Reflected iron line from a source above a Kerr black hole accretion disc

In this paper we present a fully relativistic approach to modelling both the continuum emission and the reflected fluorescent iron line from a primary X-ray source near a Kerr black hole. The X-ray source is located above an accretion disc orbiting around the black hole. The source is assumed to be a static point source located on an arbitrary position above the disc, on or off the axis of rotation. We carry out Monte Carlo simulations in order to estimate the iron line spectrum as well as its equivalent width. Because of the gravitational lensing effect, an enhancement of the iron line is expected when the primary source is located close to the central black hole. We find that for a source located on the axis of rotation the enhancement is relatively modest. An observer at inclination 30° would measure an equivalent width of ∼300 eV in the extreme case of a maximally rotating black hole and a source located at height 1.5 gravitational radii from the centre. This corresponds to an equivalent width enhancement factor of about 2 compared with the classical value where no lensing effect comes into play. However, when allowing the source to be located off the axis of rotation, much stronger enhancement can be obtained. In the extreme case of a maximally rotating black hole and a source located just above the approaching side of the disc, an observer at inclination 30° could measure an equivalent width as high as ∼1.5 keV (i.e., ∼10 times the classical value). We also find that observers located at high inclination angles observe a stronger line than observers at low inclination angles.     

Comptonization in the vicinity of the black hole horizon

Using a Monte Carlo method, we derive spectra arising from Comptonization taking place close to a Kerr black hole. We consider a model consisting of a hot thermal corona Comptonizing seed photons emitted by a cold accretion disc. We find that general relativistic effects are crucial for the emerging spectra in models, which involve significant contribution of radiation produced in the black hole ergosphere. As a result of this contribution, spectra of hard X-ray emission produced in the vicinity of a rapidly rotating black hole strongly depend on the inclination of the line of sight, with larger inclinations corresponding to harder spectra. Remarkably, such anisotropy could be responsible for properties of the X-ray spectra of Seyfert galaxies, which appear to be intrinsically harder in type 2 objects than in type 1, as reported recently.     

Small-scale inviscid accretion discs around black holes

Gas falling quasi-spherically on to a black hole forms an inner accretion disc if its specific angular momentum l exceeds l ∗∼ r _g c , where r _g is the Schwarzschild radius. The standard disc model assumes l ≫ l ∗. We argue that, in many black hole sources, accretion flows have angular momenta just above the threshold for disc formation, l ≳ l ∗, and assess the accretion mechanism in this regime. In a range l ∗< l < l _cr, a small-scale disc forms in which gas spirals fast into the black hole without any help from horizontal viscous stresses. Such an 'inviscid' disc, however, interacts inelastically with the feeding infall. The disc–infall interaction determines the dynamics and luminosity of the accretion flow. The inviscid disc radius can be as large as 14 r _g, and the energy release peaks at 2 r _g. The disc emits a Comptonized X-ray spectrum with a break at ∼100 keV. This accretion regime is likely to take place in wind-fed X-ray binaries and is also possible in active galactic nuclei.     

Effects of non-thermal tails in Maxwellian electron distributions on synchrotron and Compton processes

We investigate how the presence of a non-thermal tail beyond a Maxwellian electron distribution affects the synchrotron process as well as Comptonization in plasmas with parameters typical for accretion flows on to black holes. We find that the presence of the tail can significantly increase the net (after accounting for self-absorption) cyclo-synchrotron emission of the plasma, which then provides seed photons for Compton upscattering. Thus, the luminosity in the thermally Comptonized spectrum is enhanced as well. The importance of these effects increases with both increasing Eddington ratio and black hole mass. The enhancement of the Comptonized synchrotron luminosity can be as large as ∼10³ and ∼10⁵ for stellar and supermassive black holes, respectively, when the energy content in the non-thermal tail is 1 per cent.
The presence of the tail only weakly hardens the thermal Comptonization spectrum but it leads to the formation of a high-energy tail beyond the thermal cut-off, which two effects are independent of the nature of the seed photons. Since observations of high-energy tails in Comptonization spectra can constrain the non-thermal tails in the electron distribution and thus the Comptonized synchrotron luminosity, they provide upper limits on the strength of magnetic fields in accretion flows. In particular, the measurement of an MeV tail in the hard state of Cyg X-1 by McConnell et al. implies the magnetic field strength in this source to be at most an order of magnitude below equipartition.     

Profiles of spectral lines of an accretion ring around a Kerr black hole

Profiles of spectral lines emitted from an accretion ring around an object with strong gravitational field should be affected by Doppler shift, gravitational redshift, and deflection of light. Taking these effects into account, precise line profile of a Keplerian ring around a Kerr black hole for a distant observer is obtained by solving the kinetic equation of photons.     

X‐ray spectra and polarization from accreting black holes: polarization from an orbiting spot

The polarization from a spot orbiting around Schwarzschild and extreme Kerr black holes is studied. We assume different models of local polarization. Firstly, as a toy model we set the local polarization vector either normal to the disc plane, or perpendicular to the toroidal magnetic field. Then we examine the more realistic situation with a spot arising due to the emission from the primary source above the disc. We employ either Rayleigh single scattering or Compton multiple scattering approximations. The time dependence of the degree and angle of polarization during the spot revolution is examined as a function of the observer's inclination angle and black hole angular momentum. The gravitational and Doppler shifts, lensing effect as well as time delays are taken into account. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physics of accretion in the millisecond pulsar XTE J1751 − 305

We have undertaken an extensive study of X-ray data from the accreting millisecond pulsar XTE J1751 − 305 observed by RXTE and XMM–Newton during its 2002 outburst. In all aspects this source is similar to the prototypical millisecond pulsar SAX J1808.4 − 3658, except for the higher peak luminosity of 13 per cent of Eddington, and the optical depth of the hard X-ray source, which is larger by a factor ∼2. Its broad-band X-ray spectrum can be modelled by three components. We interpret the two soft components as thermal emission from a colder  ( kT ∼ 0.6 keV)  accretion disc and a hotter (∼1 keV) spot on the neutron star surface. We interpret the hard component as thermal Comptonization in plasma of temperature ∼40 keV and optical depth ∼1.5 in a slab geometry. The plasma is heated by the accretion shock as the material collimated by the magnetic field impacts on to the surface. The seed photons for Comptonization are provided by the hotspot, not by the disc. The Compton reflection is weak and the disc is probably truncated into an optically thin flow above the magnetospheric radius. Rotation of the emission region with the star creates an almost sinusoidal pulse profile with an rms amplitude of 3.3 per cent. The energy-dependent soft phase lags can be modelled by two pulsating components shifted in phase, which is naturally explained by a different character of emission of the optically thick spot and optically thin shock combined with the action of the Doppler boosting. The observed variability amplitude constrains the hotspot to lie within 3°–4° of the rotational pole. We estimate the inner radius of the optically thick accreting disc to be about 40 km. In that case, the absence of emission from the antipodal spot, which can be blocked by the accretion disc, gives the inclination of the system as ≳70°.     

The fraction of galaxies that contain active nuclei and their accretion rates

We investigate the relationship between the present-day optical luminosity function of galaxies and the X-ray luminosity function of Seyfert 1s to determine the fraction of galaxies that host Seyfert 1 nuclei and their Eddington ratios. The local type 1 active galactic nuclei (AGN) X-ray luminosity function is well reproduced if ∼1 per cent of all galaxies are type 1 Seyferts which have Eddington ratios of ∼10⁻³. However, in such a model the X-ray luminosity function is completely dominated by AGN in E and S0 galaxies, contrary to the observed mix of Seyfert host galaxies. To obtain a plausible mix of AGN host galaxy morphologies requires that the most massive black holes in E and S0 galaxies accrete with lower Eddington ratios, or have a lower incidence of Seyfert activity, than the central black holes of later-type galaxies.     

A possible energy mechanism for cosmological γ-ray bursts

We suggest that an extreme Kerr black hole with a mass ∼10⁶ M_⊙, a dimensionless angular momentum     and a marginally stable orbital radius     located in a normal galaxy may produce a γ -ray burst (GRB) by capturing and disrupting a star. During the capture period, a transient accretion disc is formed and a strong transient magnetic field ∼     lasting for     may be produced at the inner boundary of the accretion disc. A large amount of rotational energy of the black hole is extracted and released in an ultrarelativistic jet with a bulk Lorentz factor Γ larger than 10³ via the Blandford–Znajek process. The relativistic jet energy can be converted into γ -radiation via an internal shock mechanism. The GRB duration should be the same as the lifetime of the strong transient magnetic field. The maximum number of sub-bursts is estimated to be     because the disc material is likely to break into pieces with a size about the thickness of the disc h at the cusp     The shortest risetime of the burst estimated from this model is ∼     The model GRB density rate is also estimated.     

The structure of superposed Weyl fields

The properties of four superposed static axisymmetric (Weyl) space–times are illustrated by plotting their gravitational field lines and the shapes of their event horizons. The superpositions considered represent multiple Weyl systems, which are the most realistic astrophysically: the Schwarzschild black hole and the Appell ring are chosen as 'background' sources (each of them bears some features of the non -static Kerr source), and the Bach–Weyl ring and the 'annular' disc (inverted first Morgan–Morgan disc) of Lemos & Letelier are considered in their equatorial planes as additional sources. We study the influence of the parameters of additional sources on the fields of the central bodies.     

Reprocessing of X-rays in the outer accretion disc of the black hole binary XTE J1817−330

We build a simple model of the optical/ultraviolet (UV) emission from irradiation of the outer disc by the inner disc and coronal emission in black hole binaries. We apply this to the broad-band Swift data from the outburst of the black hole binary XTE J1817−330 to confirm previous results that the optical/UV emission in the soft state is consistent with a reprocessing a constant fraction of the bolometric X-ray luminosity. However, this is very surprising as the disc temperature drops by more than a factor of 3 in the soft state, which should produce a marked change in the reprocessing efficiency. The easiest way to match the observed constant reprocessed fraction is for the disc skin to be highly ionized (as suggested 30 yr ago by van Paradijs), so that the bulk of the disc flux is reflected and only the hardest X-rays heat the disc. The constant reprocessed fraction also favours direct illumination of the disc over a scattering origin as the optical depth/solid angle of any scattering material (wind/corona) over the disc should decrease as the source luminosity declines. By contrast, the reprocessed fraction increases very significantly (by a factor of ∼6) as the source enters the hard state. This dramatic change is not evident from X-ray/UV flux correlations as it is masked by bandpass effects. However, it does not necessarily signal a change in emission, for example, the emergence of the jet dominating the optical/UV flux as the reflection albedo must change with the dramatic change in spectral shape.     

A detailed study of the 5-Hz quasi-periodic oscillations in the bright X-ray transient and black hole candidate GRS 1739–278

We present a detailed study of the 5-Hz quasi-periodic oscillation (QPO) recently discovered in the bright X-ray transient and black hole candidate (BHC) GRS     (Borozdin & Trudolyubov) during a Rossi X-ray Timing Explorer observation taken on 1996 March 31. In total 6.6 ksec of on-source data were obtained, divided in two data sets of 3.4 and 3.2 ksec which were separated by ∼2.6 ksec. The 5-Hz QPO was only present during the second data set. The QPO increased in strength from below 2 per cent rms amplitude for photon energies below 4 keV to ∼5 per cent rms amplitude for energies above 10 keV. The soft QPO photons (below 5 keV) lagged the hard ones (above 10 keV) by almost 1.5 rad. Besides the QPO fundamental, its first overtone was detected. The strength of the overtone increased with photon energy (from < 2 per cent rms below 5 keV to ∼8 per cent rms above 10 keV). Although limited statistics did not allow for an accurate determination of the lags of the first overtone, indications are that also for this QPO the soft photons lagged the hard ones. When the 5-Hz QPO was not detected (i.e., during the first part of the observation), a broad noise component was found for photon energies below 10 keV but it became almost a true QPO (with a Q value of ∼1.9) above that energy, with a frequency of ∼3 Hz. Its hard photons preceded the soft ones in a way reminiscent of the 5-Hz QPO, strongly suggesting that both features are physically related. We discuss our finding in the framework of low-frequency QPOs and their properties in BHCs.     

Application of a relativistic accretion disc model to X-ray spectra of LMC X-1 and GRO J1655-40

We present a general relativistic accretion disc model and its application to the soft-state X-ray spectra of black hole binaries. The model assumes a flat, optically thick disc around a rotating Kerr black hole. The disc locally radiates away the dissipated energy as a blackbody. Special and general relativistic effects influencing photons emitted by the disc are taken into account. The emerging spectrum, as seen by a distant observer, is parametrized by the black hole mass and spin, the accretion rate, the disc inclination angle and the inner disc radius.
We fit the ASCA soft-state X-ray spectra of LMC X-1 and GRO J1655-40 by this model. We find that, having additional limits on the black hole mass and inclination angle from optical/UV observations, we can constrain the black hole spin from X-ray data. In LMC X-1 the constraint is weak, and we can only rule out the maximally rotating black hole. In GRO J1655-40 we can limit the spin much better, and we find 0.68 a 0.88 . Accretion discs in both sources are radiation-pressure dominated. We do not find Compton reflection features in the spectra of any of these objects.     

Hot accretion discs with thermal Comptonization and advection in luminous black hole sources

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonization of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to ≲ 0.15 y^3/5 α^7/5 of the Eddington limit, where y and α are the Compton and viscosity parameters, respectively. The characteristic electron temperature and Thomson optical depth of the inner flow at accretion rates within an order of magnitude of that upper limit are ∼ 10⁹ K and ∼ 1, respectively. The resulting spectra are then in close agreement with the X-ray and soft γ-ray spectra from black hole binaries in the hard state and Seyferts. At low accretion rates, bremsstrahlung becomes the dominant radiative process.     

Self-consistent computation of γ-ray spectra due to proton–proton interactions in black hole systems

In the inner regions of an accretion disc around a black hole, relativistic protons can interact with ambient matter to produce electrons, positrons and γ-rays. The resultant steady-state electron and positron particle distributions are self-consistently computed taking into account Coulomb and Compton cooling,  e⁻ e⁺  pair production (due to γ–γ annihilation) and pair annihilation. While earlier works used the diffusion approximation to obtain the particle distributions, here we solve a more general integro-differential equation that correctly takes into account the large change in particle energy that occurs when the leptons Compton scatter off hard X-rays. Thus this formalism can also be applied to the hard state of black hole systems, where the dominant ambient photons are hard X-rays. The corresponding photon energy spectrum is calculated and compared with broad-band data of black hole binaries in different spectral states. The results indicate that the γ-ray spectra  ( E > 0.8 MeV)  of both the soft and hard spectral states and the entire hard X-ray/γ-ray spectrum of the ultrasoft state could be due to p–p interactions. These results are consistent with the hypothesis that there always exists in these systems a γ-ray spectral component due to p–p interactions that can contribute between 0.5 and 10 per cent of the total bolometric luminosity. The model predicts that GLAST would be able to detect black hole binaries and provide evidence for the presence of non-thermal protons, which in turn would give insight into the energy dissipation process and jet formation in these systems.     

The mass dependence of the overshooting parameter determined from eclipsing binary data

We report the discovery of emission features in the X-ray spectrum of GRO J1655–40 obtained with RXTE during the observation of 1997 February 26. We have fitted the features first by two Gaussian lines which in four spectra analysed have average energies of 5.85±0.08 and 7.32±0.13 keV, strongly suggestive that these are the red- and blueshifted wings of an iron disc line. These energies imply a velocity of ∼0.33 c . The blue wing is less bright than in the calculated profiles of disc lines near a black hole subject to Doppler boosting; however, known Fe absorption lines in GRO J1655–40 at energies between ∼7 and 8 keV can reduce the apparent brightness of the blue wing. Secondly, we have fitted the spectra using the disc line model of Laor based on a full relativistic treatment plus an absorption line, and show that good fits are obtained. This gives a rest-frame energy of the disc line between 6.4 and 6.8 keV, indicating that the line is iron K α emission probably of significantly ionized material. The Laor model shows that the line originates in a region of the accretion disc extending from ∼10 Schwarzschild radii from the black hole outwards. The line is direct evidence for the black hole nature of the compact object, and is the first discovery of a highly red- and blueshifted iron disc line in a Galactic source.     

Black hole masses from power density spectra: determinations and consequences

We analyse the scaling of the X-ray power density spectra with the mass of the black hole in the examples of Cyg X-1 and the Seyfert 1 galaxy NGC 5548. We show that the high-frequency tail of the power density spectrum can be successfully used for the determination of the black hole mass. We determine the masses of the black holes in six broad-line Seyfert 1 galaxies, five narrow-line Seyfert 1 galaxies and two quasi-stellar objects (QSOs) using the available power density spectra. The proposed scaling is clearly appropriate for other Seyfert galaxies and QSOs. In all but one of the normal Seyferts, the resulting luminosity to Eddington luminosity ratio is smaller than 0.15, with the source MCG -6-15-30 being an exception. The applicability of the same scaling to a narrow-line Seyfert 1 is less clear and there may be a systematic shift between the power spectra of NLS1 and S1 galaxies of the same mass, leading to underestimation of the black hole mass. However, both the method based on variability and the method based on spectral fitting show that those galaxies have relatively low masses and a high luminosity to Eddington luminosity ratio, supporting the view of those objects as analogues of galactic sources in their high, soft or very high state, based on the overall spectral shape. The bulge masses of their host galaxies are similar to that of normal Seyfert galaxies, so they do not follow the black hole mass–bulge mass relation for Seyfert galaxies, being evolutionarily less advanced, as suggested by Mathur. The bulge mass–black hole mass relation in our sample is consistent with being linear, with the black hole to bulge ratio ∼0.03 per cent, similar to Wandel and Laor for low-mass objects, but significantly shifted from the relation of Magorrian et al. and McLure & Dunlop.     

Delayed X-ray emission from fallback in compact-object mergers

When double neutron star or neutron star–black hole binaries merge, the final remnant may comprise a central solar-mass black hole surrounded by a  ∼0.01–0.1 M_⊙  torus. The subsequent evolution of this disc may be responsible for short γ-ray bursts (SGRBs). A comparable amount of mass is ejected into eccentric orbits and will eventually fallback to the merger site after ∼0.01 s. In this paper, we investigate analytically the fate of the fallback matter, which may provide a luminous signal long after the disc is exhausted. We find that matter in the eccentric tail returns at a super-Eddington rate and eventually (≳0.1 s) is unable to cool via neutrino emission and accrete all the way to the black hole. Therefore, contrary to previous claims, our analysis suggests that fallback matter is not an efficient source of late-time accretion power and unlikely to cause the late-flaring activity observed in SGRB afterglows. The fallback matter rather forms a radiation-driven wind or a bound atmosphere. In both the cases, the emitting plasma is very opaque and photons are released with a degraded energy in the X-ray band. We therefore suggest that compact binary mergers could be followed by an 'X-ray renaissance', as late as several days to weeks after the merger. This might be observed by the next generation of X-ray detectors.     

Broad Iron Lines in AGN and X-Ray Binaries

Several AGN and black hole X-ray binaries show a clear very broad iron line, which is strong evidence that the black holes are rapidly spinning. Detailed analysis of these objects shows that the emission line is not significantly affected by absorption and that the source variability is principally due to variation in amplitude of a power-law. Underlying this is a much less variable, relativistically-smeared, reflection-dominated, component which carries the imprint of strong gravity at a few gravitational radii. The strong gravitational light bending in these regions then explains the power-law variability as due to changes in height of the primary X-ray source above the disc. The reflection component, in particular its variability and the profile of the iron line, enables us to study the innermost regions around an accreting, spinning, black hole.     

Discovery of a broad iron line in the black hole candidate Swift J1753.5−0127, and the disc emission in the low/hard state revisited

We analysed simultaneous archival XMM–Newton and Rossi X-ray Timing Explorer observations of the X-ray binary and black hole candidate Swift J  1753.5−0127  . In a previous analysis of the same data, a soft thermal component was found in the X-ray spectrum, and the presence of an accretion disc extending close to the innermost stable circular orbit was proposed. This is in contrast with the standard picture in which the accretion disc is truncated at large radii in the low/hard state. We tested a number of spectral models and found that several of them fit the observed spectra without the need of a soft disc-like component. This result implies that the classical paradigm of a truncated accretion disc in the low/hard state cannot be ruled out by these data. We further discovered a broad iron emission line between 6 and 7 keV in these data. From fits to the line profile we found an inner disc radius that ranges between ∼6 and 16 gravitational radii, which can be in fact much larger, up to ∼250 gravitational radii, depending on the model used to fit the continuum and the line. We discuss the implications of these results in the context of a fully or partially truncated accretion disc.