Molecular Line Profiles of Collapsing Gas Clouds

Emission line profiles of tracer molecule H2CO 140 GHz transition from gravitational core collapsing clouds in the dynamic process of forming protostars are calculated, using a simple ray-tracing radiative transfer model. Three self-similar dynamic insideout core collapse models – the conventional polytropic model, the empirical hybrid model and the isothermal model – for star-forming molecular clouds are examined and compared. The isothermal model cannot produce observed asymmetric double-peak molecular line profiles. The conventional polytropic model, which gives flow velocity, mass density and temperature profiles self-consistently, can produce asymmetric double-peak line profiles for a core collapsing cloud. In particular, the blue peak is stronger than the red peak, consistent with a broad class of molecular line profile observations. We find that line profiles are robust against variations in the polytropic index γ once the effective line-centre opacity κ0 is specified. The relative strengths of the blue and red peaks within a molecular line profile are determined by the cloud temperature gradient, but the emission at frequencies between the two line peaks is determined by detailed density and velocity profiles in the cloud core. In the presence of a static dense kernel at the centre of a collapsing cloud, strong internal absorption along the line-of-sight may occur, causing a suppression to the red wing of the blue line peak. If reliably resolved in frequency by observations, this signature may be potentially useful for probing the environs of an infant protostar. The conventional polytropic model can be utilized to produce molecular line-profile templates, for extracting dynamical information from line spectra of molecular globules undergoing a gravitational core collapse. We show a sample fit using the 140 GHz H2CO emission line from the central region of the molecular globule B335 by our model with γ = 1.2. The calculation of line profiles and fitting processes also offer a scenario to estimate the protostellar mass, the kernel mass accretion rate, and the evolution time scale of a core collapsing cloud. Our model can be readily adapted to other tracer molecules with more or less constant abundances in star-forming clouds.