The ionization fraction of Barnard 68: Implications for star and planet formation

We present a detailed study of the ionization fraction of the Barnard 68 prestellar core, using millimeter (HCO+)-C-13 and DCO+ lines observations. These observations are compared to the predictions of a radiative transfer model coupled to a chemical network that includes depletion on grains and gas-phase deuterium fractionation. Together with previous observations and modeling of CO and isotopologues, our (HCO+)-C-13 and DCO+ observations and modeling allow us to place constraints on the metal abundance and the cosmic ionization rate. The (HCO+)-C-13 emission is well reproduced for metal abundances lower than 3x10(-9) and a standard cosmic-ray ionization rate. However, the observations are also consistent with a complete depletion of metals, i.e., with cosmic rays as the only source of ionization at visual extinctions greater than a few A(V). The DCO+ emission is found to be dependent of the ortho-to-para H-2 ratio and indicates a ratio of similar to 10(-2). The derived ionization fraction is about 5x10(-9) with respect to H nuclei, which is about an order of magnitude lower than that observed in the L1544 core. The corresponding ambipolar diffusion timescale is found to be an order of magnitude larger than the free fall timescale at the center of the core. The inferred metal abundance suggests that magnetically inactive regions (dead zones) are present in protostellar disks.