APPARENT SIZES AND SPECTRAL-LINE PROFILES FOR SPHERICAL (3-DIMENSIONAL) ASTROPHYSICAL MASERS

Calculations are performed for the frequency-dependent transport of ra diation in a uniform spherical maser. Coupling between the intensities at different frequencies is treated. Spherical masers are commonly ut ilized as idealized geometries in which to assess possible deviations (sometimes, ''three-dimensional effects'') from the approximation of a linear geometry. We find that the spectral line profile rebroadens in approximately the same manner as that for a linear maser so that the relationship between the line breadth and the luminosity, beaming angl e, and degree of saturation is essentially unchanged. The variation of the apparent size of a spherical maser with frequency is not found to be significant at frequencies within the line profile at which the in tensity is appreciable. The ''standard approximation'' is adequate for obtaining most of the basic properties of spherical masers that have been examined including the relationship between the pumping (or molec ular populations) and the intensity of maser radiation. The improved m ethods employed here are, however, necessary to obtain variation of th e apparent size with frequency in the saturated regime. These conclusi ons differ from those of previous investigators. The calculations here are more reliable than those of previous investigations because these are self-consistent and avoid certain inaccurate simplifications.