Molecular Hydrogen in Diffuse Interstellar Clouds of Arbitrary Three-Dimensional Geometry

Abstract

We have constructed three-dimensional models for the equilibrium abundance of molecular hydrogen in diffuse interstellar clouds of arbitrary geometry that are illuminated by ultraviolet radiation. The position-dependent photodissociation rate of H2 in such clouds was computed with a 26 ray approximation to model the attenuation of the incident ultraviolet radiation field by dust and by H2 line absorption. We have applied our modeling technique to the isolated diffuse cloud G236+39, assuming that the cloud has a constant density and that the thickness of the cloud along the line of sight is at every point proportional to the 100 micron continuum intensity measured by IRAS. We find that our model can successfully account for observed variations in the ratio of 100 micron continuum intensity to H I column density, with larger values of that ratio occurring along lines of sight in which the molecular hydrogen fraction is expected to be the largest. Using a standard chi square analysis to assess the goodness of fit of our models, we find (at the 60 a level) that a three-dimensional model is more successful in matching the observational data than a one-dimensional model in which the geometrical extent of the cloud along the line of sight is assumed to be much smaller than its extent in the plane of the sky. If D is the distance to G236 + 39, and given standard assumptions about the rate of grain-catalyzed H2 formation, we find that the cloud has an extent along the line of sight that is 0.9 +/- 0.1 times its mean extent projected onto the plane of the sky and a gas density of 53 +/- 8 (100 pc/D) H nuclei/cc and is illuminated by a radiation field of 1.1 +/- 0.2 (100 pc/D) times the mean interstellar radiation field. The derived 100 micron emissivity per nucleon is 1.13 +/- 0.06 x 10(exp -20) MJy/sr sq cm.