F. Varosi et E. Dwek, Analytical approximations for calculating the escape and absorption of radiation in clumpy dusty environments, ASTROPHYS J, 523(1), 1999, pp. 265-305
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.