Multiple Scattering in Clumpy Media. I. Escape of Stellar Radiation from a Clumpy Scattering Environment

We studied the radiative transfer in a spherical, two-phase clumpy medium, in which coherent, nonconservative scattering is the dominant opacity source and where the source of photons is situated at the center. The structure of the medium is random but statistically homogeneous and is characterized by the density ratio between the low- and high-density phases, the optical depth radius of the equivalent homogeneous dust distribution, the filling factor of high-density clumps, and the length scale of individual clumps. We examined in detail the cloud mass spectrum, the distribution of optical depths, and the apparent fractal nature of the projected cloud structures. The photometric characteristics of the clumpy scattering system are studied as a function of density contrast between the two phases, of the filling factor, and of the length scale of high-density clumps, and they are compared with those of homogeneous, constant-density distributions of equal effective optical depth. Direction-averaged surface brightness distributions of the scattered light are studied for both optically thick and optically thin cases, which reveal the important role of scattering by the optically thin interclump medium. The conversion of UV/optical/near-IR radiation into thermal far-IR dust radiation in a dusty system is profoundly affected by the structure of the medium; the homogeneous, constant-density distribution always provides the highest conversion efficiency for any given geometry and dust mass. The effective optical depth of a clumpy distribution is known not to scale linearly with the equivalent optical depth of a homogeneous distribution of equal dust mass; this leads to effective attenuation laws that differ from the original opacity law assumed for the dust in the system. The expected reddening is substantially reduced for clumpy media. Finally, since the scattering response of a clumpy system is consistently that of an equivalent system of lower effective optical depth and lower effective albedo, efforts to determine the dust albedo of real systems with clumpy dust distributions by employing models, which are homogeneous, can lead to a bias toward albedo values that are too low.