Optical caustics in a kerr spacetime and the origin of rapid X-ray variability in active galactic nuclei

Abstract

A detailed analysis of the optical caustic structure around rotating black holes is given, including a discussion of their possible relevance to rapid X-ray variability in active galactic nuclei (AGNs). It is found that the primary caustic surface takes the form of a small tube with an astroid (four-cusped) cross section. At large distances behind the hole, the tube is oriented parallel to the optic axis, but displaced transversely from it by a distance a sin θ_0_, where a is the spin of the hole in geometrical units and θ_0_ is the inclination angle of the distant observer from the pole. The transverse size s and central magnification M_0_ of the caustic are found to vary asymptotically as s~0.34a^2^ sin^2^ θ_0_r^-1^ and M_sun_~[22M^1/2^/(a^2^ sin^2^ {theta_0_)]r^3/2^ (where M is the hole mass), respectively, in agreement with the results of an analytic, asymptotic analysis performed for θ_0_ = π/2. The magnification is surprisingly high everywhere within the caustic. A fast, efficient, general-purpose code to trace geodesics in a Kerr metric is described, the calculation of the caustic structure of the Kerr metric representing an initial application. Sample light curves for point sources on geodesic orbits crossing the caustic are computed; in general, the lensing dominates all other features. The influence of caustics in computing the appearance of thick accretion disk models is examined. The importance of caustics in real AGNs depends on the geometry of the emitting matter; they could be important for disks and especially for jets, in which a significant fraction of the emitting material can reside near a caustic, for suitably oriented observers.