HI narrow self-absorption in dark clouds: Correlations with molecular gas and implications for cloud evolution and star formation

We present the results of a comparative study of H I narrow self-absorption (HINSA), OH, (CO)-C-13, and (CO)-O-18 in five dark clouds. We find that the HINSA generally follows the distribution of the emission of the carbon monoxide isotopologs and has a characteristic size close to that of (CO)-C-13. This confirms earlier work that determined that the HINSA is produced by cold H I that is well mixed with molecular gas in well-shielded regions. The OH and (CO)-C-13 column densities are essentially uncorrelated for the sources other than L1544. Our observations indicate that the central number densities of H I are between 2 and 6 cm(-3) and that the ratio of the hydrogen density to total proton density for these sources is (5-27) x 10(-4). Using cloud temperatures and the density of atomic hydrogen, we set an upper limit to the cosmic-ray ionization rate of 10(-16) s(-1). We present a model for H I to H-2 conversion in well-shielded regions that includes cosmic-ray destruction of H-2 and formation of this species on grain surfaces. We include the effect of a distribution of grain sizes, and we find that for an MRN distribution, the rate of H-2 formation is increased by a factor of 3.4 relative to that for a model with a single grain radius of 1700 angstrom. Comparison of observed and modeled fractional H I abundances indicates ages for these clouds, defined as the time since the initiation of H I -> H-2 conversion, to be 10(6.5)-10(7) yr. Several effects may make this time a lower limit, but the low values of n(H I) that we have determined make it certain that the timescale for evolution from a possibly less dense atomic phase to an almost entirely molecular phase must be a minimum of several million years. This clearly sets a lower limit to the overall timescale for the process of star formation and the lifetime of molecular clouds.