EMISSION-LINE PROFILES FROM A RELATIVISTIC ACCRETION DISK AND THE ROLE OF ITS MULTIPLE IMAGES

Emission lines from a relativistic accretion disk around a black hole are studied by using quasi-analytic solutions of photon geodesics. Unlike the previous approaches, in this paper, the effects of the multiple images of the disk are considered, i.e., the contribution to the line profiles of the photons from the upper side of the disk as well as that from the back side with the photon trajectories crossing the plane of the disk. Different from the Newtonian case, the gravitational bending of light and the central black hole makes the photons visible to the observer at infinity. Because they are near the black hole, the trajectories of these higher order-image photons have more probability of penetrating the disk plane below the inner edge of the optically thick accreting matter and to reach us. For an optically thin disk, all the higher order-image photons can be observed; the two sides of a disk with an edge-on geometry should, in principle, make equal contribution to the observed flux. Therefore, the contribution to the line intensity from the back side of an accretion disk for a highly inclined system is as important as that from its upper side. Profiles with various free parameters are shown. Lines of higher order-image photons contrast both in strength and in shape from those of zero order. Higher order-image photons contribute nonnegligibly to the observed line intensity. Our calculations show that the first-order-image line can contribute as much as 80% or even more of the zero-order-image line intensity to the observed line for a highly inclined disk.