Analytical approximations for calculating the escape and absorption of radiation in clumpy dusty environments

We present analytical approximations for calculating the scattering, absorp tion, and escape of non-ionizing photons from a spherically symmetric two-p hase clumpy medium, with either a central point source of isotropic radiati on, a uniform distribution of isotropic emitters, or uniformly illuminated by external sources. The analytical approximations are based on the mega-gr ains model of two-phase clumpy media, as proposed by Hobson & Padman, combi ned with escape and absorption probability formulae for homogeneous media. The accuracy of the approximations is examined by comparison with three-dim ensional Monte Carlo simulations of radiative transfer, including multiple scattering. Our studies show that the combined mega-grains and escape/absor ption probability formulae provide a good approximation of the escaping and absorbed radiation fractions for a wide range of parameters characterizing the clumpiness and optical properties of the medium. A realistic test of t he analytic approximations is performed by modeling the absorption of a sta rlike source of radiation by interstellar dust in a clumpy medium and by ca lculating the resulting equilibrium dust temperatures and infrared emission spectrum of both the clumps and the interclump medium. In particular, we f ind that the temperature of dust in clumps is lower than in the interclump medium if the clumps are optically thick at wavelengths at which most of th e absorption occurs. Comparison with Monte Carlo simulations of radiative t ransfer in the same environment shows that the analytic model yields a good approximation of dust temperatures and the emerging UV-FIR spectrum of rad iation for all three types of source distributions mentioned above. Our ana lytical model provides a numerically expedient way to estimate radiative tr ansfer in a variety of interstellar conditions and can be applied to a wide range of astrophysical environments, from clumpy star-forming regions to s tal;burst galaxies.