Iron line profiles and self-shadowing from relativistic thick accretion discs

We present Fe Kα line profiles from and images of relativistic discs with finite thickness around a rotating black hole using a novel code. The line is thought to be produced by iron fluorescence of a relatively cold X-ray-illuminated material in the innermost parts of the accretion disc and provides an excellent diagnostic of accretion flows in the vicinity of black holes. Previous studies have concentrated on the case of a thin, Keplerian accretion disc. This disc must become thicker and sub-Keplerian with increasing accretion rates. These can affect the line profiles and in turn can influence the estimation of the accretion disc and black hole parameters from the observed line profiles. We here embark on, for the first time, a fully relativistic computation which offers key insights into the effects of geometrical thickness and the sub-Keplerian orbital velocity on the line profiles. We include all relativistic effects such as frame-dragging, Doppler boost, time dilation, gravitational redshift and light bending. We find that the separation and the relative height between the blue and red peaks of the line profile diminish as the thickness of the disc increases. This code is also well suited to produce accretion disc images. We calculate the redshift and flux images of the accretion disc and find that the observed image of the disc strongly depends on the inclination angle. The self-shadowing effect appears remarkable for a high inclination angle, and leads to the black hole shadow being in this case, completely hidden by the disc itself.     

A steady-state solution for warped accretion discs

We consider a thin accretion disc warped due to the Bardeen–Petterson effect, presenting both analytical and numerical solutions for the situation in which the two viscosity coefficients vary with radius as a power law, with the two power-law indices not necessarily equal. The analytical solutions are compared with numerical ones, showing that our new analytical solution is more accurate than the previous one, which overestimated the inclination change in the outer disc. Our new analytical solution is appropriate for moderately warped discs, while for extremely misaligned discs only a numerical solution is appropriate.     

Reprocessed emission from warped accretion discs with application to X-ray iron line profiles

Fluorescent iron line profiles currently provide the best diagnostic for engine geometries of active galactic nuclei (AGN). Here we construct a method for calculating the relativistic iron line profile from an arbitrarily warped accretion disc, illuminated from above and below by hard X-ray sources. This substantially generalizes previous calculations of reprocessing by accretion discs by including non-axisymmetric effects. We include a relativistic treatment of shadowing by ray-tracing photon paths along Schwarzschild geodesics. We apply this method to two classes of warped discs, and generate a selection of resulting line profiles. New profile features include a time-varying line profile if the warp precesses about the disc, profile differences between 'twisted' and 'twist-free' warps and the possibility of steeper red and softer blue fall-offs than for flat discs. We discuss some qualitative implications of the line profiles in the context of Type I and II Seyfert AGN and other sources.     

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.     

Luminous hot accretion discs

We find a new two-temperature hot branch of equilibrium solutions for stationary accretion discs around black holes. In units of Eddington accretion rate defined as 10 L _Edd c ², the accretion rates to which these solutions correspond are within the range ̇ ₁≲ ̇ ≲1, where ̇ ₁ is the critical rate of advection-dominated accretion flow (ADAF). In these solutions, the energy loss rate of the ions by Coulomb energy transfer between the ions and electrons is larger than the viscously heating rate and it is the advective heating together with the viscous dissipation that balances the Coulomb cooling of ions. When ̇ ₁≲ ̇ ≲ ̇ ₂, where ̇ ₂∼5 ̇ ₁<1, the accretion flow remains hot throughout the disc. When ̇ ₂≲ ̇ ≲1, Coulomb interaction will cool the inner region of the disc within a certain radius ( r _tr∼several tens of Schwarzschild radii or larger depending on the accretion rate and the outer boundary condition) and the disc will collapse on to the equatorial plane and form an optically thick cold annulus. Compared with ADAF, these hot solutions are much more luminous because of the high accretion rate and efficiency; therefore, we call them luminous hot accretion discs.     

Effects of Kerr space–time on spectral features from X-ray illuminated accretion discs

We performed detailed calculations of the relativistic effects acting on both the reflection continuum and the iron line from accretion discs around rotating black holes. Fully relativistic transfer of both illuminating and reprocessed photons has been considered in Kerr space–time. We calculated overall spectra, line profiles and integral quantities, and present their dependences on the black hole angular momentum. We show that the observed EW of the lines is substantially enlarged when the black hole rotates rapidly and/or the source of illumination is near above the hole. Therefore, such calculations provide a way to distinguish between different models of the central source.     

Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass M _BH and spin parameter a evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction     . We develop an iterative scheme based on the adiabatic approximation to study the BH–disc co-evolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen–Petterson effect) and interacts with the BH until the spin   J _BH  aligns with     . For a BH aligning with a corotating disc, the fractional increase in mass is typically less than a few per cent, while the spin modulus can increase up to a few tens of per cent. The alignment time-scale     is of  ∼10⁵–10⁶ yr  for a maximally rotating BH accreting at the Eddington rate. BH–disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular corotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.     

Concave accretion discs and X-ray reprocessing

Spectra of Seyfert 1s are commonly modelled as emission from an X-ray-illuminated flat accretion disc orbiting a central black hole. This provides both reprocessed and direct components of the X-ray emission, as required by observations of individual objects, and possibly a fraction of the cosmological X-ray background. There is some observational motivation for us to at least consider the role that an effectively concave disc surface might play: (1) a reprocessed fraction ≳1/2 in some Seyferts and possibly in the X-ray background, and (2) the commonality of a sharp iron line peak for Seyferts at 6.4 keV despite a dependence of peak location on inclination angle for flat disc models. Here it is shown that a concave disc may not only provide a larger total fraction of reprocessed photons, but can also reprocess a much larger fraction of photons in its outer regions compared with a flat disc. This reduces the sensitivity of the 6.4-keV peak location to the inner disc inclination angle because the outer regions are less affected by Doppler and gravitational effects. If the X-ray source is isotropic, the reprocessed fraction is directly determined by the concavity. If the X-ray source is anisotropic, the location of iron line peak can still be determined by concavity but the total reflected fraction need not be as large as for the isotropic emitter case. The geometric calculations herein are applicable to general accretion disc systems illuminated from the centre.     

Fractal features in accretion discs

Fractal concepts have been introduced in the accretion disc as a new feature. Due to the fractal nature of the flow, its continuity condition undergoes modifications. The conserved stationary fractal flow admits only saddle points and centre-type points in its phase portrait. Completely analytical solutions of the equilibrium point conditions indicate that the fractal properties enable the flow to behave like an effective continuum of lesser density, and facilitate the generation of transonicity. However, strongly fractal flows inhibit multitransonicity from developing. The mass accretion rate exhibits a fractal scaling behaviour, and the entire fractal accretion disc is stable under linearized dynamic perturbations.     

Gravitational instability of discs with dissipative coronae around supermassive black holes

We study the dynamical structure of a self-gravitating disc with coronae around a supermassive black hole. Assuming that the magnetorotational instability responsible for generating the turbulent stresses inside the disc is also the source for a magnetically dominated corona, a fraction of the power released when the disc matter accretes is transported to and dissipated in the corona. This has a major effect on the structure of the disc and its gravitational (in)stability according to our analytical and self-consistent solutions. We determine the radius where the disc crosses the inner radius of gravitational instability and forms the first stars. Not only the location of this radius which may extend to very large distances from the central black hole, but also the mass of the first stars highly depends on the input parameters, notably the viscosity coefficient, the mass of the central object and the accretion rate. For accretion discs around quasi-stellar objects (QSOs) and the Galactic Centre, we determine the self-gravitating radius and the mass of the first clumps. Comparing the cases with a corona and without a corona for typical discs around QSOs or the Galactic Centre, when the viscosity coefficient is around 0.3, we show that the self-gravitating radius decreases by a factor of approximately 2, but the mass of the fragments increases with more or less the same factor. The existence of a corona implies a more gravitationally unstable disc according to our results. The effect of a corona on the instability of the disc is more effective when the viscosity coefficient increases.