A Simple Model of Spectral-Line Profiles from Contracting Clouds

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Abstract
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 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, Vin σ, and red-shoulder profiles for "fast" infall, Vin ~ σ. A simple formula expresses Vin 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, 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) × 10-6 M☉ yr-1 and agrees within a factor ~2 in each core with the independently determined rate ~σ3 G-1 for a gravitationally collapsing isothermal sphere. This agreement suggests that the inward motions derived from the line profiles are gravitational in origin.