Modeling UV Radiation Feedback from Massive Stars: III. Escape of
  Radiation from Star-forming Giant Molecular Clouds
  Using a suite of radiation hydrodynamic simulations of star cluster formation
in turbulent clouds, we study the escape fraction of ionizing (Lyman continuum)
and non-ionizing (FUV) radiation for a wide range of cloud masses and sizes.
The escape fraction increases as H II regions evolve and reaches unity within a
few dynamical times. The cumulative escape fraction before the onset of the
first supernova explosion is in the range 0.05-0.58; this is lower for higher
initial cloud surface density, and higher for less massive and more compact
clouds due to rapid destruction. Once H II regions break out of their local
environment, both ionizing and non-ionizing photons escape from clouds through
fully ionized, low-density sightlines. Consequently, dust becomes the dominant
absorber of ionizing radiation at late times and the escape fraction of
non-ionizing radiation is only slightly larger than that of ionizing radiation.
The escape fraction is determined primarily by the mean $\langle \tau\rangle$
and width $\sigma$ of the optical-depth distribution in the large-scale cloud,
increasing for smaller $\langle \tau\rangle$ and/or larger $\sigma$. The escape
fraction exceeds (sometimes by three orders of magnitude) the naive estimate
$e^{-\langle \tau\rangle}$ due to non-zero $\sigma$ induced by turbulence. We
present two simple methods to estimate, within $\sim20\%$, the escape fraction
of non-ionizing radiation using the observed dust optical depth in clouds
projected on the plane of sky. We discuss implications of our results for
observations, including inference of star formation rates in individual
molecular clouds, and accounting for diffuse ionized gas on galactic scales.
