On the SEDs of passively heated condensed cores

Abstract

The dust emission spectrum and the brightness profile of passively heated condensed cores is analyzed in relation to their astrophysical environment. The cores are modeled as critically stable self-gravitating spheres embedded at the center of self-gravitating filaments that are assumed to be either spherical or cylindrical in shape. The filaments are heated by an isotropic interstellar radiation field (ISRF). The calculations are based on a physical dust model of stochastically heated grains of diffuse interstellar dust. The spectral energy distribution (SED) of the cores is calculated using a ray-tracing technique where the effects of scattered emission and re-heating by dust grains are accurately taken into account. To compare with observational studies, the dust re-emission spectrum is approximated by a modified black-body function and the brightness profile with a Gaussian source. A simplified single-zone model for cores is presented that incorporates on the basis of the derived emissivities a first order approximation of their SED. Colder dust temperatures are, independent of the core mass, related to a higher pressure both inside and around the filament. The pressure-temperature relation for given external pressure is found to be largely independent of the true shape of the filament. The calculations show that the radiative transfer leads to a lower emission coefficient at 250 micron and to a flatter emissivity law of typically beta<1.8 in the far-infrared sub-millimeter regime. These effects cause the core mass to be underestimated by more than a factor of 2 based on the typical assumptions used in observational programs. A larger uncertainty is expected for high pressure regions.