Molecular Hydrogen in Diffuse Interstellar Clouds of Arbitrary Three‐dimensional Geometry

We have constructed three-dimensional models for the equilibrium abundance ofmolecular hydrogen within diffuse interstellar clouds of arbitrary geometrythat are illuminated by ultraviolet radiation. The position-dependent photo-dissociation rate of H$_2$ within such clouds was computed using a 26-rayapproximation to model the attenuation of the incident ultraviolet radiationfield by dust and by H$_2$ line absorption. We have applied our modelingtechnique to the isolated diffuse cloud G236+39, assuming that the cloud has aconstant density and that the thickness of the cloud along the line of sight isat every point proportional to the 100 um continuum intensity measured by IRAS.We find that our model can successfully account for observed variations in theratio of 100 umu continuum intensity to HI column density, with larger valuesof that ratio occurring along lines of sight in which the molecular hydrogenfraction is expected to be largest. Using a standard chi^2 analysis to assessthe goodness of fit of our models, we find (at the 60sigma level) that athree-dimensional model is more successful in matching the observational datathan a one-dimensional model in which the geometrical extent of the cloud alongthe line of sight is assumed to be very much smaller than its extent in theplane-of-the-sky. If D is the distance to G236+39, and given standardassumptions about the rate of grain-catalysed H_2 formation, we find that thecloud has an extent along the line of sight that is 0.9+-0.1 times its meanextent projected onto the plane of the sky; a gas density of (53+-8)(100 pc/D)cm^-3; and is illuminated by a radiation field of (1.1+-0.2) (100 pc/D) timesthe mean interstellar radiation field estimated by Draine (1978). The derived100 um emissivity per nucleon is (1.13+-0.06)x10^-20 MJy sr^-1 cm^2.Comment: 27 pages LaTex, uses aaspp4.sty, ApJ August