  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.
