Radiative Transfer in Spherically Symmetric Systems-IV: SOLUTION OF THE LINE TRANSFER PROBLEM WITH RADIAL VELOCITY FIELDS

A numerical procedure is presented for solving the line transfer problem with complete redistribution in spherically symmetric atmospheres in which the radial velocity is an arbitrary function of radius, limited by practical considerations to maximum velocities a few times the mean thermal velocity. In this procedure the transfer equation, written in the observer's frame, is differenced along rays and the resulting very large set of coupled linear equations is cast into the novel form, proposed by Rybicki, that allows for extremely rapid solution of the system. Numerical results are discussed for three sequences of models, two with linear velocity laws and one with constant velocities, in which the effect of the transverse velocity gradient is demonstrated. It is shown that velocities as small as 0.05 of the mean thermal velocity produce observable asymmetries in the flux profile.