On the spectral energy distributions of passively heated condensed cores

Aims. The dust emission spectrum and the brightness profile of passively heated condensed cores is analyzed in relation to their astrophysical environment. The model is used to study systematically the radiative transfer effects on essential parameters such as the dust emissivity, dust temperature, and luminosity of the cores and to derive uncertainties in typical estimates of the IR flux and size. Methods. 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. Results. 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 μm and to a flatter emissivity law of typically β < 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. Fitting the core using a Gaussian source approximation overestimates the flux by ∼10%. For highly embedded cores and in general for cores in high pressure regions, the surface brightness profile is flatter with respect to the profile of the column density and a Gaussian profile. These effects can lead to an overestimate of the core size of 10-30% based on marginally resolved 250 μ m observations