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We describe the methodology and compute the illumination of geometricallythin accretion disks around black holes of arbitrary spin parameter $a$ exposedto the radiation of a point-like, isotropic source at arbitrary height abovethe disk on its symmetry axis. We then provide analytic fitting formulae forthe illumination as a function of the source height $h$ and the black holeangular momentum $a$. We find that for a source on the disk symmetry axis and$h/M > 3$, the main effect of the parameter $a$ is allowing the disk to extendto smaller radii (approaching $r/M \to 1$ as $a/M \to 1$) and thus allow theillumination of regions of much higher rotational velocity and redshift. Wealso compute the illumination profiles for anisotropic emission associated withthe motion of the source relative to the accretion disk and present thefractions of photons absorbed by the black hole, intercepted by the disk orescaping to infinity for both isotropic and anisotropic emission for $a/M=0$and $a/M=0.99$. As the anisotropy (of a source approaching the disk) increasesthe illumination profile reduces (approximately) to a single power-law, whoseindex, $q$, because of absorption of the beamed photons by the black hole,saturates to a value no higher than $q \gtrsim 3$. Finally, we compute thefluorescence Fe line profiles associated with the specific illumination andcompare them among various cases.

Accretion Disk Illumination in Schwarzschild and Kerr Geometries: Fitting Formulae