H i-to-H₂Transitions in Dust-free Interstellar Gas

We present numerical computations and analysis of atomic-to-molecular (H i-to-H2) transitions in cool (∼100 K), low-metallicity, dust-free (primordial) gas in which molecule formation occurs via cosmic-ray-driven negative ion chemistry and removal is by a combination of far-UV photodissociation and cosmic-ray ionization and dissociation. For any gas temperature, the behavior depends on the ratio of the Lyman-Werner (LW) band FUV intensity to gas density, I LW/n, and the ratio of the cosmic-ray ionization rate to the gas density, ζ/n. We present sets of H i-to-H2 abundance profiles for a wide range of ζ/n and I LW/n for dust-free gas. We determine the conditions for which H2 absorption-line self-shielding in optically thick clouds enables a transition from atomic to molecular form for ionization-driven chemistry. We also examine the effects of cosmic-ray energy losses on the atomic and molecular density profiles and transition points. For a unit Galactic interstellar FUV field intensity (I LW = 1) with LW flux 2.07 107 photons cm-2 s-1 and a uniform cosmic-ray ionization rate ζ = 10-16 s-1, an H i-to-H2 transition occurs at a total hydrogen gas column density of 4 1021 cm-2, within 3 107 yr, for a gas volume density of n = 106 cm-3 at 100 K. For these parameters, the dust-free limit is reached for a dust-to-gas ratio Z′d ≲ 10-5, which may be reached for overall metallicities Z′d ≲ 0.01 relative to Galactic solar values.