A Simple Model for the Absorption of Starlight by Dust in Galaxies

We present a new model for computing the effects of dust on the integrated spectral properties of galaxies, based on an idealized description of the main features of the interstellar medium (ISM). The model includes the ionization of H II regions in the interiors of the dense clouds in which stars form and the influence of the finite lifetime of these clouds on the absorption of radiation. We compute the production of emission lines and the absorption of continuum radiation in the H II regions and the subsequent transfer of line and continuum radiation in the surrounding H I regions and the ambient ISM. This enables us to interpret simultaneously all the observations of an ultraviolet-selected sample of nearby starburst galaxies, including the ratio of far-infrared to ultraviolet luminosities, the ratio of Hα to Hβ luminosities, the Hα equivalent width, and the ultraviolet spectral slope. We show that the finite lifetime of stellar birth clouds is a key ingredient for resolving an apparent discrepancy between the attenuation of line and continuum photons in starburst galaxies. In addition, we find that an effective absorption curve proportional to λ-0.7 reproduces the observed relation between the ratio of far-infrared to ultraviolet luminosities and the ultraviolet spectral slope. We interpret this relation most simply as a sequence in the overall dust content of the galaxies. The shallow wavelength dependence of the effective absorption curve is compatible with the steepness of known extinction curves if the dust has a patchy distribution. In particular, we find that a random distribution of discrete clouds with optical depths similar to those in the Milky Way provides a consistent interpretation of all the observations. A noteworthy outcome of our detailed analysis is that the observed mean relations for starburst galaxies can be closely approximated by the following simple recipe: use an effective absorption curve proportional to λ-0.7 to attenuate the line and continuum radiation from each stellar generation, and lower the normalization of the curve, typically by a factor of 3 after 107 yr, to account for the dispersal of the birth clouds. This recipe or our full model for absorption can be incorporated easily into any population synthesis model.