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Register a new userRelativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit
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The shapes of relativistic iron lines observed in spectra of candidate black holes carry the signatures of the strong gravitational fields in which the accretion disks lie. These lines result from the sum of the contributions of all images of the disk created by gravitational lensing, with the direct and first-order images largely dominating the overall shapes. Higher order images created by photons tightly winding around the black holes are often neglected in the modeling of these lines, since they require a substantially higher computational effort. With the help of the strong deflection limit, we present the most accurate semi-analytical calculation of these higher order contributions to the iron lines for Schwarzschild black holes. We show that two regimes exist depending on the inclination of the disk with respect to the line of sight. Many useful analytical formulae can be also derived in this framework.
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When an accretion disk falls prey to the runaway instability, a large portion of its mass is devoured by the black hole within a few dynamical times. Despite decades of effort, it is still unclear under what conditions such an instability can occur. The technically most advanced relativistic simulations to date were unable to find a clear sign for the onset of the instability. In this work, we present three-dimensional relativistic hydrodynamics simulations of accretion disks around black holes in dynamical space-time. We focus on the configurations that are expected to be particularly prone to the development of this instability. We demonstrate, for the first time, that the fully self-consistent general relativistic evolution does indeed produce a runaway instability.
We study the contributions to the relativistic Fe $K_{alpha}$ line profile from higher order images (HOIs) produced by strongly deflected rays from the disk which cross the plunging region, located between the innermost stable circular orbit (ISCO) radius and the event horizon of a Kerr black hole. We investigate the characteristics features imprinted by the HOIs in the line profile for different black hole spins, disk emissivity laws and inclinations. We find that they extend from the red wing of the profile up to energies slightly lower than those of the blue peak, adding $sim 0.4 - 1.3$% to the total line flux. The contribution to the specific flux is often in the $sim 1$% to 7% range, with the highest values attained for low and negative spin ($alesssim 0.3$) black holes surrounded by intermediate inclination angle ($isim40^{circ}$) disks. We simulate future observations of a black hole X-ray binary system with the Large Area Detector of the planned X-ray astronomy emph{enhanced X-ray Timing and Polarimetry Mission} (eXTP) and find that the fekal of systems accreting at $lesssim 1 $% the Eddington rate are affected by the HOI features for a range of parameters. This would provide evidence of the extreme gravitational lensing of HOI rays. Our simulations show also that not accounting for HOI contributions to the Fe $K_{alpha}$ line profile may systematically bias measurements of the black hole spin parameter towards values higher by up to $sim 0.3$ than the inputted ones.
A number of neutron star low-mass X-ray binaries have recently been discovered to show broad, asymmetric Fe K emission lines in their X-ray spectra. These lines are generally thought to be the most prominent part of a reflection spectrum, originating in the inner part of the accretion disk where strong relativistic effects can broaden emission lines. We present a comprehensive, systematic analysis of Suzaku and XMM-Newton spectra of 10 neutron star low-mass X-ray binaries, all of which display broad Fe K emission lines. Of the 10 sources, 4 are Z sources, 4 are atolls and 2 are accreting millisecond X-ray pulsars (also atolls). The Fe K lines are well fit by a relativistic line model for a Schwarzschild metric, and imply a narrow range of inner disk radii (6 - 15 GM/c^2) in most cases. This implies that the accretion disk extends close to the neutron star surface over a range of luminosities. Continuum modeling shows that for the majority of observations, a blackbody component (plausibly associated with the boundary layer) dominates the X-ray emission from 8 - 20 keV. Thus it appears likely that this spectral component produces the majority of the ionizing flux that illuminates the accretion disk. Therefore, we also fit the spectra with a blurred reflection model, wherein a blackbody component illuminates the disk. This model fits well in most cases, supporting the idea that the boundary layer is illuminating a geometrically thin disk.
We present an analytical treatment of gravitational lensing by a Kerr black hole in the weak deflection limit. Lightlike geodesics are expanded as a Taylor series up to and including third-order terms in m/b and a/b, where m is the black hole mass, a the angular momentum and b the impact parameter of the light ray. Positions and magnifications of individual images are computed with a perturbative analysis. At this order, the degeneracy with the translated Schwarzschild lens is broken. The critical curve is still a circle displaced from the black hole position in the equatorial direction and the corresponding caustic is point-like. The degeneracy between the black hole spin and its inclination relative to the observer is broken through the angular coordinates of the perturbed images.
In most accreting black-hole systems the copious X-rays commonly observed from the inner-most regions are accompanied by a reflection spectrum. The latter is the signature of energetic photons reprocessed by the optically thick material of an accretion disk. Given their abundance and fluorescence yield, the iron K-shell lines are the most prominent features in the X-ray reflected spectrum. Their line profiles can be grossly broadened and skewed by Doppler effects and gravitational redshift. Consequently, modeling the reflection spectrum provides one of the best methods to measure, among other physical quantities, the black-hole spin. At present the accuracy of the spin estimates is called into question because the data fits require very high iron abundances: typically several times the solar value. Concurrently no plausible physical explanation has been proffered for these black-hole systems to be so iron rich. The most likely explanation for the supersolar iron abundances is model shortfall at very high densities ($>10^{18}$ cm$^{-3}$) due to atomic data shortcomings in this regime. We review the current observational evidence for the iron supersolar abundance in many black-hole systems, and show the effects of high density in state-of-the-art reflection models. We also briefly discuss our current efforts to produce new atomic data for high-density plasmas, which are required to refine the photoionization models.
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