Implications of Gamma-Ray Transparency Constraints in Blazars: Minimum Distances and Gamma-Ray Collimation

Abstract

We develop a general expression for the gamma-gamma absorption coefficient for gamma-rays propagating in an arbitrary direction at an arbitrary point in space above an X-ray emitting accretion disk. The X-ray intensity is assumed to vary as a power law in energy and radius between the outer disk radius and the inner radius, which is the radius of marginal stability for a Schwarzschild black hole. We use our result for the absorption coefficient to calculate the gamma-gamma optical depth for gamma-rays created at an arbitrary height and propagating at an arbitrary angle relative to the disk axis. As an application, we use our formalism to compute the minimum distance between the central black hole and the site of production of the gamma-rays detected by EGRET during the June 1991 flare of 3C 279. Our results indicate that the ``focusing'' of the gamma-rays along the disk axis due to pair production is strong enough to explain the observed degree of alignment in blazar sources. If the gamma-rays are produced isotropically in gamma-ray blazars, then these objects should appear as bright MeV sources when viewed along off-axis lines of sight.