2006A&A...453..773S

We extend the investigation of general relativistic effects on the observed X-ray continuum of Kerr black holes in the context of the light bending model (Miniutti & Fabian 2004). Assuming a ring-like illuminating source, co-rotating with the underlying accretion disk, we study the shape and normalisation of the primary and disc reflected continuum as well as the dependence of the observed spectrum on the line of sight for various source heights and radii. These calculations are performed using Monte-Carlo methods to compute the angle dependent reflection spectrum from the disc. The effects of general relativity are illustrated by a comparison with Newtonian and Special Relativity calculations. Relativistic distortions can strongly affect the shape of the reflected spectrum. Light bending can dramatically increase the observable reflected flux and reduce the primary emission. In addition, multiple reflections due to the reflected photons deflected toward the disc can alter significantly the shape of the spectrum above 10 keV. We explore the predicted variations of the observed reflected and primary fluxes with the height and radius of the source. Large variations of the ring radius at constant height can lead to an (unobserved) anti-correlation between primary and reflected flux. In another side, the variability behaviour of several sources can be reproduced if the ring source radius is small (<5r_g), and its height varies by a large factor. In particular, a non-linear flux-flux relation, similar to that observed in several sources, can be produced. We compare our model with the flux-flux plot of NGC 4051, and find an agreement for low inclination angles (<20°), ring source radius ≲3r_g and a height varying between 0.5 to 10r_g. Regarding the angular distribution of the radiation, we find some important qualitative differences with respect to the Newtonian case. The reflected flux at larger inclination is relatively stronger than in the Newtonian model, the reflection fraction increasing with inclination.