The ionization fraction in dense cloud cores

The degree of ionization, x(e)= n(e)/n(H(2)), and the cosmic-ray ionization rate, zeta, 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 HC(3)N/CO abundance ratios using model results. We find that the range of fractional ionization In the dark cores extends from similar to 10(-6) to similar 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 x 10(7) and 3 x 10(5) yr, with a median value of 5 x 10(6) 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.