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 Vin, 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, Vin << sigma , and red-shoulder profiles for "fast" infall, Vin ~ sigma . A simple formula expresses Vin 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, Vin = 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 Vin and the map size varies from (2--40) x 10-6 Msolar yr-1 and agrees within a factor ~2 in each core with the independently determined rate ~ 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.