![]() ![]() Their approximations are valid provided that the clump volume filling is less than about one-third. ![]() ![]() By treating the clumps as large grains with an effective absorption and scattering coefficient, they obtained a set of equations, which they called the mega-grain approximation. They assumed a medium consisting of spherical clumps, with uniform size and density, embedded in a more tenuous interclump medium. An approximate method to describe the radiative transfer inside a two-phase medium has been discussed by Hobson & Padman (1993). The transport of continuum photons for a clumpy model cloud has been investigated by Boissé (1990), Hobson & Scheuer (1993), Witt & Gordon (1996), Wolf, Fischer & Pfau (1998) and Witt & Gordon (2000). In the context of line formation, the influence of an inhomogeneous density distribution has been studied by Juvela (1996), Park & Hong (1995), Pagani (1998) and Hegmann & Kegel (2000). As has been shown by many authors, radiative transfer calculations have to account for such an inhomogeneity. Observations of the interstellar medium often reveal a highly inhomogeneous medium, which is structured down to the smallest accessible scales (see, for example, Falgarone & Phillips 1996). Radiative transfer, dust, extinction 1 Introduction 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. Also the amount of reflected radiation is affected significantly by an inhomogeneous, stochastic density distribution.įurthermore, we compare our findings with the results drawn from the two-phase model of Boissé, in which the spatial variation of the extinction coefficient is also modelled by a Markov process. In both cases, we find a substantial higher radiation field inside the cloud than in the case of a homogeneous density distribution. Results are presented for a plane-parallel slab and a spherical geometry. As a consequence, the ordinary radiative transfer equation has to be replaced by a generalized transfer equation, of Fokker–Planck type. Caused by the stochastic nature of the density, the intensity becomes a stochastic variable, too. It is assumed to correspond to a continuous Markov process along each line of sight. The spatial variation of the density n is given in a statistical sense only. We consider clouds that are, on average, homogeneous and have a continuous stochastic density distribution. The physical processes considered are absorption and anisotropic scattering by dust grains. We study the effects of stochastic density fluctuations on the transport of far-ultraviolet radiation in interstellar clouds. ![]()
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