Simulating the Formation of Molecular Clouds. II. Rapid Formation from Turbulent Initial Conditions

(Abridged). In this paper, we present results from a large set of numericalsimulations that demonstrate that H2 formation occurs rapidly in turbulent gas.Starting with purely atomic hydrogen, large quantities of molecular hydrogencan be produced on timescales of 1 -- 2 Myr, given turbulent velocitydispersions and magnetic field strengths consistent with observations.Moreover, as our simulations underestimate the effectiveness of H2self-shielding and dust absorption, we can be confident that the molecularfractions that we compute are strong lower limits on the true values. Theformation of large quantities of H2 on the timescale required by rapid cloudformation models therefore appears to be entirely plausible. We also investigate the density and temperature distributions of gas in ourmodel clouds. We show that the density probability distribution function isapproximately log-normal, with a dispersion that agrees well with theprediction of Padoan, Nordlund & Jones (1997). The temperature distribution issimilar to that of a polytrope, with an effective polytropic index gamma_eff\simeq 0.8, although at low gas densities, the scatter of the actual gastemperature around this mean value is considerable, and the polytropicapproximation does not capture the full range of behaviour of the gas.Comment: 66 pages, 34 figures, AASTex. Minor revisions to match version accepted by Ap