The spectral energy distribution of self-gravitating interstellar clouds. I. Spheres

We derive the spectral energy distribution (SED) of dusty, isothermal, self-gravitating, stable and spherical clouds externally heated by the ambient interstellar radiation field (ISRF). For a given radiation field and dust properties, the radiative transfer problem is determined by the pressure of the surrounding medium and by the cloud mass expressed as a fraction of the maximum stable cloud mass above which the clouds become gravitationally unstable. To solve the radiative transfer problem, a ray-tracing code is used to accurately derive the light distribution inside the cloud. This code considers both anisotropic scattering on dust grains and multiple scattering events. The dust properties inside the clouds are assumed to be the same as in the diffuse interstellar medium in our Galaxy. We analyze the effect of the pressure, the critical mass fraction, and the ISRF on the SED and present brightness profiles in the visible, the IR/FIR, and the submillimeter/millimeter regime with the focus on the scattered emission and the thermal emission from PAH molecules and dust grains.