On the SEDs of passively heated condensed cores
  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.
