The Time Relaxation of a Resonance-Line Profile.

The scattering of Lyman-a and other resonance lines is important for many astrophysical applications. The Zanstra effect, by which radiation is redistributed within the resonance-line profile, has a profound effect on the change of the profile in time and space. Here we study the time development of an isotropic radiation field as a clue to understanding the more complex transfer problem. It is found, by using previously unnoticed properties of the redistribution probability, that the time-dependent scattering equation for isotropic Doppler scattering with zero damping has an analytic solution; it amounts to progressive widening of the profile approximately as (log t)1/2 with a simultaneous flattening of the line center. The effects of recoil due to the finite atomic mass are taken into account by a perturbation method and are shown to result in a slope - h/kT, for the central portion of the profile. The possibi]ity of extending the analysis to the transfer problem is discussed. Applications are made to the excitation of the 21-cm line by Lyman-a.