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 which are initially gravitationally unstable
predict similar abundances despite differing densities and collapse timescales,
while ambipolar diffusion produces more extended inner depleted regions which
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 ambipolar
diffusion 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 ambipolar
diffusion is an important process for diffuse gas, but becomes less significant
as cores collapse to higher densities.
