Apparent Sizes and Spectral Line Profiles for Spherical and Disk Masers: Solutions to the Full Equations

Calculations are performed for the spectral line profiles and images of astrophysical maser radiation that emerges from isolated spheres and thin disks viewed edge-on. In contrast to previous investigations in which various approximations are made, the full equations are solved here for the frequency-dependent radiative transport that includes the thermal motion of the molecules. The spectral line profiles for spheres and disks are found to rebroaden to the full thermal Doppler breadth with increasing saturation in essentially the same way as is well known to occur for a linear maser. The variation with frequency in the apparent angular sizes of masing spheres and thin disks is found to be negligible at frequencies within the spectral line at which the flux is significant. Calculations are also performed for spherical and disk masers that are not isolated but for which the seed radiation for the masers is incident from one side, as would occur when a strong continuum source is on the far side of the masers. Again, the spectral line profiles are found to rebroaden to the full thermal breadths with increasing saturation, and there are no significant variations in the apparent angular sizes with frequency. However, the full rebroadening does occur at somewhat higher saturation, and the variation of the apparent angular sizes as a function of the degree of saturation is quite different from that of the isolated masers. Spheres and disks have served as idealized geometries with which to examine possible deviations from the linear approximation for astrophysical masers.