Accretion Disk Illumination in Schwarzschild and Kerr Geometries: Fitting Formulae

Abstract

We describe the methodology and compute the illumination of geometrically thin accretion disks around black holes of arbitrary spin parameter a exposed to the radiation of a pointlike isotropic source at arbitrary height above the disk on its symmetry axis. We then provide analytic fitting formulae for the illumination as a function of the source height h and the black hole angular momentum a. We find that for a source on the disk symmetry axis and with h/M > 3, the main effect of the parameter a is allowing the disk to extend to smaller radii (approaching r/M ! 1 as a/M ! 1) and thus allowing the illumination of regions of much higher rotational velocity and redshift. We also compute the illumination profiles for anisotropic emission associated with the motion of the source relative to the accretion disk and present the fractions of photons absorbed by the black hole, intercepted by the disk, or escaping to infinity for both isotropic and anisotropic emission for a/M ¼ 0 and 0.99. As the anisotropy (of a source approaching the disk) increases, the illumination profile reduces (approximately) to a single power law, whose index q, because of absorption of the beamed photons by the black hole, saturates to a value no higher than q k 3. Finally, we compute the fluorescent Fe line profiles associated with the specific illumination and compare them among various cases.

The role of the reflection fraction in constraining black hole spin

“…The maximum reflection fraction is obtained for the case of the accretion disc extending from the innermost stable circular orbit (ISCO) out to infinity, for the cases covered by Fukumura & Kazanas (2007), our results agree with the earlier calculations. Fig.…”

Soft X-Ray Excess From Shocked Accreting Plasma in Active Galactic Nuclei

“…To clearly address the modeled excess intensity, a more rigorous consideration of the compsh normalization is necessary as a future work. While it is still open to debate how much Comptonized flux can be produced from the small downstream region, one might argue that relativistic beaming (via a light bending effect) of seed photons toward small radii could preferentially allow for a sufficient centrally concentrated illumination (e.g., Fukumura & Kazanas 2007a). This may yield enough Comptonized photons, possibly in a scenario analogous to the observed double-peaked Hα emission line from the AGN accretion disk (e.g., Chen et al 1989;Eracleous & Halpern 1994;Strateva et al 2008).…”

Light Echoes in Kerr Geometry: A Source of High‐Frequency QPOs from Random X‐Ray Bursts

“…The small height of the disk and the source of the X-ray flares guarantee that except for the photons intercepted by the disk, the remainder can reach the observer unimpeded at infinity at nearly equatorial orbits. We assume that the photons are emitted isotropically in the rotating plasma rest frame (this entails some subtleties; see, e.g., Fukumura & Kazanas 2007) and that their trajectories are influenced by both the motion of the emitter and the dragging of inertial frames (the marginal orbit is inside the ergosphere for sufficiently large values of the black hole spin). We collect the photons at a large radial distance (r 1 /M ¼ 600, where M is black hole mass) as a function of time for different relative positions between the X-ray flare source and the observer to compile the response function of the system for observers at small disk latitudes.…”