Radiative transfer and limb darkening of accretion disks

Abstract

The transfer equation in a geometrically thin accretion disk is reexamined under the plane-parallel approximation with a finite optical depth. The emergent intensity is analytically obtained in cases with or without internal heating. For large or infinite optical depth, the emergent intensity exhibits the usual limb-darkening effect, where the intensity changes linearly as a function of the direction cosine. For a small optical depth, on the other hand, the angle-dependence of the emergent intensity changes drastically. In the case without heating, but with uniform incident radiation at the disk equator, the emergent intensity becomes isotropic for a small optical depth. In the case with uniform internal heating, limb brightening takes place for a small optical depth. We also emphasize and discuss the limb-darkening effect in an accretion disk for several cases. © 2006. Astronomical Society of Japan.