Effect of ambipolar diffusion on ion abundances in contracting protostellar cores

Numerical simulations and analytical solutions have established that ambipolar diffusion can reduce the dust-to-gas ratio in magnetically and thermally supercritical cores during the epoch of core formation. We study the effect that this has on the ion chemistry in contracting protostellar cores and present a simplified analytical method that allows one to calculate the ion power-law exponent k (=d ln n_id ln a_n, where H, and n_n are the ion and neutral densities, respectively) as a function of core density. We find that, as in earlier numerical simulations, no single value of k can adequately describe the ion abundance for n_n ≲ 10⁹ cm^-3, a result that is contrary to the "canonical" value of k = found in previous static equilibrium chemistry calculations and often used to study the effect of ambipolar diffusion in interstellar clouds. For typical cloud and grain parameters, reduction of the abundance of grains results in k > 1/2 during the core formation epoch (densities ; 10⁵ cm^-3). As a consequence, observations of the degree of ionization in cores could be used, in principle, to determine whether ambipolar diffusion is responsible for core formation in interstellar molecular clouds. For densities ≫ 10⁵ cm^-3, k is generally 1/2.