IMPLICATIONS OF GAMMA-RAY TRANSPARENCY CONSTRAINTS IN BLAZARS - MINIMUM DISTANCES AND GAMMA-RAY COLLIMATION

We develop a general expression for the gamma-gamma absorption coefficient, alpha(gamma gamma), 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, R(0), and the inner radius, R(ms), which is the radius of marginal stability for a Schwarzschild black hole. We use our result for alpha(gamma gamma) to calculate the gamma - gamma optical depth, tau(gamma gamma), for gamma-rays created at height z and propagating at angle phi relative to the disk axis, and we show that for phi = 0 and z greater than or similar to R(0), tau(gamma gamma)alpha E(alpha)Z(-2 alpha-3), where alpha is the X-ray spectral index and E is the gamma-ray energy. 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 1991 June flare of 3C 279. In order to obtain an upper limit, we assume that all of the X-rays observed contemporaneously by Ginga were emitted by the disk. Our results suggest that the observed gamma-rays may have originated within less than or similar to 45GM/c(2) from a black hole of mass greater than or similar to 10(9) M., perhaps in active plasma located above the central funnel of the accretion disk. This raises the possibility of establishing a direct connection between the production of the observed gamma-rays and the accretion of material onto the black hole. We also consider the variation of the optical depth as a function of the angle of propagation phi. 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.