  Stars form when filaments and dense cores in molecular clouds fragment and
collapse due to self-gravity. In the most basic analyses of gravitational
stability, the competition between self-gravity and thermal pressure sets the
critical (i.e. maximum stable) mass of spheres and the critical line density of
cylinders. Previous work has considered additional support from magnetic fields
and turbulence. Here, we consider the effects of non-ionizing radiation,
specifically the inward radiation pressure force that acts on dense structures
embedded in an isotropic radiation field. Using hydrostatic, isothermal models,
we find that irradiation lowers the critical mass and line density for
gravitational collapse, and can thus act as a trigger for star formation. For
structures with moderate central densities, $\sim10^3$ cm$^{-3}$, the
interstellar radiation field in the Solar vicinity has an order unity effect on
stability thresholds. For more evolved objects with higher central densities, a
significant lowering of stability thresholds requires stronger irradiation, as
can be found closer to the Galactic center or near stellar associations. Even
when strong sources of ionizing radiation are absent or extincted, our study
shows that interstellar irradiation can significantly influence the star
formation process.
