Spectral shifting strongly constrains molecular cloud disruption by
  radiation pressure on dust
  ${\bf Aim:}$ To test the hypothesis that radiation pressure from star
clusters acting on dust is the dominant feedback agent disrupting the largest
star-forming molecular clouds and thus regulating the star-formation process.
${\bf Methods:}$ We perform multi-frequency, 3D, RT calculations including
scattering, absorption, and re-emission to longer wavelengths for clouds with
masses of $10^4$-$10^7\,$M$_{\odot}$, with embedded clusters and a star
formation efficiencies of 0.009%-91%, and varying maximum grain sizes up to
200$\,\mu$m. We calculate the ratio between radiative force and gravity to
determine whether radiation pressure can disrupt clouds. ${\bf Results:}$ We
find that radiation acting on dust almost never disrupts star-forming clouds.
UV and optical photons to which the cloud is optically thick do not scatter
much. Instead, they quickly get absorbed and re-emitted by at thermal
wavelengths. As the cloud is typically optically thin to far-IR radiation, it
promptly escapes, depositing little momentum. The resulting spectrum is more
narrowly peaked than the corresponding Planck function with an extended tail at
longer wavelengths. As the opacity drops significantly across the sub-mm and
mm, the resulting radiative force is even smaller than for the corresponding
single-temperature black body. The force from radiation pressure falls below
the strength of gravitational attraction by an order of magnitude or more for
either Milky Way or starbust conditions. For unrealistically large maximum
grain sizes, and star formation efficiencies far exceeding 50% do we find that
the strength of radiation pressure can exceed gravity. ${\bf Conclusions:}$ We
conclude that radiation pressure acting on dust does not disrupt star-forming
molecular clouds in any Local Group galaxies. Radiation pressure thus appears
unlikely to regulate the star-formation process on either local or global
scales.
