Relaxation of molecular velocities and spectral line profiles of astrophysical masers

The rates at which the velocities of water molecules relax to a Maxwellian distribution are calculated under conditions that are representative of those in astrophysical water masers. Populations are calculated as a function of velocity for the lowest 40 rotational energy levels of ortho-water in order to make a detailed determination of the velocity relaxation rate. Relaxation rates for the 22 GHz maser at H2 densities of 10 exp 9/cu cm are 2.0/s and 5.1/s for temperatures of 400 K and 1000 K, respectively. Under these and other conditions, as well as for other maser transitions, the relaxation rate far exceeds the loss rate - usually by more than a factor of 10. Thus maser lines can remain narrow up to intensities that are at least a factor of 10 greater than the saturation intensity, and to path lengths that are at least a factor of 10 greater than the path length at which saturation occurs. Relaxation is dominated by the effects of trapped infrared radiation, though elastic and inelastic collisions are also included in the calculations. These relaxation rates, together with the observed line breadths of the 22 GHz masers, provide limits on maser luminosities which indicate that the brightest 22 GHz masers are highly beamed, with solid angles smaller than 10 exp -5 to 10 exp -4 Sr.