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 σ, 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 ≪ σ, and red-shoulder profiles for "fast" infall, V in ~ σ. A simple formula expresses V in solely in terms of σ 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) × 10 -6 M ☉ yr -1 and agrees within a factor ~2 in each core with the independently determined rate ~σ 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.