The Ionization Fraction in Dense Cloud Cores

The degree of ionization, x(e) = n(e)/n(H₂), and the cosmic-ray ionization rate, ζ, in 24 cloud cores have been determined by comparing observational data from Butner et al. on the abundance ratios R_D = [DCO⁺]/[HCO⁺] and R_H = [HCO⁺]/[CO] with a simple analytical chemical model and with a detailed "pseudo-time-dependent" chemical model. The results are dependent on the depletion of elemental carbon and oxygen from their cosmic abundances, especially for cores with a low degree of ionization. We determine the depletion of C and O from the measured HC₃N/CO abundance ratios using model results. We find that the range of fractional ionization in the dark cores extends from ~10^-6 to ~10^-8, with inferred cosmic ray ionization rates in the range of 10^-16-10^-18 s^-1. This corresponds to ambipolar diffusion timescales of between 3 × 10⁷ and 3 × 10⁵ yr, with a median value of 5 × 10⁶ yr. The ratio of ambipolar diffusion to the free-fall timescales varies between 3 and 200, with a median value of 50. We find, rather surprisingly, no clear segregation in the ambipolar diffusion timescales between cores with embedded stars and those without. An interesting by-product of our results is the conclusion that the cyanopolyyne-rich core in TMC-1 is atypical in its abundance distribution and may be unusually young.