BH is believed to dominate the gravitational potential out to at least 105M. Secondly,the ubiquitous presence of plasma in the galactic environment precludes any significant chargebuild-up on the BH. Assuming standard GR (as we shall do henceforth), these two conditionsimply that the spacetime is characterized by the Kerr metric [16], parameterized solely by themass M and dimensionless spin parameter a ≡ Jc/GM2, where J is the angular momentum

2

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

of the BH. Following the usual astrophysical convention, we shall work in Boyer–Lindquistcoordinates [17] in which the Kerr line element is given by

ds2 = −(

1 − 2Mr

�

)dt2 − 4aM2r sin2 θ

�dt dφ + �

�dr2

+� dθ2 +(

r2 + a2M2 + 2a2M3r sin2 θ

�

)sin2 θ dφ2, (1)

where � = r2 − 2Mr + a2M2, � = r2 + a2M2 cos2 θ . The event horizon is given by the outerroot of � = 0, i.e., revt = M(1 + √

1 − a2).There are two other locations of special astrophysical importance within the Kerr metric.

The surface defined by � = 0 (which completely encompasses the event horizon) is thestatic limit; within the static limit, any (time-like or light-like) particle trajectory is forcedto rotate in the same sense as the BH as seen by a distant observer (i.e. dφ/dt > 0). Thestationary nature of the spacetime (i.e. the existence of a time-like Killing vector, ∂t) allowsus to define the total conserved energy of any test-particle orbit around the BH. A curiousproperty of the Kerr metric is the existence of orbits within the static limit (but exterior to theevent horizon) for which this conserved energy is negative. Penrose [18, 19] showed that theexistence of these orbits permits, in principle, the complete extraction of the rotational energyof a spinning BH, resulting in this region being called the ergosphere. Blandford and Znajek[10] demonstrated that magnetic fields supported by currents in the surrounding plasma caninteract with a spinning BH to realize a Penrose process; this is the basis of spin-poweredmodels for BH jets.

A second astrophysically important location is the innermost stable circular orbit (ISCO),i.e. the radius inside of which circular test-mass (time-like) orbits in the θ = π/2 plane becomeunstable to small perturbations. This is given by the expression,

risco = M(3 + Z2 ∓ [(3 − Z1)(3 + Z1 + 2Z2)]1/2), (2)

where the ∓ sign is for test particles in prograde and retrograde orbits, respectively, relativeto the spin of the BH and we have defined,

Z1 = 1 + (1 − a2)1/3[(1 + a)1/3 + (1 − a)1/3], (3)

Z2 = (3a2 + Z2

1

)1/2. (4)

For a = 1 (maximal spin in the prograde sense relative to the orbiting particle), we haverisco = M. This is the same coordinate value as possessed by the event horizon but, in fact, thecoordinate system is singular at this location and there exists finite proper distance betweenthe two locations. As a decreases, risco monotonically increases through risco = 6M whena = 0 to reach a maximum of r = 9M when a = −1 (maximal spin retrograde to theorbiting particle). As we discuss below, the ISCO sets an effective inner edge to the accretiondisc (at least for the disc configurations that we shall be considering here). Thus, the spindependence of the ISCO directly translates into spin-dependent observables; as spin increasesand the radius of the ISCO decreases, the disc becomes more efficient at extracting/radiatingthe gravitational binding energy of the accreting matter, the disc becomes hotter, temporalfrequencies associated with the inner disc are increased, and the gravitational redshifts of thedisc emission are increased.

3. X-ray spectroscopic measurements of SMBH spin

We now turn to a discussion of the main observational technique that has been used to date toobtain robust measurements of SMBH spin—x-ray reflection spectroscopy.

3

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

Figure 1. Schematic sketch of the accretion disc geometry discussed in section 3.1. The accretiondisc is geometrically-thin and flat (in the symmetry plane of the Kerr BH). Within the ISCO, theflow plunges into the BH, effectively truncating the disc signatures at the ISCO. In SMBH systems,the disc has a temperature of ∼105 K and the x-rays arise from a geometrically extended structure(the ‘corona’) elevated off the disc plane. The x-ray source irradiates the accretion disc’s surface,producing observable reflection signatures in the x-ray spectrum. Figure courtesy of Lijun Gou,closely following similar figure in [20].

3.1. Basic structure of a SMBH accretion disc

In order to characterize the rather subtle effects of BH spin, we must select astrophysicalsystems that we believe possess particularly simple and well-defined accretion geometries. Inour discussion, we only consider sources that have ‘moderately high’ accretion rates, i.e., thosewith luminosities in the range ∼10−2LEdd to ∼0.3LEdd where LEdd ≈ 1.3 × 1031(M/M�) Wis the usual Eddington limit (the luminosity above which fully ionized hydrogen is blownaway from the BH by radiation pressure). This means that we are studying bonafide activegalactic nuclei (AGN). For such systems, the accretion geometry is described by the cartoonshown in figure 1. Outside of the ISCO, the accretion disc is geometrically-thin and consistsof gas following almost test-particle circular orbits (hereafter, we shall use the term ‘Keplerianmotion’ to mean test-particle circular orbits). The gradual re-distribution of angular momentumby magnetohydrodynamic (MHD) turbulence within the disc [21, 22] leads to a gradualinwards radial drift of matter superposed on this background of circular motion. Inside ofthe ISCO, material spirals rapidly into the BH approximately conserving energy and angularmomentum. The radial velocities become relativistic (becoming c at the horizon itself) andso, by conservation of baryon number, the density of the flow plummets within this region,and the matter becomes fully ionized. Indeed, it may even become optically-thin as indicatedin the cartoon. The transition of the accretion flow from approximately circular motion toinward plunging at the ISCO is particularly important for our discussion—it sets an innerradius to the region of the disc that produced any observable effects. This transition is seen inMHD simulations of accretion discs [23, 24], although a full characterization of the inner discstructure must await the development of global, radiation-dominated GR-MHD simulations.Noting that accretion disc theory is still an active and on-going field of research, we shallproceed under the assumption that this transition occurs at the ISCO (although, as we shallpoint out when appropriate, small shifts in the transition away from the ISCO due to finite discthickness effects may well be an important source of systematic error for BH spin).

In general, of course, the angular momentum vector of the incoming material about theBH (and hence the orientation of the accretion disc at large radius) may be misaligned with the

4

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

spin angular momentum of the BH. In what is now the standard picture, Bardeen and Peterson[25] argue that the effects of differential Lens–Thirring precession slave the inner accretiondisc to the BH symmetric plane (θ = π/2), producing a disc that gradually twists fromalignment with the mass reservoir at the outside, to alignment with the BH in its inner region.The Bardeen–Petterson argument suggests that the inner r ∼ 100M of the accretion disc willbe essentially flat in the θ = π/2 plane. However, the details of this process, including thevalue of the characteristic warp radius, depends upon the transport of the out-of-plane angularmomentum in an MHD turbulent disc; only now has it become tractable to examine thisproblem with MHD simulations and we eagerly await results. For the rest of the discussion,the effects of disc warping shall be neglected.

The temperature of the inner accretion disc around a SMBH for these accretion rates isgenerally in the range 105–106 K; the resulting thermal (quasi-blackbody) emission producesa strong bump peaking in the UV/EUV. Indeed, this UV bump can often dominate theobserved energy output of an AGN. However, essentially every AGN also shows significantemission in the x-ray band. This has the form of a power-law component with flux-density F(ν) ∝ ν−α , α ≈ 1, and can carry up to 10–20% of the total power radiatedby the AGN. This ‘hard component’ emission must arise from much hotter, optically-thinmaterial associated with either a magnetically heated ‘corona’ above the disc or dissipationin the base regions of a jet (the yellow cloud in figure 1). On the basis of detailedspectral studies, the most likely physical process producing the x-ray emission is the inverseCompton scattering of optical/UV photons from the accretion disc by ∼109 K electrons in thecorona.

3.2. X-ray ‘reflection’ from the SMBH accretion disc

This configuration of a flat, thin, cold, Keplerian disc below a strong continuum x-ray sourceproves to be fortuitous. The observed x-ray emission is (usually) dominated by radiation thatcomes straight from the corona to us. However, the x-rays from the corona also irradiate theaccretion disc. With energy-dependent ratios, the incident photons are either photoelectrically-absorbed by ions in the surface layers of the disc or Compton scattered back out of the disc.The de-excitation of the resulting excited ions produces a rich x-ray spectrum of radiative-recombination features and fluorescent emission lines. Collectively, the Compton scatteredcontinuum and these emission features make up (what is poorly termed) the x-ray reflectionspectrum [26–29].

A representative calculation of the rest-frame x-ray reflection (using the xillver codeof [29]) is shown in figure 2 (left). Particularly important is the iron-Kα line at 6.4 keV [30].This line is strong due to the high astrophysical abundance and high fluorescence yield of iron.It is also relatively isolated in the spectrum, making it easy to identify and characterize evenif it is strongly broadened and distorted (as we will discuss in section 3.3). However, there areother characteristic features of the reflection spectrum. At low x-ray energies, the spectrumis dominated by a dense forest of emission lines from low atomic number elements (with N,O, Ne, Mg, Si, and S being particularly important). At high x-ray energies, the absorptioncross-sections become small and Compton scattering dominates, producing a broad hump inthe spectrum that peaks at 20–30 keV. Of course, the precise form of the spectrum dependsupon several things, most notable (i) the ionization state of the disc surface (characterizedby the ionization parameter ξ = 4πFion/n where Fion is the ionizing flux impinging on thedisc surface and n is the electron number density at the x-ray photosphere), (ii) the elementalcomposition of the disc matter (with the iron fraction being of special importance), and (iii)the shape of the irradiating continuum.

5

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

0.1 1 10 100

0.01

0.1

110

F(E

) [a

rb. u

nits

]

Energy (keV)0.1 1 10 100

0.01

0.1

110

F(E

) [a

rb. u

nits

]

Energy (keV)

Figure 2. Left panel: incident power-law continuum (red dashed line) and rest-frame reflectionspectrum produced by the accretion disc (solid blue line) computed using the xillver modelof [29] assuming an ionization parameter of ξ = 5 erg cm s−1 and cosmic iron abundance. Rightpanel: effects of relativistic Doppler and gravitational redshift effects on this reflection spectrumassuming a viewing inclination of i = 30◦, irradiation index of q = 3, and a rapidly spinning BH(a = 0.99; black line) or non-spinning (a = 0; blue line) BH.

3.3. Relativistic effects and spin effects in the x-ray spectrum

The geometry outlined above is a relativists dream—the accretion disc is a thin structurefollowing almost test-particle orbits close to the BH and emitting well-defined, sharp spectralfeatures. The observed spectrum will thus be strongly modified by relativistic Doppler shiftsand gravitational redshift (see figure 2 (right)). By identifying these spectral features andmodeling the broadening effects we can determine the properties of the accretion disc itself(e.g., the ionization state of the surface layers and the elemental abundances of the disc) aswell as the inclination of the disc and the location of the ISCO (hence the BH spin).

Operationally, the analysis of real data is facilitated by making the approximation that therest-frame disc reflection spectrum is invariant across the region of interest. We then modelthe observer-frame spectrum by convolving the reflection spectrum with a kernel describingthe GR photon transfer effects (Doppler and gravitational shifts). This kernel is constructed byray-tracing from the disc surface (θ = π/2 plane) to the observer, taking full advantage of theconserved quantities in the Kerr metric (see [31] for a review of this calculation). The kerneldepends upon the viewing inclination of the accretion disc and the BH spin. It also dependsupon the radial distribution of the irradiating x-ray flux (and hence the weight that shouldbe given to each radius of the disc in the blurring kernel); this is an unknown function andsomething we would like to determine from the data. Thus, these kernels are calculated andtabulated as a function of emission radius, and the full kernel is constructed (for a given viewinginclination and spin) by integrating over radii weighted by the irradiation profile [30, 32–34].We commonly parameterize the irradiation profile with a power-law form, Fion ∝ r−q, where qis known as the irradiation index. High-quality datasets sometimes require a broken power-lawform in order to fully capture the shape of the broadened reflection spectrum in which case wehave two irradiation indices (q1, q2) and a break radius [35–37]. A non-parametric treatmentof the irradiation profile [38] confirms the appropriateness of a broken power-law form.

3.4. A worked example: the spin of the SMBH in NGC3783

In principle, the procedure to determine SMBH spin is now straightforward. We take ahigh signal-to-noise x-ray spectrum of an AGN with a high throughput observatory such as

6

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

011 2 5 20

0.5

11.

5

Rat

io

Energy (keV)

Figure 3. The 2009 Suzaku spectrum of NGC3783 ratioed against a power-law continuum. Figurefrom [39].

XMM-Newton, Suzaku or NuSTAR. We then compare model spectra (such as illustrated infigure 2 (right)) with the observed spectrum and, using standard techniques (e.g. direct χ2-minimization or Monte Carlo Markov chain (MCMC) methods), determine the best-fittingvalues and error ranges on all model parameters, including spin.

However, AGN possess complex structures in addition to the accretion disc, includingwinds of photoionized plasma that are blown off the disc as well as large-scale cold structuresthat may act as the reservoir for the accretion disc. These structures imprint their own patternsof absorption, emission and reflection on the x-ray spectrum and these must be included in ourspectral model. We illustrate this with a discussion of the AGN in the spiral galaxy NGC3783,one of the targets of the Suzaku Key Project on BH spin. Figure 3 shows the ratio of the Suzakudata to a reference power-law model. The soft x-ray spectrum is dominated by an absorptionfeature from a highly-subrelativistic wind of photoionized plasma flowing away from the BH(the so-called warm absorber, [40–43]). This absorption can be accurately modeled by spectralsynthesis codes such as xstar [44]. Shifting attention to the iron-K band around 6 keV, wesee in figure 3 a strong narrow iron line due to the fluorescence of cold gas that is distant fromthe SMBH. This can be accurately described by a low-ionization x-ray reflection spectrum.

Our final spectral model must include all of these additional components (with theirassociated parameters), and the spin constraints must be derived marginalizing over all otherparameters. Figure 4 shows the constraints for NGC3783 derived by both a simple χ2-minimization procedure and an MCMC approach. Both approaches constrain the spin tobe a > 0.89 at the 90% confidence level [36, 45]. Figure 5 illustrates precisely how the modelsare constraining the spin by showing the residuals between the model prediction and the datawhen the ‘wrong’ spin is forced into the fit. We see that, when a non-spinning BH is imposedin the fit to the NGC3783 data, the broad iron line is too narrow and over-predicts the fluxin the 5–6 keV band. For further detailed discussion of the statistical robustness of these fits,including a treatment of the subtle statistical correlation between BH spin and iron abundance,see [45].

7

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

0.4 0.6 0.8 1

020

40

Δχ2

a0.8 0.85 0.9 0.95

00.

050.

10.

15

p(a)

Δa

(Δa=

0.01

)

a

Figure 4. Spin constraints on the SMBH in NGC3783 from the 2009 Suzaku observation. Leftpanel: �χ2 as a function of the spin parameter a. Different lines show the effects of differentdata analysis assumptions; a fiducial analysis (black), an analysis in which the warm absorberparameters are frozen at their best values (red), an analysis in which the cross normalization of thetwo Suzaku instruments (the XIS and HXD/PIN) are allowed to float (blue), and an analysis thatignores all data below 3 keV (green). Figure from [36]. Right panel: probability distribution forspin parameter a from a MCMC analysis using the fiducial spectral model. Figure from [45].

0

0.01

0.02

0.03

νF(ν

)

(a) a=0.94, q1=7.3, q2=2.8

4 6 8

0.95

1

1.05

ratio

Energy (keV)

0

0.01

0.02

0.03

νF( ν

)

(b) a=0, q1=q2=3

4 6 8

0.95

1

1.05

ratio

Energy (keV)

Figure 5. Left panel: Suzaku/XIS spectra overlaid with the best-fitting model (top) and thecorresponding data/model ratio (bottom). Right panel: same, except that the spin parameter hasbeen frozen at a = 0 and (for physical consistency) the irradiation indices have been frozen atq1 = q2 = 3. All other parameters have been allowed to fit freely. For both panels, the modelcomponents are colored as follows: absorbed power-law continuum (red), distant reflection (green),and relativistically smeared disc reflection (blue). Figure from [45].

3.5. Health warnings

As in any field of experimental physics, we must be aware of the systematic errors in ourmeasurements or, worse, the possible ways that our methodology may completely fail to

8

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

capture the reality of a given astrophysical source. Here, we walk through some of the mainconcerns relevant for SMBH spin measurements.

The single biggest concern is that, in some sources, we may be fundamentally mis-characterizing the spectrum. In [46], it is shown that multiple absorbers that partially coverthe x-ray source can mimic the relativistically-blurred reflection spectrum, at least in the0.5–10 keV band. A significant issue faced by these models is their geometric plausibility—the absorbers are postulated to be some significant distance from the SMBH (r 100M)whereas the x-ray source is very compact, lying within 10M of the SMBH (the compactnessof the x-ray source has recently been confirmed by gravitational microlensing studies ofmultiply-lensed quasars, e.g. [47]). Thus, partial covering of the x-ray source requires eithera very special viewing angle (so that our line of sight just clips the edge of the absorber) ora finely clumped wind with tuned clumping factors (such that, at any given time, ∼50% ofour sight-lines to the compact source are covered by clumps). Still, it is important to addressthis model from a hard-headed data point of view. This was recently achieved using a jointXMM-Newton/NuSTAR observation of the AGN in the spiral galaxy NGC 1365 that, for thefirst time, allowed a high-quality x-ray spectrum of an AGN to be measured in the 0.5–60 keVband. As reported in [48], the canonical partial-covering absorption model can fit the0.5–10 keV spectrum but fails when extrapolated up to the higher-energy portion of thespectrum. Adding in an extra partial-covering component that is marginally optically-thick toCompton scattering can produce agreement with the observed spectrum, but then the inferredabsorption-corrected luminosity of the AGN would exceed the Eddington limit and hencethis solution would be unphysical. It was concluded by [48] that the data strongly favor therelativistic disc reflection model over partial-covering absorption.

Within the disc reflection paradigm, there are some important issues to note. Firstly, ourmethod assumes that the accretion disc observables truncate at the ISCO; the spin constraintis almost entirely driven by this fact. While there is support for this assumption from MHDsimulations of accretion discs [23, 24], our knowledge of disc physics is incomplete. Inparticular, the inner accretion disc may be subject to visco-thermal instabilities that could,sporadically, truncate disc outside of the ISCO. Although there is no evidence for this transitorydisc truncation in most AGN, there is an important class of AGN that do appear to showthis phenomenon—the broad-line radio galaxies (BLRGs). BLRGs are in our target range ofaccretion rates, display the strong optical/UV/x-ray emission characteristic of a geometrically-thin accretion discs and corona, but also possess powerful relativistic jets. The jet experiencesabrupt and sporadic injections of energy (i.e., geyser-like eruptions) and, during one of theseinjection-events, the inner regions of the thin-disc appear to be destroyed before refilling backdown to the ISCO [49–52]. Thus, some monitoring of the object is required to know whetherthe spin measurement can be considered robust or not [52].

Secondly, there is the question of which aspect of the data is driving the fit. In the mostrobust cases, such as NGC3783 discussed in section 3.4, the constraint is clearly driven by theprofile of the broad iron line. However, in addition to the broad iron line, the ionized reflectionspectrum also contributes to the soft part of the spectrum (<1 keV); the forest of emissionfeatures in the soft reflection spectrum are broadened into a pseudo-continuum that producesa rather smooth ‘soft excess’ in the spectrum. Many sources do indeed display a soft excessand, in some cases, the high signal-to-noise in the soft part of the spectrum can drive theconstraints on the spin parameter. If the observed soft excess is truly due to disc reflection,this is a valid and powerful use of the data. However, there are other possible origins for thesoft excess, most notably inverse Compton scattering of UV photons from the cold disc by‘warm’ material (possibly a ‘chromosphere’ lying on the disc surface). Thus, in some sources,the origin of the soft excess and the value of the spin parameter are coupled questions that are

9

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

)

Figure 6. Masses M and spin parameters a of the 19 SMBHs for which both parameters areconstrained. Following the conventions of the primary literature, the spin measurements are shownwith 90% error ranges, whereas the masses are shown with 1σ . This is an updated version of asimilar figure appearing in [56].

still under examination (see detailed discussion of this issue for the luminous AGN Fairall 9in [53]).

3.6. Survey of current results

Without further ado, we present the current state of the field of SMBH spin measurements.Over the past few years there have been an explosion in the number of published SMBHspin measurements, including samples by Walton et al [54] and Patrick et al [55]. Spinshave been published by multiple groups and, in the same timeframe, the spectral models andmethodologies have been improved. Thus, with some hindsight, one cannot simply harvestSMBH spin measurements from the literature without exercising caution. Following [56], wepropose filtering the published values with quality-control criteria; (i) the spin measurementis based on spectral models employing full disc reflection spectra and not just isolated ‘pureiron line’ models, (ii) the iron abundance is treated as a free parameter (required since ironabundance and spin are correlated variables), (iii) the inclination is treated as a free parameterand can be constrained (this helps protect against fits that are driven purely by the soft excess),(iv) the irradiation index can be constrained and fits to give q > 2 (required for a well-posedmodel in which the reflection spectrum is not unphysically dominated by the outer disc radius).These filter criteria eliminate 13 sources from the Walton [54] and Patrick [55] samples; theexcluded sources span the range of AGN type and luminosity. Taking the compilation describedin table 1 of [56] and updating with the XMM-Newton/NuSTAR result on NGC1365 [48] andthe multi-epoch study of 3C120 [52], we now have spin constraints on 22 AGN that satisfythe quality-control criteria.

In figure 6 we take the 19 of these objects that also have mass estimates (from varioustechniques; see [56]) and place them on the (M, a)-plane. There are several interesting pointsto note about this plot. Firstly, there is clearly a population of rapidly spinning BHs (a > 0.9),especially below masses of 4 × 107M�. This is a strong indication that these SMBHs grew (at

10

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

0 2×105 4×105 6×105

05

1015

20

ph/s

time (s)

Figure 7. The 2–10 keV Rossi x-ray Timing Explorer light curve of the AGN MCG–6-30-15 froma long observation in August 1997.

least in their final mass doubling) by the accretion of gas with a coherent angular momentum.Secondly, there are some SMBHs for which intermediate spins (0.4 < a < 0.8) are inferred,and these tend to be the highest mass systems (M > 4 × 107M�). While the small numberstatistics and ill-defined selection effects prevent firm conclusions from being drawn, this maybe the first hints for a mass-dependence to the SMBH spin distribution, with a more slowlyspinning population (corresponding to growth via BH–BH mergers or incoherent accretion[57]) emerging at the highest masses. Lastly, there are no retrograde spins measured eventhough our technique is capable of finding them. A single epoch analysis of the BLRG 3C120suggested an accretion disc truncated at r ∼ 10M, possibly indicating a rapid retrograde spin[58], but a multi-epoch analysis revealed that this was a rapidly rotating prograde BH with adisc that undergoes transitory truncation related to jet activity [52].

3.7. The emerging field of broad iron line reverberation

An important characteristic of accretion onto BHs that we have not yet addressed is thetime-variability. Fundamentally, the variability is driven by a combination of local instabilities(such as the magnetorotational instability that drives MHD turbulence [22]) and more poorlyunderstood global instabilities (that may drive limit-cycle or explosive behavior). In AGN,this variability is particularly dramatic in the x-ray band since this emission comes from thecentral regions of accretion disc (where all of the characteristic timescales are shortest) andoriginates from a corona which may be unstable to, for example, reconnection-driven eruptions.An example x-ray light curve from the Rossi x-ray Timing Explorer (RXTE) is shown infigure 7.

Since the x-ray source is elevated off the disc surface, we can use this rapid variability to‘echo map’ the reflection from the inner accretion disc. In essence, by characterizing the time-delays between flares in the direct x-ray continuum and the reflection spectrum, we can mapout the geometry of the SMBH/disc/corona system. This was examined theoretically by theauthor some years ago [59] who computed transfer functions relating the observed responseof the iron-Kα emission line from the disc to a δ-function continuum flare. An example ofsuch a transfer function for a rapidly spinning BH (a = 0.998) is shown in figure 8. Beyondthe obvious fact that the time-delay gives information on the actual location of the x-raysource (something which is hard to obtain via a pure spectral analysis), it is interesting to

11

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

Figure 8. Relativistic transfer function showing the response of a 6.4 keV iron line from thedisc surface to a δ-function flare in the driving x-ray continuum source. For the purposes of thisillustration, the continuum source is assume to be a point source on the spin axis at r = 10M, theBH is rapidly spinning a = 0.998 and the accretion disc has an inclination of i = 30◦.

note that the transfer function bifurcates into two branches. The upper branch corresponds tothe normal echo sweeping out to larger radii (and irradiating more slowly moving material)giving an ever narrowing line. The lower branch corresponds to strongly Shapiro-delayed[60] reflection from the very innermost regions of the disc close to the event horizon. Theslope of this branch is a function of the spin parameter a, especially when the BH is close toextremal.

While our observatories do not yet have the collecting area to allow us to see this responseof the iron line to a single flare, reverberation has recently been discovered via statisticalanalyzes of long XMM-Newton datasets of bright AGN. The analysis is subtle and mustaccount for the fact that (i) there is no single time-delay that characterizes the response of thereflection continuum and, in fact, the measured time delays are both a function of energy andthe temporal-frequency being probes; and (ii) the direct continuum source itself has intrinsicenergy- and temporal-frequency dependent time lags. Most analyses use Fourier methods. Fortwo given (non-overlapping) energy bands, time-sequences of x-ray flux (a(t) and b(t)) areextracted and their Fourier transforms (a(ω) and b(ω) )are computed. We then form the cross-spectrum C(ω) ≡ a∗b, which we can write in terms of a frequency-dependent amplitude andphase,C(ω) = |C(ω)|eiφ(ω). The frequency-dependent time-delay between the two lightcurvesis then given by �t = φ(ω)/ω.

The first detections of reverberation from the inner accretion disc were made by probingdelays between the continuum and the soft excess [62–64]. However, recently, there are cleardetections of reverberation associated with the broad iron line [61, 65, 66]. Figure 9 showsthe first such detection of broad iron line reverberation in the bright AGN NGC4151. Themagnitude of the lags suggests that the x-ray source is displaced ∼4M above the center of thedisc; this is not necessarily a natural location for strong coronal emission and may suggestthat the x-ray source is actually associated with the dissipative base of a jet or some otherdissipative structure associated with a BH magnetosphere. The exact shape of the lag-spectrumdepends upon the temporal-frequency being probes, with the line appearing broader and morehighly redshifted at higher temporal-frequencies. This is expected since the higher temporal-frequencies are probing smaller radii in the accretion disc, and suggests that we are gainingour first hints at the nature of the transfer function.

12

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

Energy (keV)

Gaussian width (keV)

0

0.5

1

1.5

2

4 5 6

Lag (s)

−3000

−2000

0

1000

2000

3000

102 5

Figure 9. Right panel: time-lags as a function of energy (i.e. the lag-spectrum) for the XMM-Newton data of the bright AGN NGC4151. Show here is the lag-spectrum for temporal frequencies< 2 × 10−5 Hz (blue triangles) and (5–50) × 10−5 Hz (red diamonds). Left panel: simpleGaussian fits to these lag spectra, demonstrating that the iron-line feature in the lag-spectrum has acentroid energy that decreases and (marginally) a width that increases as one probes high temporalfrequencies. Figure from [61].

One important point to note (in the spirit of a sanity check) is that the size/location of thex-ray source as inferred from x-ray reverberation is broadly consistent with recent estimatesderived from a completely different technique, studies of microlensing in multiply lensedquasars [67, 68].

4. Conclusions

In this review, we have summarized the methodology by which we can measure SMBH spinsusing x-ray reflection spectroscopy and have described the current status of such measurements.Today, we have spins for approximately two dozen SMBHs; we find a population of rapidlyrotating BHs (a > 0.9) but hints of a more slowly rotating population emerging at higherSMBH masses. The main limitation to applying this technique more widely are the longintegration times needed with current observatories in order to obtain spectra with sufficientsignal-to-noise. The next generation of proposed high throughput x-ray observatories suchas LOFT, ATHENA+ and AXSIO will permit us to push these studies to fainter and moredistant objects. This, in turn, will allow well-defined samples to be obtained and permitinvestigations of the SMBH spin distribution as a function of cosmic time. These high-throughput observatories will also unlock the full power of reverberation studies, allowing usto detect strong-field Shapiro delays in the reverberation transfer function.

The long-term future of SMBH spin measurements will likely be dominated byspace-based GWA, once such observatories are deployed. GWA will permit SMBH spinmeasurements with a precision and accuracy probably unattainable with x-ray spectroscopy.However, given the uncertain timeframe for the deployment of space-based GW observatories,it is interesting to pursue electromagnetic probes of SMBH spin as vigorously as possible.We end this review by mentioning a few other electromagnetic techniques that have beendiscussed or are actively being developed.

If the accretion disc is efficient at radiating away the gravitational potential energy of theaccreting matter, the overall efficiency of the accretion disc (defined as η ≡ L/Mc2, whereL is the total radiative luminosity of the system and M ≡ dM/dt) is a function of spin. With

13

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

some work, the total L can be estimated straightforwardly. The mass accretion rate M is morechallenging to constrain, but it can be estimated through the detailed temperature/shape of thethermal emission from the accretion disc. Applying this method to a sample of 80 quasars,[69] found tentative evidence for efficiencies (and hence spin parameters) that increase withincreasing SMBH mass. Of course, this is discrepant with the result presented in figure 6—future explorations of this discrepancy must properly account for selection effects as well asthe systematic errors in the efficiency-based measurements.

One interesting technique focuses on powerful jetted systems. If we assume that thejets are powered by the Blandford–Znajek (i.e. magnetic Penrose) process, and if we canmake an estimate of the magnetic field in the immediate vicinity of the BH (from accretiontheory), then the BH spin parameter can be determined once the jet power is measured.Practical difficulties include the significant uncertainty in deriving jet powers from observables(which may be strongly influenced by an unknown relativistic beaming factor). However,it is encouraging that a careful application of this method [70] produces results that aresensible; given the analytic approximation used to relate spin and jet power, it would bepossible to infer a > 1, but the observed population of AGN seem to obey the constraint|a| < 1.

Of course, a tremendous amount of observational firepower (including a recent 3 Mscampaign by Chandra) has been directed at the SMBH at the center of our own Galaxy(coincident with the radio source Sgr A∗). Unfortunately, the x-ray reflection technique cannotbe applied here—the accretion rate is extremely small, and the disc is believed to be in ahot, geometrically-thick (quasi-spherical) state that is optically-thin to x-ray emission andhence does not produce any x-ray reflection features [71, 72]. Instead, calculations of photonproduction/propagation through GR-MHD simulations of the hot flow have been used tomake predictions of the radio spectrum and frequency-dependent polarization as a function ofsystem parameters. In principle, comparison with the observations can then constrain the spin.However, due to the inherent uncertainties in the calculation of this complex radio continuum,the constraints to date have not yet proved conclusive, with some groups obtaining highinferred spin [73, 74] and others obtaining rather lower values [75].

Another particularly exciting development, again aimed squarely at Sgr A∗ and the SMBHin the nearby elliptical galaxy M87, are the attempts to directly image the horizon-scalestructures using mm- or submm-wave very long baseline interferometry. At these short radiowavelengths, the accretion flow is optically-thin to synchrotron self-absorption and hence wemight hope to see the shadowing effect of the event horizon against the background radioemission [76]. The properties of the shadow depend upon the spin (and spin-orientation) ofthe SMBH [12, 77]. Great strides have already been made towards the goal of detecting thesestructures, with current interferometry being able to detect horizon-scale structure but withan insufficient number of baselines to enable true image reconstruction [78]. In M87, currentdata have also resolved a compact (10M) structure possibly related to the jet-launching region[79] which may, itself, probe SMBH spin as well as jet launching [74]. It will be exciting towatch these developments in the next few years.

Throughout this review, we have assumed the validity of standard GR (and hence theKerr metric) and have focused on attempts to extract the spin parameter. A more ambitiousproblem is to use (electromagnetic) observations of accreting BHs to explore deviations fromand/or extensions to GR [80–84]. A generic difficulty encountered in these studies is that, tolowest order, the deviations from GR are present in the quadrupole moment of the potentialand hence are degenerate with the spin parameter. Still, the implications are profound, andincreasingly detailed studies of BH systems with electromagnetic and, eventually, gravitationalwave probes remain our best hope for breaking GR.

14

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

Acknowledgments

The author thanks Laura Brenneman, Philip Cowperthwaite, Andrew Fabian, Anne Lohfink,Jon Miller, Rubens Reis, and Abdu Zoghbi for stimulating conservations that have helpedformulate the discussion presented here. The author also gratefully acknowledges thehospitality of the Institute of Astronomy at the National Central University (Jhongli, Taiwan)during which much of this review was written, as well as funding from NASA under grantsNNX10AE41G (Astrophysics Theory), NNX10AR31G (Suzaku Guest Observer Program)and NNX12AE13G (Astrophysics Data Analysis).

References

[1] Kormendy J and Richstone D 1995 Inward bound—the search for supermassive black holes in galactic nucleiAnn. Rev. Astron. Astrophys. 33 581

[2] Rees M J 1984 Black hole models for active galactic nuclei Ann. Rev. Astron. Astrophys. 22 471–506[3] Benson A J 2010 Galaxy formation theory Phys. Rep. 495 33–86[4] Fabian A C 2012 Observational evidence of active galactic nuclei feedback Ann. Rev. Astron.

Astrophys. 50 455–89[5] Berti E 2013 Astrophysical black holes as natural laboratories for fundamental physics and strong-field gravity

Braz. J. Phys. arXiv:1302.5702 [gr-qc][6] Miller J M 2007 Relativistic x-ray lines from the inner accretion disks around black holes Ann. Rev. Astron.

Astrophys. 45 441–79[7] McClintock J E, Narayan R and Steiner J F 2013 Black hole spin via continuum fitting and the role of spin in

powering transient jets arXiv:1303.1583[astro-ph.HE][8] Moderski R and Sikora M 1996 On black hole evolution in active galactic nuclei Mon. Not. R. Astron.

Soc. 283 854–64[9] Volonteri M, Madau P, Quataert E and Rees M J 2005 The distribution and cosmic evolution of massive black

hole spins Astrophys. J. 620 69–77[10] Blandford R D and Znajek R L 1977 Electromagnetic extraction of energy from Kerr black holes Mon. Not. R.

Astron. Soc. 179 433–56[11] McKinney J C, Tchekhovskoy A and Blandford R D 2012 General relativistic magnetohydrodynamic

simulations of magnetically choked accretion flows around black holes Mon. Not. R. Astron.Soc. 423 3083–117

[12] Johannsen T and Psaltis D 2010 Testing the no-hair theorem with observations in the electromagnetic spectrum:II. Black hole images Astrophys. J. 718 446–54

[13] Brito R, Cardoso V and Pani P 2013 Massive spin-2 fields on black hole spacetimes: instability of theSchwarzschild and Kerr solutions and bounds on graviton mass Phys. Rev. D 88 023514

[14] Brito R, Cardoso V and Pani P 2013 Partially massless gravitons do not destroy general relativity black holesPhys. Rev. D 87 124024

[15] Consortium T e et al 2013 The gravitational universe arXiv:1305.5720[astro-ph.CO][16] Kerr R P 1963 Gravitational field of a spinning mass as an example of algebraically special metrics Phys. Rev.

Lett. 11 237–8[17] Boyer R H and Lindquist R W 1967 Maximal analytic extension of the Kerr metric J. Math. Phys. 8 265–81[18] Penrose R 1969 Gravitational collapse: the role of general relativity Riv. Nuovo Cimento 1 252–76[19] Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (San Francisco, CA: Freeman)[20] Gou L, McClintock J E, Reid M J, Orosz J A, Steiner J F, Narayan R, Xiang J, Remillard R A, Arnaud K A

and Davis S W 2011 The extreme spin of the black hole in Cygnus X-1 Astrophys. J. 742 85[21] Shakura N I and Sunyaev R A 1973 Black holes in binary systems. Observational appearance Astron. Astrophys.

24 337–55[22] Balbus S A and Hawley J F 1991 A powerful local shear instability in weakly magnetized disks: I. Linear

analysis: II. Nonlinear evolution Astrophys. J. 376 214–33[23] Reynolds C S and Fabian A C 2008 Broad iron-kα emission lines as a diagnostic of black hole spin Astrophys.

J. 675 1048–56[24] Penna R F, McKinney J C, Narayan R, Tchekhovskoy A, Shafee R and McClintock J E 2010 Simulations of

magnetized discs around black holes: effects of black hole spin, disc thickness and magnetic field geometryMon. Not. R. Astron. Soc. 408 752–82

15

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

[25] Bardeen J M and Petterson J A 1975 The Lense–Thirring effect and accretion disks around Kerr black holesAstrophys. J. Lett. 195 L65

[26] Lightman A P and White T R 1988 Effects of cold matter in active galactic nuclei—a broad hump in the x-rayspectra Astrophys. J. 335 57–66

[27] George I M and Fabian A C 1991 X-ray reflection from cold matter in active galactic nuclei and x-ray binariesMon. Not. R. Astron. Soc. 249 352–67

[28] Ross R R and Fabian A C 2005 A comprehensive range of x-ray ionized-reflection models Mon. Not. R. Astron.Soc. 358 211–6

[29] Garcıa J, Dauser T, Reynolds C S, Kallman T R, McClintock J E, Wilms J and Eikmann W 2013 X-ray reflectedspectra from accretion Disk models: III. A complete grid of ionized reflection calculations Astrophys.J. 768 146

[30] Fabian A C, Rees M J, Stella L and White N E 1989 X-ray fluorescence from the inner disc in Cygnus X-1Mon. Not. R. Astron. Soc. 238 729–36

[31] Dauser T, Wilms J, Reynolds C S and Brenneman L W 2010 Broad emission lines for a negatively spinningblack hole Mon. Not. R. Astron. Soc. 409 1534–40

[32] Cunningham C T 1975 The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerrblack hole Astrophys. J. 202 788–802

[33] Laor A 1991 Line profiles from a disk around a rotating black hole Astrophys. J. 376 90–94[34] Brenneman L W and Reynolds C S 2006 Constraining black hole spin via x-ray spectroscopy Astrophys.

J. 652 1028–43[35] Fabian A C, Vaughan S, Nandra K, Iwasawa K, Ballantyne D R, Lee J C, De Rosa A, Turner A and Young A J

2002 A long hard look at MCG-6-30-15 with XMM-Newton Mon. Not. R. Astron. Soc. 335 L1–L5[36] Brenneman L W et al 2011 The spin of the supermassive black hole in NGC 3783 Astrophys. J. 736 103[37] Fabian A C et al 2012 On the determination of the spin of the black hole in Cyg X-1 from x-ray reflection

spectra Mon. Not. R. Astron. Soc. 424 217–23[38] Wilkins D R and Fabian A C 2011 Determination of the x-ray reflection emissivity profile of 1H 0707-495 Mon.

Not. R. Astron. Soc. 414 1269–77[39] Reis R C, Fabian A C, Reynolds C S, Brenneman L W, Walton D J, Trippe M, Miller J M, Mushotzky R F

and Nowak M A 2012 X-ray spectral variability in NGC 3783 Astrophys. J. 745 93[40] Halpern J P 1984 Variable x-ray absorption in the QSO MR 2251-178 Astrophys. J. 281 90–94[41] Reynolds C S 1997 An x-ray spectral study of 24 type 1 active galactic nuclei Mon. Not. R. Astron.

Soc. 286 513–37[42] Netzer H et al 2003 The ionized gas and nuclear environment in NGC 3783: IV. Variability and modeling of the

900 Kilosecond Chandra spectrum Astrophys. J. 599 933–48[43] McKernan B, Yaqoob T and Reynolds C S 2007 A soft x-ray study of type I active galactic nuclei

observed with Chandra high-energy transmission grating spectrometer Mon. Not. R. Astron. Soc.379 1359–72

[44] Kallman T and Bautista M 2001 Photoionization and high-density gas Astrophys. J. Suppl. 133 221–53[45] Reynolds C S, Brenneman L W, Lohfink A M, Trippe M L, Miller J M, Fabian A C and Nowak M A 2012 A

Monte Carlo Markov Chain based investigation of black hole spin in the active galaxy NGC 3783 Astrophys.J. 755 88

[46] Miller L, Turner T J and Reeves J N 2008 An absorption origin for the x-ray spectral variability of MCG-6-30-15Astron. Astrophys. 483 437–52

[47] Morgan C W et al 2012 Further evidence that quasar x-ray emitting regions are compact: x-ray and opticalmicrolensing in the lensed quasar Q J0158-4325 Astrophys. J. 756 52

[48] Risaliti G et al 2013 A rapidly spinning supermassive black hole at the centre of NGC1365 Nature494 449–51

[49] Marscher A P, Jorstad S G, Gomez J-L, Aller M F, Terasranta H, Lister M L and Stirling A M 2002 Observationalevidence for the accretion-disk origin for a radio jet in an active galaxy Nature 417 625–7

[50] Chatterjee R et al 2009 Disk-jet connection in the radio galaxy 3C 120 Astrophys. J. 704 1689–703[51] Chatterjee R et al 2011 Connection between the accretion disk and jet in the radio galaxy 3C 111 Astrophys.

J. 734 43[52] Lohfink A M et al 2013 An x-ray view of the jet-cycle in the radio loud AGN 3C120 Astrophys. J 772 83[53] Lohfink A M, Reynolds C S, Miller J M, Brenneman L W, Mushotzky R F, Nowak M A and Fabian A C 2012

The black hole spin and soft x-ray excess of the luminous Seyfert galaxy Fairall 9 Astrophys. J. 758 67[54] Walton D J, Nardini E, Fabian A C, Gallo L C and Reis R C 2013 Suzaku observations of ‘bare’ active galactic

nuclei Mon. Not. R. Astron. Soc. 428 2901–20[55] Patrick A R, Reeves J N, Porquet D, Markowitz A G, Braito V and Lobban A P 2012 A Suzaku survey of Fe K

lines in Seyfert 1 active galactic nuclei Mon. Not. R. Astron. Soc. 426 2522–65

16

Class. Quantum Grav. 30 (2013) 244004 C S Reynolds

[56] Reynolds C S 2013 Measuring black hole spin using x-ray reflection spectroscopy arXiv:1302.3260[astro-ph.HE]

[57] King A R, Pringle J E, West R G and Livio M 2004 Variability in black hole accretion discs Mon. Not. R. Astron.Soc. 348 111–22

[58] Cowperthwaite P S and Reynolds C S 2012 The central engine structure of 3C120: evidence for a retrogradeblack hole or a refilling accretion disk Astrophys. J. Lett. 752 L21

[59] Reynolds C S, Young A J, Begelman M C and Fabian A C 1999 X-ray iron line reverberation from black holeaccretion disks Astrophys. J. 514 164–79

[60] Shapiro I I 1964 Fourth test of general relativity Phys. Rev. Lett. 13 789–91[61] Zoghbi A, Fabian A C, Reynolds C S and Cackett E M 2012 Relativistic iron K x-ray reverberation in NGC

4151 Mon. Not. R. Astron. Soc. 422 129–34[62] Fabian A C et al 2009 Broad line emission from iron K- and L-shell transitions in the active galaxy 1H0707-495

Nature 459 540–2[63] Zoghbi A, Fabian A C, Uttley P, Miniutti G, Gallo L C, Reynolds C S, Miller J M and Ponti G 2010 Broad iron

L line and x-ray reverberation in 1H0707-495 Mon. Not. R. Astron. Soc. 401 2419–32[64] De Marco B, Ponti G, Cappi M, Dadina M, Uttley P, Cackett E M, Fabian A C and Miniutti G 2013 Discovery

of a relation between black hole mass and soft x-ray time lags in active galactic nuclei Mon. Not. R. Astron.Soc. 431 2441–52

[65] Zoghbi A, Reynolds C, Cackett E M, Miniutti G, Kara E and Fabian A C 2013 Discovery of Fe Kα x-rayreverberation around the black holes in MCG-5-23-16 and NGC 7314 Astrophys. J. 767 121

[66] Kara E, Fabian A C, Cackett E M, Uttley P, Wilkins D R and Zoghbi A 2013 Discovery of high-frequency ironK lags in Ark 564 and Mrk 335 Mon. Not. R. Astron. Soc. 434 1129

[67] Chartas G, Kochanek C S, Dai X, Poindexter S and Garmire G 2009 X-ray microlensing in RXJ1131-1231 andHE1104-1805 Astrophys. J. 693 174–85

[68] Dai X, Kochanek C S, Chartas G, Kozłowski S, Morgan C W, Garmire G and Agol E 2010 The sizes of thex-ray and optical emission regions of RXJ 1131-1231 Astrophys. J. 709 278–85

[69] Davis S W and Laor A 2011 The radiative efficiency of accretion flows in individual active galactic nucleiAstrophys. J. 728 98

[70] Daly R A 2011 Estimates of black hole spin properties of 55 sources Mon. Not. R. Astron. Soc. 414 1253–62[71] Rees M J, Begelman M C, Blandford R D and Phinney E S 1982 Ion-supported tori and the origin of radio jets

Nature 295 17–21[72] Narayan R, Yi I and Mahadevan R 1995 Explaining the spectrum of Sagittarius A∗ with a model of an accreting

black hole Nature 374 623–5[73] Moscibrodzka M, Gammie C F, Dolence J C, Shiokawa H and Leung P K 2009 Radiative models of SGR A*

from GRMHD simulations Astrophys. J. 706 497–507[74] Dexter J, McKinney J C and Agol E 2012 The size of the jet launching region in M87 Mon. Not. R. Astron.

Soc. 421 1517–28[75] Shcherbakov R V, Penna R F and McKinney J C 2012 Sagittarius A* accretion flow and black hole parameters

from general relativistic dynamical and polarized radiative modeling Astrophys. J. 755 133[76] Falcke H, Melia F and Agol E 2000 Viewing the shadow of the black hole at the galactic center Astrophys. J.

Lett. 528 L13–L16[77] Huang L, Cai M, Shen Z-Q and Yuan F 2007 Black hole shadow image and visibility analysis of Sagittarius A*

Mon. Not. R. Astron. Soc. 379 833–40[78] Doeleman S S et al 2008 Event-horizon-scale structure in the supermassive black hole candidate at the galactic

centre Nature 455 78–80[79] Doeleman S S et al 2012 Jet launching structure resolved near the supermassive black hole in M87

Science 338 355[80] Bambi C and Freese K 2009 Apparent shape of super-spinning black holes Phys. Rev. D 79 043002[81] Bambi C and Yoshida N 2010 Shape and position of the shadow in the δ = 2 Tomimatsu–Sato spacetime Class.

Quantum Grav. 27 205006[82] Johannsen T and Psaltis D 2013 Testing the no-hair theorem with observations in the electromagnetic spectrum:

IV. Relativistically broadened iron lines Astrophys. J. 773 57[83] Bambi C 2013 Testing the space-time geometry around black hole candidates with the analysis of the broad Kα

iron line Phys. Rev. D 87 023007[84] Bambi C and Malafarina D 2013 Kα iron line profile from accretion disks around regular and singular exotic

compact objects arXiv:1307.2106 [gr-qc]

17