A short review of relativistic iron lines from stellar‐mass black holes

In this contribution, I briefly review recent progress in detecting and measuring the properties of relativistic iron lines observed in stellar‐mass black hole systems, and the aspects of these lines that are most relevant to studies of similar lines in Seyfert‐1 AGN. In particular, the lines observed in stellar‐mass black holes are not complicated by complex low‐energy absorption or partial‐covering of the central engine, and strong lines are largely independent of the model used to fit the underlying broad‐band continuum flux. Indeed, relativistic iron lines are the most robust diagnostic of black hole spin that is presently available to observers, with specific advantages over the systematics–plagued disk continuum. If accretion onto stellar‐mass black holes simply scales with mass, then the widespread nature of lines in stellar‐mass black holes may indicate that lines should be common in Seyfert‐1 AGN, though perhaps harder to detect. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

XMM‐Newton and broad iron lines

Iron line emission is common in the X‐ray spectra of accreting black holes. When the line emission is broad or variable then it is likely to originate from close to the black hole. X‐ray irradiation of the accretion flow by the power‐law X‐ray continuum produces the X‐ray ‘reflection’ spectrum which includes the iron line. The shape and variability of the iron lines and reflection can be used as a diagnostic of the radius, velocity and nature of the flow. The inner radius of the dense flow corresponds to the innermost stable circular orbit and thus can be used to determine the spin of the black hole. Studies of broad iron lines and reflection spectra offer much promise for understanding how the inner parts of accretion flows (and outflows) around black holes operate. There remains great potential for XMM‐Newton to continue to make significant progress in this work. The need for high quality spectra and thus for long exposure times is paramount. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Unifying Scheme for Low-Luminosity XRBs and AGN

In recent years, significant evidence for the similar nature of active galactic nuclei (AGN) and X-ray binaries (XRBs) has been gathered. We describe a unification scheme for accreting black holes following the idea that weakly accreting systems may be jet dominated. This is tested with the radio/X-ray correlation of XRBs and AGN. The established correlation is further used to diagnose ultra-luminous X-ray sources. For higher accretion rates, we explore high-power jets and the effect of Compton cooling of the jet by the accretion disk.     

Relativistic dynamical friction in a collisional fluid

The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is calculated for straight-line motion and circular motion, generalizing previous results by several authors. Possible applications to the study of extreme mass-ratio inspirals around strongly accreting supermassive black holes are suggested.     

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.     

X-rays from cusps of compact remnants near galactic centres

Compact remnants – stellar mass black holes and neutron stars formed in the inner few parsec of galactic centres are predicted to sink into the central parsec due to dynamical friction on low-mass stars, forming a high concentration cusp. Same physical region may also contain very high-density molecular clouds and accretion discs that are needed to fuel supermassive black hole (SMBH) activity. Here we estimate gas capture rates on to the cusp of stellar remnants, and the resulting X-ray luminosity, as a function of the accretion disc mass. At low disc masses, most compact objects are too dim to be observable, whereas in the high disc case most of them are accreting at their Eddington rates. We find that for low accretion disc masses, compact remnant cusps may be more luminous than the central SMBHs. This 'diffuse' emission may be of importance for local moderately bright active galactic nuclei (AGNs), especially low-luminosity AGNs. We also briefly discuss how this expected emission can be used to put constraints on the black hole cusp near our Galactic Centre.     

Magnetic fields of accretion disks and outflows in prograde and retrograde black holes

We show that for the accretion disk with equipartition between magnetic and radiative pressures, prograde black holes generate outflowing energy in jets more efficiently than retrograde black holes do. Both viscous radiative and irradiative disks provide more efficient outflow jets in the case of a prograde black hole than in the case of a retrograde black hole. Our results confirm the conclusion of Tchekhovskoy & McKinney (2012) that, for the same absolute value of the spin, prograde black holes with geometrically thick accretion disks generate outflows several times more efficiently than retrograde black holes do. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the absence of winds in advection-dominated accretion flows

We show that recently published assertions that advection-dominated accretion flows (ADAFs) require the presence of strong winds are unfounded because they assume that low radiative efficiency in flows accreting at low rates on to black holes implies vanishing radial energy and angular momentum fluxes through the flow (which is also formulated in terms of the 'Bernoulli function' being positive). This, however, is a property only of self-similar solutions which are an inadequate representation of global accretion flows. We recall general properties of accretion flows on to black holes and show that such, necessarily transonic, flows may have either d positive or negative Bernoulli function depending on the flow viscosity. Flows with low viscosities ( α ≲0.1 in the α -viscosity model) have a negative Bernoulli function. Without exception, all 2D and 1D numerical models of low-viscosity flows constructed to date experience no significant outflows. At high viscosities the presence of outflows depends on the assumed viscosity, on the equation of state and on the outer boundary condition. The positive sign of the Bernoulli function invoked in this context is irrelevant to the presence of outflows. As an illustration, we recall 2D numerical models with moderate viscosity that have positive values of the Bernoulli function and experience no outflows. ADAFs, therefore, do not differ from this point of view from thin Keplerian discs: they may have, but they do not have to have, strong winds.     

Stellar parameters of young brown dwarfs

We present X‐shooter observations of two brown dwarf candidates. We focus on the determination of stellar parameters and their errors. The targets, an accreting class II and a non‐accreting class III objects, are members of the σ Orionis star‐forming region. We derive the spectroscopic spectral types from the VIS spectrum and the stellar parameters. We find that the uncertainties on the stellar parameters have a minor effect on the determination of the mass accretion rate for the accreting star, thus confirming that the discrepancies between the mass accretion rate estimates found with different (simultaneous) tracers are probably due to different physical conditions where the accretion/wind indicators are produced (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of mass outflow rate from relativistic quasi-spherical accretion on to black holes

We compute the mass outflow rate R _m˙ from relativistic matter that is accreting quasi-spherically on to the Schwarzschild black holes. Taking the pair-plasma pressure-mediated shock surface as the effective boundary layer (of the black hole) from where the bulk of the outflow is assumed to be generated, computation of this rate is done using combinations of exact transonic inflow and outflow solutions. We find that R _m˙ depends on the initial parameters of the flow, the polytropic index of matter, the degree of compression of matter near the shock surface and the location of the shock surface itself. We thus not only study the variation of the mass outflow rate as a function of various physical parameters governing the problem, but also provide a sufficiently plausible estimation of this rate.     

Instability of spherical accretion — I. Shock-free Bondi accretion

We examine the spatial stability of spherical adiabatic Bondi accretion on to a point gravitating mass against external perturbations. Both transonic critical and subsonic subcritical accretion are shown to be stable against purely radial acoustic, vortex or entropy perturbations. In the case of non-radial perturbations the amplitude of the perturbations grows without limit with smaller radii. Instability manifests itself only if the size of the accreting body is much less than the Bondi radius so that the inflow is highly supersonic or highly subsonic at the surface of the accretor in the case of critical or subcritical accretion respectively. These asymptotics hold and consequently the instability may develop for adiabatic index of accreting gas γ < 5/3. We suggest that this instability may lead to an essential thermalization of accreting flow thus, particularly, solving the problem of otherwise inefficient energy release in spherical accretion on to a black hole.     

Constraining the number of compact remnants near Sgr A*

Due to dynamical friction stellar mass black holes and neutron stars are expected to form high-density cusps in the inner parsec of our Galaxy. These compact remnants, expected to number around 20 000, may be accreting cold dense gas present there, and give rise to potentially observable X-ray emission. Here we build a simple but detailed time-dependent model of such emission. The possibility that these accretion flows are radiatively inefficient is taken into account and brings in some uncertainty in the conclusions. Despite this uncertainty, we find that at least several X-ray sources of this nature should be detectable with Chandra at any one time. Turning this issue around, we also ask a question of what current observational constraints might be telling us about the total number of compact remnants. In our 'best guess' model, a cusp of ∼40 000 remnants overpredicts the number of discrete sources and the total X-ray luminosity of the inner parsec, and is hence ruled out. In the most radiatively inefficient scenario that we consider, the radiative efficiency is set to be as small as  ɛ= 10⁻⁵  . In this rather unlikely scenario, a cusp of ∼40 000 black holes would be allowed by the data, but several individual sources should still be visible. Future observations of the distribution and orbits of the cold ionized gas in the inner parsec of our Galaxy will put tighter constraints on the cusp of compact remnants.     

Low-Luminosity Accretion in Black Hole X-Ray Binaries and Active Galactic Nuclei

At luminosities below a few percent of Eddington, accreting black holes switch to a hard spectral state which is very different from the soft blackbody-like spectral state that is found at higher luminosities. The hard state is well-described by a two-temperature, optically thin, geometrically thick, advection-dominated accretion flow (ADAF) in which the ions are extremely hot (up to 10¹² K near the black hole), the electrons are also hot (∼10^9−10.5 K), and thermal Comptonization dominates the X-ray emission. The radiative efficiency of an ADAF decreases rapidly with decreasing mass accretion rate, becoming extremely low when a source reaches quiescence. ADAFs are expected to have strong outflows, which may explain why relativistic jets are often inferred from the radio emission of these sources. It has been suggested that most of the X-ray emission also comes from a jet, but this is less well established.     

Radiatively driven winds from effective boundary layer around black holes

Matter accreting onto black holes suffers a standing or oscillating shock wave in much of the parameter space. The post-shock region is hot, puffed up and reprocesses soft photons from a Keplerian disc to produce the characteristic hard tail of the spectrum of accretion discs. The post-shock torus is also the base of the bipolar jets. We study the interaction of these jets with the hard photons emitted from the disc. We show that radiative force can accelerate outflows but the drag can limit the terminal speed. We introduce an equilibrium speed υ_eq as a function of distance, above which the flow will experience radiative deceleration.     

Quasi-stars: accreting black holes inside massive envelopes

We study the structure and evolution of 'quasi-stars', accreting black holes embedded within massive hydrostatic gaseous envelopes. These configurations may model the early growth of supermassive black hole seeds. The accretion rate on to the black hole adjusts so that the luminosity carried by the convective envelope equals the Eddington limit for the total mass,   M _*+ M _BH≈ M _*  . This greatly exceeds the Eddington limit for the black hole mass alone, leading to rapid growth of the black hole. We use analytic models and numerical stellar structure calculations to study the structure and evolution of quasi-stars. We show that the photospheric temperature of the envelope scales as   T _ph∝ M ^−2/5_BH M ^7/20_*  , and decreases with time while the black hole mass increases. Once   T _ph < 10⁴ K  , the photospheric opacity drops precipitously and T _ph hits a limiting value, analogous to the Hayashi track for red giants and protostars, below which no hydrostatic solution for the convective envelope exists. For metal-free (Population III) opacities, this limiting temperature is approximately 4000 K. After a quasi-star reaches this limiting temperature, it is rapidly dispersed by radiation pressure. We find that black hole seeds with masses between 10³ and  10⁴ M_⊙  could form via this mechanism in less than a few Myr.     

Bridging the gap between stellar-mass black holes and ultraluminous X-ray sources

The X-ray spectral and timing properties of ultraluminous X-ray sources (ULXs) have many similarities with the very high state of stellar-mass black holes (power-law dominated, at accretion rates greater than the Eddington rate). On the other hand, their cool disk components, large characteristic inner-disk radii and low characteristic timescales have been interpreted as evidence of black hole masses ～1000 M _⊙ (intermediate-mass black holes). Here we re-examine the physical interpretation of the cool disk model, in the context of accretion states of stellar-mass black holes. In particular, XTE J1550–564 can be considered the missing link between ULXs and stellar-mass black holes, because it exhibits a high-accretion-rate, low-disk-temperature state (ultraluminous branch). On the ultraluminous branch, the accretion rate is positively correlated with the disk truncation radius and the bolometric disk luminosity, while it is anti-correlated with the peak temperature and the frequency of quasi-periodic-oscillations. Two prototypical ULXs (NGC?1313 X-1 and X-2) also seem to move along that branch. We use a phenomenological model to show how the different range of spectral and timing parameters found in the two classes of accreting black holes depends on both their masses and accretion rates. We suggest that ULXs are consistent with black hole masses ～50–100 M _⊙, moderately inefficiently accreting at ≈20 times Eddington.     

The evolution of misaligned accretion discs and spinning black holes

In this paper, we consider the process of alignment of a spinning black hole and a surrounding misaligned accretion disc. We use a simplified set of equations, that describe the evolution of the system in the case where the propagation of warping disturbances in the accretion disc occurs diffusively, a situation likely to be common in the thin discs in active galactic nuclei (AGN). We also allow the direction of the hole spin to move under the action of the disc torques. In such a way, the evolution of the hole–disc system is computed self-consistently. We consider a number of different situations and we explore the relevant parameter range, by varying the location of the warp radius R _w and the propagation speed of the warp. We find that the dissipation associated with the twisting of the disc results in a large increase in the accretion rate through the disc, so that AGN accreting from a misaligned disc are likely to be significantly more luminous than those accreting from a flat disc. We compute explicitly the time-scales for the warping of the disc and for the alignment process and compare our results with earlier estimates based on simplified steady-state solutions. We also confirm earlier predictions that, under appropriate circumstances, accretion can proceed in a counter-aligned fashion, so that the accreted material will spin-down the hole, rather than spinning it up. Our results have implication in a number of different observational features of AGN such as the orientation and shape of jets, the shape of X-ray iron lines and the possibility of obscuration and absorption of X-ray by the outer disc as well as the general issue of the spin history of black holes during their growth.     

Relativistic reflection X-ray spectra of accretion disks

We have calculated the relativistic reflection component of the X-ray spectra of accretion disks in active galactic nuclei (AGN). Our calculations have shown that the spectra can be significantly modified by the motion of the accretion flow, and the gravity and rotation of the central black hole. The absorption edges in the spectra suffer severe en- ergy shifts and smearing, and the degree of distortion depends on the system parameters, in particular, the inner radius of the accretion disk and the disk viewing inclination angles. The effects are significant. Fluorescent X-ray emission lines from the inner accretion disk could be a powerful diagnostic of space-time distortion and dynamical relativistic effects near the event horizons of accreting black holes. However, improper treatment of the re- flection component in fitting the X-ray continuum could give rise to spurious line-like features. These features mimic the true fluorescent emission lines and may mask their relativistic signatures. Fully relativistic models for reflection continua together with the emission lines are needed in order to extract black-hole parameters from the AGN X-ray spectra.     

Behaviour of dissipative accretion flows around black holes

We investigate the behaviour of dissipative accreting matter close to a black hole, as this provides important observational features of galactic and extragalactic black hole candidates. We find a complete set of global solutions in the presence of viscosity and synchrotron cooling. We show that advective accretion flow can have a standing shock wave and the dynamics of the shock is controlled by the dissipation parameters (both viscosity and cooling). We study the effective region of the parameter space for standing as well as oscillating shock. We find that the shock front always moves towards the black hole as the dissipation parameters are increased. However, viscosity and cooling have opposite effects in deciding the solution topologies. We obtain two critical cooling parameters that separate the nature of the accretion solution.