Aims. To demonstrate the time-approach to equilibrium of H2-formation and protonation in models of diffuse or H I interstellar gas clouds previously published by the author. Methods. The microscopic equations of H2-formation and protonation are integrated numerically over time in such a manner that the overall structures evolve self-consistently under benign conditions. Results. The equilibrium H2 formation timescale in an H I cloud with N(H) ≈ 4×10 20 cm−2 is 1−3×10 7 yr, nearly independent of the assumed density or H2 formation rate on grains, etc. Attempts to speed up the evolution of the H2-fraction would require densities well beyond the range usually considered typical of diffuse gas. The calculations suggest that, under benign, quiescent conditions, H2 in the diffuse ISM formation of H2 is favored in larger regions having moderate density, consistent with the rather high mean kinetic temperatures measured in H2, 70-80 K. Formation of H3 + is essentially complete when H2-formation equilibrates but the final abundance of H3 + appears more nearly at the very last instant. Chemistry in a weakly-molecular gas has particular properties so that the abundance patterns change appreciably as gas becomes more fully molecular, either in model sequences or with time in a single model. One manifestation of this is that the predicted abundance of H3 + is much more weakly dependent on the cosmic-ray ionization rate when n(H2)/n(H)< ∼ 0.05. In general
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