Radiative transfer in clumpy environments: absorption and scattering by dust

We study the effects of stochastic density fluctuations on the transport of far-ultraviolet radiation in interstellar clouds. The physical processes considered are absorption and anisotropic scattering by dust grains. We consider clouds that are, on average, homogeneous and have a continuous stochastic density distribution. The spatial variation of the density n is given in a statistical sense only. It is assumed to correspond to a continuous Markov process along each line of sight. Caused by the stochastic nature of the density, the intensity becomes a stochastic variable, too. As a consequence, the ordinary radiative transfer equation has to be replaced by a generalized transfer equation, of Fokker-Planck type. Results are presented for a plane-parallel slab and a spherical geometry. In both cases, we find a substantial higher radiation field inside the cloud than in the case of a homogeneous density distribution. Also the amount of reflected radiation is affected significantly by an inhomogeneous, stochastic density distribution. Furthermore, we compare our findings with the results drawn from the two-phase model of Boisse, in which the spatial variation of the extinction coefficient is also modelled by a Markov process. Finally, we address the question of whether the results obtained from the generalized radiative transfer equation can be approximated by calculations for a homogeneous medium consisting of grains with effective optical properties.