An Efficient Method for Determining the Chemical Evolution of Gravitationally Collapsing Prestellar Cores

We develop analytic approximations to the density evolution of prestellar cores, based on the results of hydrodynamical simulations. We use these approximations as input for a time-dependent gas-grain chemical code to investigate the effects of differing modes of collapse on the molecular abundances in the core. We confirm that our method can provide reasonable agreement with an exact numerical solution of both the hydrodynamics and chemistry while being significantly less computationally expensive, allowing a large grid of models varying multiple input parameters to be run. We present results using this method to illustrate how the chemistry is affected not only by the collapse model adopted but also by the large number of unknown physical and chemical parameters. Models that are initially gravitationally unstable predict similar abundances despite differing densities and collapse timescales, while ambipolar diffusion (AD) produces more extended inner depleted regions that are not seen in observations of prestellar cores. Molecular observations are capable of discriminating between modes of collapse despite the unknown values of various input parameters. We also investigate the evolution of the AD timescale for a range of collapse modes, metallicities, and cosmic-ray ionization rates, finding that it remains comparable to or larger than the collapse timescale during the initial stages for all models we consider, but becomes smaller at later evolutionary stages. This confirms that AD is an important process for diffuse gas but becomes less significant as cores collapse to higher densities.