Black Hole Spin Parameter Research Articles

ASuzakusurvey of Fe K lines in Seyfert 1 active galactic nuclei

We construct full broadband models in an analysis of Suzaku observations of nearby Seyfert 1 AGN (z<0.2) with exposures >50ks and with greater than 30000 counts in order to study their iron line profiles. This results in a sample of 46 objects and 84 observations. After a full modelling of the broadband Suzaku and Swift-BAT data (0.6-100 keV) we find complex warm absorption is present in 59% of the objects in this sample which has a significant bearing upon the derived Fe K region parameters. Meanwhile 35% of the 46 objects require some degree of high column density partial coverer in order to fully model the hard X-ray spectrum. We also find that a large number of the objects in the sample (22%) require high velocity, high ionization outflows in the Fe K region resulting from Fe XXV and Fe XXVI. A further four AGN feature highly ionized Fe K absorbers consistent with zero outflow velocity, making a total of 14/46 (30%) AGN in this sample showing evidence for statistically significant absorption in the Fe K region. Narrow Fe K alpha emission from distant material at 6.4 keV is found to be almost ubiquitous in these AGN. Examining the 6-7 keV Fe K region we note that narrow emission lines originating from Fe XXV at 6.63-6.70 keV and from Fe XXVI at 6.97 keV are present in 52% and 39% of objects respectively. Our results suggest statistically significant relativistic Fe K alpha emission is detected in 23 of 46 objects (50%) at >99.5% confidence, measuring an average emissivity index of q=2.4\pm0.1 and equivalent width EW=96\pm10 eV using the relline model. When parameterised with a Gaussian we find an average line energy of 6.32\pm0.04 keV, sigma width=0.470\pm0.05 keV and EW=97\pm19 eV. Where we can place constraints upon the black hole spin parameter a, we do not require a maximally spinning black hole in all cases.

OBSERVATIONAL EVIDENCES FOR SPINNING BLACK HOLES: A PROOF OF GENERAL RELATIVITY FOR SPACETIME AROUND ROTATING BLACK HOLES

Since it was theorized by Kerr in 1963, determining the spin of black holes from observed data was paid very little attention until few years back. The main reasons behind this were the unavailability of adequate data and the lack of appropriate techniques. In this paper, we explore determining/predicting the spin of several black holes in X-ray binaries (XRBs) and in the center of galaxies, using X-ray and gamma-ray satellite data. For X-ray binaries, in order to explain observed quasi-periodic oscillations (QPOs), our model predicts the spin parameter of underlying black holes. On the other hand, the nature of spin parameters of black holes in BL Lacs and flat spectrum radio quasars (FSRQs) is predicted by studying the total luminosities of systems based on Fermi γ-ray data. All sources considered here exhibit characteristics of spinning black holes, which verifies natural existence of the Kerr metric.

A MONTE CARLO MARKOV CHAIN BASED INVESTIGATION OF BLACK HOLE SPIN IN THE ACTIVE GALAXY NGC 3783

The analysis of relativistically broadened X-ray spectral features from the inner accretion disk provides a powerful tool for measuring the spin of supermassive black holes (SMBH) in active galactic nuclei (AGN). However, AGN spectra are often complex and careful analysis employing appropriate and self-consistent models are required if one is to obtain robust results. In this paper, we revisit the deep July-2009 Suzaku observation of the Seyfert galaxy NGC3783 in order to study in a rigorous manner the robustness of the inferred black hole spin parameter. Using Monte Carlo Markov Chain (MCMC) techniques, we identify a (partial) modeling degeneracy between the iron abundance of the disk and the black hole spin parameter. We show that the data for NGC3783 strongly require both supersolar iron abundance (Z_Fe=2-4Zsun) and a rapidly spinning black hole (a>0.88). We discuss various astrophysical considerations that can affect the measured abundance. We note that, while the abundance enhancement inferred in NGC3783 is modest, the X-ray analysis of some other objects has found extreme iron abundances. We introduce the hypothesis that the radiative levitation of iron ions in the innermost regions of radiation-dominated AGN disks can enhance the photospheric abundance of iron. We show that radiative levitation is a plausible mechanism in the very inner regions of high accretion rate AGN disks.

CONSTRAINTS ON JET FORMATION MECHANISMS WITH THE MOST ENERGETIC GIANT OUTBURSTS IN MS 0735+7421

Giant X-ray cavities lie in some active galactic nuclei (AGNs) locating in central galaxies of clusters, most of these cavities are thought to be inflated by jets of AGNs. The jets can be either powered by rotating black holes or the accretion disks surrounding black holes, or both. In this work, we choose the most energetic cavity, MS 0735+7421, with stored energy ~ 10^62 erg, to constrain the jet formation mechanisms and the evolution of the central massive black hole in this source. The bolometric luminosity of the AGN in this cavity is ~ 10^(-5) L_Edd, however, the mean power of the jet required to inflate the cavity is estimated as ~ 0.02 L_Edd, which implies that the source has experienced strong outbursts previously. During outbursts, the jet power and the mass accretion rate should be significantly higher than its present values. We construct an accretion disk model, in which the angular momentum and energy carried away by jets is properly included, to calculate the spin and mass evolution of the massive black hole. In our calculations, different jet formation mechanisms are employed, and we find that the jets generated with the Blandford-Znajek (BZ) mechanism are unable to produce the giant cavity with ~ 10^62 erg in this source. Only the jets accelerated with the combination of the Blandford-Payne (BP) and BZ mechanisms can successfully inflate such a giant cavity, if the magnetic pressure is close to equipartition with the total (radiation+gas) pressure of the accretion disk. For dynamo generated magnetic field in the disk, such an energetic giant cavity can be inflated by the magnetically driven jets only if the initial black hole spin parameter a_0 > 0.95. Our calculations show that the final spin parameter a of the black hole is always ~ 0:9 - 0.998 for all the computational examples which can provide sufficient energy for the cavity of MS 0735+7421.

A disc-corona model for a rotating black hole

We propose a disc-corona model in which a geometrically thin, optically thick disc surrounds a Kerr black hole, and magnetic fields exert a time-steady torque on the inner edge of the accretion disc. The analytical expression of the total gravitational power is derived from the thin-disc dynamics equations by using this new boundary condition. It is shown that the magnetic torque can considerably enhance the amount of energy released in the disc-corona system. Furthermore, the global solutions of this disc-corona system are obtained numerically. We find that the fraction of the power dissipated into the corona in the total for such disc-corona system increases with the increasing dimensionless black hole spin parameter $a_\ast $, but is insensitive on the $\Delta \varepsilon $ which is the additional radiative efficiency parameter relevant to magnetic torque, for $\Delta\varepsilon > 1$. In addition, the emerged spectra from this disc-corona system are simulated by using Monte-Carlo method, and the effect of the different parameters on the output spectra is discussed.

Observational evidence for a correlation between jet power and black hole spin

Abstract We show that the 5-GHz radio flux of transient ballistic jets in black hole binaries correlates with the dimensionless black hole spin parameter a* estimated via the continuum-fitting method. The data suggest that jet power scales either as the square of a* or as the square of the angular velocity of the horizon ΩH. This is the first direct evidence that jets may be powered by black hole spin energy. The observed correlation validates the continuum-fitting method of measuring spin. In addition, for those black holes that have well-sampled radio observations of ballistic jets, the correlation may be used to obtain rough estimates of their spins.

General relativistic model of hot accretion flows with global Compton cooling

We present a model of optically thin, two-temperature, accretion flows using an exact Monte Carlo treatment of global Comptonization, with seed photons from synchrotron and bremsstrahlung emission, as well as with a fully general relativistic description of both the radiative and hydrodynamic processes. We consider accretion rates for which the luminosities of the flows are between ~0.001 and 0.01 of the Eddington luminosity. The black hole spin parameter strongly affects the flow structure within the innermost 10 gravitational radii. The resulting large difference between the Coulomb heating in models with a non-rotating and a rapidly rotating black hole is, however, outweighed by a strong contribution of compression work, much less dependent on spin. The consequent reduction of effects related to the value of the black spin is more significant at smaller accretion rates. For a non-rotating black hole, the compressive heating of electrons dominates over their Coulomb heating, and results in an approximately constant radiative efficiency of approximately 0.4 per cent in the considered range of luminosities. For a rapidly rotating black hole, the Coulomb heating dominates, the radiative efficiency is ~1 per cent and it slightly increases (but less significantly than estimated in some previous works) with increasing accretion rate. We find an agreement between our model, in which the synchrotron emission is the main source of seed photons, and observations of black-hole binaries in their hard states and AGNs at low luminosities. In particular, our model predicts a hardening of the X-ray spectrum with increasing luminosity, as indeed observed below ~0.01 of the Eddington luminosity in both black-hole binaries and AGNs. Also, our model approximately reproduces the luminosity and the slope of the X-ray emission in Cen A.

Can we constrain the maximum value for the spin parameter of the super-massive objects in galactic nuclei without knowing their actual nature?

In 4-dimensional General Relativity, black holes are described by the Kerr solution and are subject to the bound |a⁎|⩽1, where a⁎ is the black hole spin parameter. If current black hole candidates are not the black holes predicted in General Relativity, this bound does not hold and a⁎ might exceed 1. In this Letter, I relax the Kerr black hole hypothesis and I find that the value of the spin parameter of the super-massive black hole candidates in galactic nuclei cannot be higher than about 1.2. A higher spin parameter would not be consistent with a radiative efficiency η>0.15, as observed at least for the most luminous AGN. While a rigorous proof is lacking, I conjecture that the bound |a⁎|≲1.2 is independent of the exact nature of these objects.

BLACK HOLE SPIN IN Sw J1644+57 and Sw J2058+05

Recently a hard X-ray transient event, Sw J1644+57, was discovered by the Swift satellite. It likely marks the onset of a relativistic jet from a supermassive black hole, possibly triggered by a tidal disruption event. Another candidate in the same category, Sw J2058+05, was also reported. The low event rate suggests that only a small fraction of TDEs launch relativistic jets. A common speculation is that these rare events are related to rapidly spinning black holes. We attribute jet launching to the Blandford-Znajek mechanism, and use the available data to constrain the black hole spin parameter for the two events. It is found that the two black holes indeed carry a moderate to high spin, suggesting that black hole spin is likely the crucial factor behind the Sw J1644+57 - like events.

EVIDENCE FOR RAPIDLY ROTATING BLACK HOLES IN FANAROFF-RILEY I RADIO GALAXIES

We investigate the correlation between 151 MHz radio luminosity, L_151MHz, and jet power, P_jet, for a sample of low-power radio galaxies, of which the jet power is estimated from X-ray cavities. The jet power for a sample of FR I radio galaxies is estimated with the derived empirical correlation. We find that P_jet/L_Edd is positively correlated with Lx(2-10 keV)/L_Edd for FR Is, where L_Edd is the Eddington luminosity and Lx(2-10 keV) is 2-10 keV X-ray luminosity. We calculate the jet power of a hybrid model, as a variant of Blandford-Znajek model proposed by Meier, based on the global solution of the advection-dominated accretion flow (ADAF) surrounding a Kerr black hole (BH). Our model calculations suggest that the maximal jet power is a function of mass accretion rate and the black hole spin parameter j. The hard X-ray emission is believed to be mainly from the ADAFs in FR Is, and the mass accretion rate is therefore constrained with the X-ray emission in our ADAF model calculations. We find that the dimensionless angular momentum of BH j>~0.9 is required in order to reproduce the observed relation of P_jet/L_Edd-Lx(2-10 keV)/L_Edd for FR Is. Our conclusion will be strengthened if part of the X-ray emission is contributed by the jets. Our results suggest that BHs in FR I radio galaxies are rapidly spinning, which are almost not affected by the uncertainty of the black hole mass estimates.

Estimates of black hole spin properties of 55 sources

Studies of black hole spin and other parameters as a function of redshift provide information about the physical state and merger and accretion histories of the systems. One way that black hole spin may be estimated is through observations of extended radio sources. These sources, powered by outflows from an AGN, allow the beam power and total outflow energy to be studied. In a broad class of models, the beam power of the outflow is related to the spin of the black hole. This relationship is used to estimate black hole spins for 55 radio sources. The samples studied include 7 FR II quasars and 19 FR II radio galaxies with redshifts between 0.056 and 1.79, and 29 radio sources associated with CD galaxies with redshifts between 0.0035 and 0.291. The FR II sources studied have estimated spin values of between about 0.2 and 1; there is a range of values at a given redshift, and the values tend to increase with increasing redshift. Results obtained for FR II quasars are very similar to those obtained for FR II galaxies. A broader range of spin values are obtained for the sample of radio sources associated with CD galaxies studied. The fraction of the spin energy extracted per outflow event is estimated and ranges from about 0.03 to 0.5 for FR II sources and 0.002 to about 1 for radio sources associated with CD galaxies; the data are consistent with this fraction being independent of redshift though the uncertainties are large. The results obtained are consistent with those predicted by numerical simulations that track the merger and accretion history of AGN, supporting the idea that, for AGN with powerful large-scale outflows, beam power is directly related to black hole spin.

The rapid X-ray variability of NGC 4051

We present an analysis of the high-frequency X-ray variability of NGC 4051 (MBH∼ 1.7 × 106 M⊙) based on a series of XMM–Newton observations taken in 2009 with a total exposure of ∼570 ks (EPIC pn). These data reveal the form of the power spectrum over frequencies from 10−4 Hz, below the previously detected power spectral break, to ≳10−2 Hz, above the frequency of the innermost stable circular orbit (ISCO) around the black hole (νISCO∼ 10−3–10−2 Hz, depending on the black hole spin parameter j). This is equivalent to probing frequencies of ≳1 kHz in a stellar mass (MBH∼ 10 M⊙) black hole binary system. The power spectrum is a featureless power law over the region of the expected ISCO frequency, suggesting no strong enhancement or change in the variability at the fastest orbital period in the system. Despite the huge amplitude of the flux variations between the observations (peak-to-peak factor of ≳50), the power spectrum appears to be stationary in shape and varies in amplitude at all observed frequencies following the previously established linear rms–flux relation. The rms–flux relation is offset in flux by a small and energy-dependent amount. The simplest interpretation of the offset is in terms of a very soft spectral component that is practically constant (compared to the primary source of variability). One possible origin for this emission is a circumnuclear shock energized by a radiatively driven outflow from the central regions and emitting via inverse-Compton scattering of the central engine’s optical–UV continuum (as inferred from a separate analysis of the energy spectrum). A comparison with the power spectrum of a long XMM–Newton observation taken in 2001 gives only weak evidence for non-stationarity in power spectral shape or amplitude. Despite being among the most precisely estimated power spectra for any active galaxy, we find no strong evidence for quasi-periodic oscillations (QPOs) and determine an upper limit on the strength of a plausible QPO of ≲2 per cent rms in the 3 × 10−3 -0.1 Hz range and ∼5–10 per cent in the 10−4 -3 × 10−3 Hz range. We compare these results to the known properties of accreting stellar mass black holes in X-ray binaries, with the further aim of developing a ‘black hole unification’ scheme.

Multistate observations of the Galactic black hole XTE J1752−223: evidence for an intermediate black hole spin

The Galactic Black hole candidate XTE J1752-223 was observed during the decay of its 2009 outburst with the Suzaku and XMM-Newton observatories. The observed spectra are consistent with the source being in the ''intermediate`` and ''low-hard state`` respectively. The presence of a strong, relativistic iron emission line is clearly detected in both observations and the line profiles are found to be remarkably consistent and robust to a variety of continuum models. This strongly points to the compact object in \j\ being a stellar-mass black hole accretor and not a neutron star. Physically-motivated and self-consistent reflection models for the Fe-\ka\ emission-line profile and disk reflection spectrum rule out either a non-rotating, Schwarzchild black hole or a maximally rotating, Kerr black hole at greater than 3sigma level of confidence. Using a fully relativistic line function in which the black hole spin parameter is a variable, we have formally constrained the spin parameter to be $0.52\pm0.11 (1\sigma)$. Furthermore, we show that the source in the low--hard state still requires an optically--thick disk component having a luminosity which is consistent with the $L\propto T^4$ relation expected for a thin disk extending down to the inner--most stable circular orbit. Our result is in contrast to the prevailing paradigm that the disk is truncated in the low-hard state.

Measuring spin of a supermassive black hole at the Galactic centre — implications for a unique spin

Abstract We determine the spin of a supermassive black hole in the context of disc-seismology by comparing newly detected quasi-periodic oscillations (QPOs) of radio emission in the Galactic centre, Sagittarius A* (Sgr A*), as well as infrared and X-ray emissions with those of the Galactic black holes. We find that the spin parameters of black holes in Sgr A* and in Galactic X-ray sources have a unique value of ≈0.44 which is smaller than the generally accepted value for supermassive black holes, suggesting evidence for the angular momentum extraction of black holes during the growth of supermassive black holes. Our results demonstrate that the spin parameter approaches the equilibrium value where spin-up via accretion is balanced by spin-down via the Blandford–Znajek mechanism regardless of its initial spin. We anticipate that measuring the spin of black holes by using QPOs will open a new window for exploring the evolution of black holes in the Universe.

Tidal interaction of a small black hole in the field of a large Kerr black hole

The rates at which the mass and angular momentum of a small black hole change as a result of a tidal interaction with a much larger black hole are calculated to leading order in the small mass ratio. The small black hole is either rotating or nonrotating, and it moves on a circular orbit in the equatorial plane of the large Kerr black hole. The orbits are fully relativistic, and the rates are computed to all orders in the orbital velocity V < V_{isco}, which is limited only by the size of the innermost stable circular orbit. We show that as V \to V_{isco}, the rates take on a limiting value that depends only on V_{isco} and not on the spin parameter of the large black hole.

CONSTRAINING THE SPIN OF THE BLACK HOLE IN FAIRALL 9 WITHSUZAKU

We report on the results of spectral fits made to data obtained from a 168 ksec Suzaku observation of the Seyfert-1 galaxy Fairall 9. The source is clearly detected out to 30 keV. The observed spectrum is fairly simple; it is well-described by a power-law with a soft excess and disk reflection. A broad iron line is detected, and easily separated from distinct narrow components owing to the resolution of the CCDs in the X-ray Imaging Spectrometer (XIS). The broad line is revealed to be asymmetric, consistent with a disk origin. We fit the XIS and Hard X-ray Detector (HXD) spectra with relativistically-blurred disk reflection models. With the assumption that the inner disk extends to the innermost stable circular orbit, the best-fit model implies a black hole spin parameter of a = 0.60(7) and excludes extremal values at a high level of confidence. We discuss this result in the context of Seyfert observations and models of the cosmic distribution of black hole spin.

Maximum spin of black holes driving jets

Unbounded outflows in the form of highly collimated jets and broad winds appear to be a ubiquitous feature of accreting black hole systems. The most powerful jets are thought to derive a significant fraction, if not the majority, of their power from the rotational energy of the black hole. Whatever the precise mechanism that causes them, these jets must therefore exert a braking torque on the black hole. We calculate the spin-up function for an accreting black hole, accounting for this braking torque. We find that the predicted black hole spin-up function depends only on the black hole spin and dimensionless parameters describing the accretion flow. Using recent relativistic magnetohydrodynamical numerical simulation results to calibrate the efficiency of angular momentum transfer in the flow, we find that an ADAF flow will spin a black hole up (or down) to an equilibrium value of about 96% of the maximal spin value in the absence of jets. Combining our ADAF system with a simple model for jet power, we demonstrate that an equilibrium is reached at approximately 93% of the maximal spin value, as found in the numerical simulation studies of the spin-up of accreting black holes, at which point the spin-up of the hole by accreted material is balanced by the braking torque arising from jet production. Our model also yields a relationship between jet efficiency and black hole spin that is in surprisingly good agreement with that seen in the simulation studies, indicating that our simple model is a useful and convenient description of ADAF inflow - jet outflow about a spinning black hole for incorporation in models of the formation and evolution of galaxies, groups and clusters of galaxies.

Measurement of the Kerr spin parameter by observation of a compact object’s shadow

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.

STELLAR-MASS BLACK HOLE SPIN CONSTRAINTS FROM DISK REFLECTION AND CONTINUUM MODELING

Accretion disk reflection spectra, including broad iron emission lines, bear the imprints of the strong Doppler shifts and gravitational red-shifts close to black holes. The extremity of these shifts depends on the proximity of the innermost stable circular orbit to the black hole, and that orbit is determined by the black hole spin parameter. Modeling relativistic spectral features, then, gives a means of estimating black hole spin. We report on the results of fits made to archival X-ray spectra of stellar-mass black holes and black hole candidates, selected for strong disk reflection features. Following recent work, these spectra were fit with reflection models and disk continuum emission models (where required) in which black hole spin is a free parameter. Although our results must be regarded as preliminary, we find evidence for a broad range of black hole spin parameters in our sample. The black holes with the most relativistic radio jets are found to have high spin parameters, though jets are observed in a black hole with a low spin parameter. For those sources with constrained binary system parameters, we examine the distribution of spin parameters versus black hole mass, binary mass ratio, and orbital period. We discuss the results within the context of black hole creation events, relativistic jet production, and efforts to probe the innermost relativistic regime around black holes.

INFERRING THE INCLINATION OF A BLACK HOLE ACCRETION DISK FROM OBSERVATIONS OF ITS POLARIZED CONTINUUM RADIATION

Spin parameters of stellar-mass black holes in X-ray binaries are currently being estimated by fitting the X-ray continuum spectra of their accretion disk emission. For this method, it is necessary to know the inclination of the X-ray-producing inner region of the disk. Since the inner disk is expected to be oriented perpendicular to the spin axis of the hole, the usual practice is to assume that the black hole spin is aligned with the orbital angular momentum vector of the binary, and to estimate the inclination of the latter from ellipsoidal modulations in the light curve of the secondary star. We show that the inclination of the disk can be inferred directly if we have both spectral and polarization information on the disk radiation. The predicted degree of polarization varies from 0% to 5% as the disk inclination changes from face-on to edge-on. With current X-ray polarimetric techniques the polarization degree of a typical bright X-ray binary could be measured to an accuracy of 0.1% by observing the source for about 10 days. Such a measurement would constrain the disk inclination to within a degree or two and would significantly improve the reliability of black hole spin estimates. In addition, it would provide new information on the tilt between the black hole spin axis and the orbital rotation axis of the binary, which would constrain any velocity kicks experienced by stellar-mass black holes during their formation.