Inclination-Dependent AGN Flux Profiles From Strong Lensing of the Kerr Space-Time

Abstract

Recent quasar microlensing observations have constrained the X-ray emission sizes of quasars to be about 10 gravitational radii, one order of magnitude smaller than the optical emission sizes. Using a new ray-tracing code for the Kerr space-time, we find that the observed X-ray flux is strongly influenced by the gravity field of the central black hole, even for observers at moderate inclination angles. We calculate inclination-dependent flux profiles of active galactic nuclei in the optical and X-ray bands by combining the Kerr lensing and projection effects for future references. We further study the dependence of the X-ray-to-optical flux ratio on the inclination angle caused by differential lensing distortion of the X-ray and optical emission, assuming several corona geometries. The strong lensing X-ray-to-optical magnification ratio can change by a factor of ~10 for normal quasars in some cases, and another factor of ~10 for broad absorption line quasars (BALs) and obscured quasars. Comparing our results with the observed distributions in normal and broad absorption line quasars, we find that the inclination angle dependence of the magnification ratios can change the X-ray-to-optical flux ratio distributions significantly. In particular, the mean value of the spectrum slope parameter $α_{ox},$ $0.3838\log F_{2 keV}/F_{2500 Å}$, can differ by ~0.1-0.2 between normal and broad absorption line quasars, depending on corona geometries, suggesting larger intrinsic absorptions in BALs.