High precision Monte Carlo radiative transfer in dusty media

In this paper, we present a refined Monte Carlo method for the solution of multi-dimensional radiative transfer problems in dusty media, for instance in the circumstellar envelopes of AGB and post AGB stars. In order to push the performance of the Monte Carlo method, we have included several basic improvements of the standard procedure which avoid the usual increase of the noise level in extremely optically thin or optically thick situations. The improvements comprise an accurate temperature determination scheme, e.g. based on the calculation of mean intensities, and an inclusion of several deterministic elements for the treatment of the absorption during the photon propagation. The method is capable of accurately modelling discontinuous opacity structures, such as clumpy media, and is applicable in a broad range of optical depths. It can provide the gas and dust temperature structures required for a more complex physical modelling, e.g. hydrodynamics, chemistry or dust formation. It may be used to predict colours, spectral energy distributions, visibilities and monochromatic images. The paper is completed by an exploration of the influence of dust clouds and small holes in dust shells on the spectral energy distribution and their optical appearance in monochromatic images. The underlying temperature structures are discussed.