The atomic-to-molecular transition in galaxies. III. A new method for determining the molecular content of primordial and dusty clouds

Understanding the molecular content of galaxies is a critical problem in star formation and galactic evolution. Here we present a new method, based on a Strömgren-type analysis, to calculate the amount of that surrounds a molecular cloud irradiated by an isotropic radiation field. We consider both planar and spherical clouds, and H₂ formation either in the gas phase or catalyzed by dust grains. Under the assumption that the transition from atomic to molecular gas is sharp, our method gives the solution without any reference to the photodissociation cross section. We test our results for the planar case against those of a photodissociation region code and find typical accuracies of about 10%. Our results are also consistent with the scaling relations found in Paper I of this series, but they apply to a wider range of physical conditions. We present simple, accurate analytic fits to our results that are suitable for comparison to observations and to implementation in numerical and semi-analytic models.