Analytical Approximations for Calculating the Escape and Absorption of Radiation in Clumpy Dusty Environments

We present analytical approximations for calculating the scattering, absorption and escape of nonionizing photons from a spherically symmetric two-phase clumpy medium, with either a central point source of isotropic radiation, a uniform distribution of isotropic emitters, or uniformly illuminated by external sources. The analytical approximations are based on the mega-grains model of two-phase clumpy media, as proposed by Hobson & Padman, combined with escape and absorption probability formulae for homogeneous media. The accuracy of the approximations is examined by comparison with 3D Monte Carlo simulations of radiative transfer, including multiple scattering. Our studies show that the combined mega-grains and escape/absorption probability formulae provide a good approximation of the escaping and absorbed radiation fractions for a wide range of parameters characterizing the medium. A realistic test is performed by modeling the absorption of a starlike source of radiation by interstellar dust in a clumpy medium, and by calculating the resulting equilibrium dust temperatures and infrared emission spectrum of both the clumps and the interclump medium. In particular, we find that the temperature of dust in clumps is lower than in the interclump medium if clumps are optically thick. Comparison with Monte Carlo simulations of radiative transfer in the same environment shows that the analytic model yields a good approximation of dust temperatures and the emerging UV to FIR spectrum of radiation for all three types of source distributions mentioned above. Our analytical model provides a numerically expedient way to estimate radiative transfer in a variety of interstellar conditions and can be applied to a wide range of astrophysical environments, from star forming regions to starburst galaxies.