Context :

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 ~ { } \mu { m } 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 .
Fitting the core using a Gaussian source approximation overestimates the flux by \sim 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 ~ { } \mu { m } observations .

Conclusions :