The Atomic to Molecular Transition in Galaxies. I: an Analytic Approximation for Photodissociation Fronts in Finite Clouds

In this series of papers we study the structure of the atomic to molecular transition in the giant atomic-molecular complexes that are the repositories of most molecular gas in galaxies, with the ultimate goal of attaining a better understanding of what determines galaxies’ molecular content. Here we derive an approximate analytic solution for the structure of a photodissociation region (PDR) in a cloud of finite size that is bathed in an external dissociating radiation field. Our solution extends previous work, which with few exceptions has been restricted to the case of a semi-infinite slab illuminated by a unidirectional radiation field. We show that our analytic results compare favorably to exact numerical calculations in this limit. However, our more general geometry provides a more realistic representation than a semi-infinite slab for atomic-molecular complexes exposed to the interstellar radiation field, particularly in environments such as low-metallicity dwarf galaxies where the curvature and finite size of the atomic envelope cannot be neglected because the molecular region occupies only a small fraction of the cloud volume. As a side benefit, our analysis helps clarify when self-shielding is the dominant process in H2 formation, and under what circumstances shielding by dust makes a significant contribution. Subject headings: ISM: clouds — ISM: molecules — molecular processes — radiative transfer