Effect of ambipolar diffusion on dust-to-gas ratio in protostellar cores

Recent numerical simulations have shown that ambipolar diffusion can reduce the abundance of grains in magnetically and thermally supercritical protostellar cores during the core formation epoch. We derive analytical expressions that relate the predicted grain abundances in dense cores to physical quantities such as the grain radii and the initial central mass-to-flux ratios of the parent molecular clouds. We find that the abundance of grains with radii ≲ 10^-5 cm can be reduced, compared to canonical values in the interstellar medium, by up to an order of magnitude. Observations previously interpreted as indicating growth of grains with increasing extinction find a new interpretation. Moreover, observations of grain abundances in the core and envelope of a molecular cloud can, at least in principle, be used to determine the initial mass-to-flux ratio of the cloud.