H i-to-H₂ Transitions in Dust-free Interstellar Gas

We present numerical computations and analysis of atomic-to-molecular (H i -to-H 2 ) 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-H 2 abundance profiles for a wide range of ζ / n and I LW / n for dust-free gas. We determine the conditions for which H 2 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 × 10 7 photons cm −2 s −1 and a uniform cosmic-ray ionization rate ζ = 10 −16 s −1 , an H i -to-H 2 transition occurs at a total hydrogen gas column density of 4 × 10 21 cm −2 , within 3 × 10 7 yr, for a gas volume density of n = 10 6 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 ′ ≲ 0.01 relative to Galactic solar values.