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.     

Reprocessed emission line profiles from dense clouds in geometrically thick accretion engines

The central engines of active galactic nuclei (AGN) contain cold, dense material as well as hot X-ray-emitting gas. The standard paradigm for the engine geometry is a cold thin disc sandwiched between hot X-ray coronae. Strong support for this geometry in Seyferts comes from the study of fluorescent iron line profiles, although the evidence is not ubiquitously airtight. The thin disc model of line profiles in AGN and in X-ray binaries should still be benchmarked against other plausible possibilities. One proposed alternative is an engine consisting of dense clouds embedded in an optically thin, geometrically thick X-ray-emitting engine. This model is also motivated by studies of geometrically thick engines such as advection-dominated accretion flows (ADAFs). Here we compute the reprocessed iron line profiles from dense clouds embedded in geometrically thick, optically thin X-ray-emitting discs near a Schwarzschild black hole. We consider a range of cloud distributions and disc solutions, including ADAFs, pure radial infall and bipolar outflows. We find that such models can reproduce line profiles similar to those from geometrically thin, optically thick discs and might help alleviate some of the problems encountered from the latter. Thus, independent of thin discs, thick disc engines can also exhibit iron line profiles if embedded dense clouds can survive long enough to reprocess radiation.     

Emission-line profiles from self-gravitating toroids around black holes

We have computed line profiles from self-gravitating toroids around black holes. The specific angular momentum of the toroids is assumed to be constant in space. The images of the toroids show peculiar features in the far sides of the black holes. Concerning the line profiles, the red wing extends to the very low frequency region because the location of the inner edge is rather near the event horizon of the black hole and consequently the velocity of the inner edges of the toroids can be greater than that of the Kepler discs.     

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 response of the Fe Kα line to changes in the X-ray illumination of accretion discs

X-ray reflection spectra from photoionized accretion discs in active galaxies are presented for a wide range of illumination conditions. The energy, equivalent width (EW) and flux of the Fe K α line are shown to depend strongly on the ratio of illuminating flux to disc flux,   F _x/ F _disc  , the photon index of the irradiating power law, Γ, and the incidence angle of the radiation, i . When   F _x/ F _disc≤2  a neutral Fe K α line is prominent for all but the largest values of Γ. At higher illuminating fluxes an He-like Fe K α line at 6.7 keV dominates the line complex. With a high-energy cut-off of 100 keV, the thermal ionization instability seems to suppress the ionized Fe K α line when  Γ≤1.6  . The Fe K α line flux correlates with   F _x/ F _disc  , but the dependence weakens as iron becomes fully ionized. The EW is roughly constant when   F _x/ F _disc  is low and a neutral line dominates, but then declines as the line progresses through higher ionization stages. There is a strong positive correlation between the Fe K α EW and Γ when the line energy is at 6.7 keV, and a slight negative one when it is at 6.4 keV. This is a potential observational diagnostic of the ionization state of the disc. Observations of the broad Fe K α line, which take into account any narrow component, would be able to test these predictions. Ionized Fe K α lines at 6.7 keV are predicted to be common in a simple magnetic flare geometry. A model that includes multiple ionization gradients on the disc is postulated to reconcile the results with observations.     

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.     

Models of the iron Kα fluorescent line and the Compton Shoulder in irradiated accretion disc spectra

We present a full set of model atmosphere equations for the accretion disc around a supermassive black hole irradiated by a hard X-ray lamp of power-law spectral distribution. Model equations allow for multiple Compton scattering of radiation on free electrons, and for large relative photon–electron energy exchange at the time of scattering. We present spectra in specific intensities integrated over the disc surface. Theoretical outgoing intensity spectra show soft X-ray excess below 1 keV, and distinct Kα and Kβ fluorescent lines of iron. We demonstrate the existence of the Compton Shoulder and claim that it can contribute to the asymmetry and equivalent widths of some observed Fe Kα lines in active galactic nuclei. Our models exhibit the effect of limb-brightening in reflected X-rays.     

General Relativity effects and line emission

General Relativity effects (gravitational redshift, light bending, …) strongly modify the characteristics of the lines emitted close to the Black Hole in Active Galactic Nuclei and Galactic Black Hole systems. These effects are reviewed and illustrated, with particular emphasis on line emission from the accretion disc. Methods, based on the iron line, to measure the two astrophysically relevant parameters of a Black Hole, the mass and spin, are briefly discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Iron Kα line profiles and the inner boundary condition of accretion flows

Recent X-ray observations have shown evidence for exceptionally broad and skewed iron Kα emission lines from several accreting black hole systems. The lines are assumed to be due to fluorescence of the accretion disc illuminated by a surrounding corona and require a steep emissivity profile increasing into the innermost radius. This appears to question both standard accretion disc theory and the zero-torque assumption for the inner boundary condition, both of which predict a much less extreme profile. Instead it argues that a torque may be present due to magnetic coupling with matter in the plunging region or even to the spinning black hole itself. Discussion so far has centred on the torque acting on the disc. However, the crucial determinant of the iron line profile is the radial variation of the power radiated in the corona. Here we study the effects of different inner boundary conditions on the coronal emissivity and on the profiles of the observable Fe Kα lines. We argue that in the extreme case where a prominent highly redshifted component of the iron line is detected, requiring a steep emissivity profile in the innermost part and a flatter one outside, energy from the gas plunging into the black hole is being fed directly to the corona.     

Iron K line profiles driven by non-axisymmetric illumination

Previous calculations of Fe K line profiles are based on axisymmetric emissivity laws. In this paper, we show line profiles driven by non-axial symmetric illumination which results from an off-axis X-ray point source. We find that source location and motion have significant effects on the red wing and blue horn of the line profiles. The disc region under the source will receive more flux, which is the most important factor to affect the line profiles. We suggest that at least part of the variation in Fe K line profiles is caused by the motion of X-ray sources. Future observations of Fe K line profiles will provide more information about the distribution and motion of the X-ray sources around black holes, and hence the underlying physics.     

Doppler tomography of accretion in binaries

Since its conception, Doppler tomography has matured into a versatile and widely used tool. It exploits the information contained in the highly‐structured spectral line‐profiles typically observed in mass‐transferring binaries. Using inversion techniques akin to medical imaging, it permits the reconstruction of Doppler maps that image the accretion flow on micro‐arcsecond scales. I summarise the basic concepts behind the technique and highlight two recent results; the use of donor star emission as a means to system parameter determination, and the real‐time movies of the evolving accretion flow in the cataclysmic variable WZ Sge during its 2001 outburst. I conclude with future opportunities in Doppler tomography by exploiting the combination of superior data sets, second generation reconstruction codes and simulated theoretical tomograms to delve deeper into the physics of accretion flows. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Observational Effects of Strong gravity

The current paradigm of high energy spectroscopy tells us that light emitted from a wide variety of objects has its origin close to the black hole event horizon. As such, these photons are subject to general relativistic effects such as light-bending, gravitational lensing and redshift, time-dilation, etc. These gravitational effects are well-understood from a theoretical standpoint and therefore, provide a natural mechanism to test the properties of strong gravitational fields. To this end, we have developed a new (semi-analytic) strong gravity code, capable of describing the contribution of photons that perform multiple orbits of the hole. We apply this code to a simple Keplerian accretion disk in order to understand the role played by the angular emissivity, black hole spin and higher order images in forming the line profile.     

Extreme gravitational lensing near rotating black holes

We describe a new approach to calculating photon trajectories and gravitational lensing effects in the strong gravitational field of the Kerr black hole. These techniques are applied to explore both the imaging and spectral properties of photons emitted from an accretion disc, which perform multiple orbits of the central mass before escaping to infinity. Viewed at large inclinations, these higher-order photons contribute ∼20 per cent of the total luminosity of the system for a Schwarzschild hole, while for an extreme Kerr black hole this fraction rises to ∼60 per cent. In more realistic models, these photons will be reabsorbed by the disc at large distances from the hole, but this returning radiation could provide a physical mechanism to resolve the discrepancy between the predicted and observed optical/ultraviolet colours in active galactic nuclei. Conversely, at low inclinations, higher-order images reintercept the disc plane close to the black hole, so need not be absorbed by the disc if this is within the plunging region. These photons form a bright ring carrying approximately 10 per cent of the total disc luminosity for a Schwarzschild black hole. The spatial separation between the inner edge of the disc and the ring is similar to the size of the event horizon. This is resolvable for supermassive black holes with proposed X-ray interferometery missions such as the Microarcsecond X-ray Imaging Mission (MAXIM), and so has the potential to provide an observational test of strong field gravity.