A simple model of spectral-line profiles from contracting clouds

A simple analytic model of radiative transfer in two parts of a contracting cloud matches a wide range of line profiles in candidate infall regions and provides a sensitive estimate of V-in, the characteristic inward speed of the gas forming the line. The model assumes two uniform regions of equal temperature and velocity dispersion sigma, whose density and velocity are attenuation-weighted means over the front and rear halves of a centrally condensed, contracting cloud. The model predicts two-peak profiles for ''slow'' infall, V-in much less than sigma and red-shoulder profiles for ''fast'' infall, V-in similar to sigma A simple formula expresses V-in solely in terms of sigma and of observable parameters of a two-peak line. We apply the model to fit profiles of high and low optical depth lines observed in a dense core with no star (L1544, V-in = 0.006 km s(-1)), with an isolated protostar (L1527, 0.025 km s(-1)), and with a small group of stars (L1251B, 0.35 km s(-1)). The mass infall rate obtained from V-in and the map size varies from (2-40) x 10(-6) M(.) yr(-1) and agrees within a factor similar to 2 in each core with the independently determined rate similar to sigma(3) G(-1) for a gravitationally collapsing isothermal sphere. This agreement suggests that the inward motions derived from the line profiles are gravitational in origin.