Dust emission from inhomogeneous interstellar clouds: Radiative transfer in 3D with transiently heated particles

Due to the complexity of their structure, the theoretical study of interstellar clouds must be based on three-dimensional models. It is already possible to estimate the distribution of equilibrium dust temperature in fairly large 3D models and, therefore, also to predict the resulting far-infrared and sub-mm emission. Transiently heated particles introduce, however, a significant complication and direct calculation of emission at wavelengths below 100 μm is currently not possible in 3D models consisting of millions of cells. Nevertheless, the radiative transfer problem can be solved with some approximations. We present a numerical code for continuum radiative transfer that is based on the idea of a "library" describing the relation between the intensity of the local radiation field and the resulting dust emission spectrum. Given this mapping it is sufficient to simulate the radiation field at only a couple of reference wavelengths. Based on the library and local intensities at the reference wavelengths, the radiative transfer equation can be integrated through the source and an approximation of the emission spectrum is obtained. Tests with small models for which the radiative transfer problem can be solved directly show that with our method, one can easily obtain an accuracy of a few per cent. This depends, however, on the opacity of the source and the type of the radiation sources included. As examples we show spectra computed from three-dimensional MHD simulations containing up to 128 3 cells. The models represent starless, inhomogeneous interstellar clouds embedded in the normal interstellar radiation field. The intensity ratios between IRAS bands show large variations that follow the filamentary structure of the density distribution. The power law index of the spatial power spectrum of the column density map is -2.8. In infrared maps temperature variations increase the power at high spatial frequencies, and in a model with average visual extinction (A v ) ∼ 10 the power law index varies between -2.5 and -2.7. Assuming constant dust properties throughout the cloud, the IRAS ratio decreases in densest cores only by a factor of ∼4 compared with the value in diffuse medium. Observations have shown that in reality the ratio can decrease twice as much even in optically thinner clouds. This requires that most of the small grains are removed in these regions, and possibly a modification of the properties of large grains.