Lyman-Werner UV Escape Fractions from Primordial Halos
  Population III stars can regulate star formation in the primordial Universe
in several ways. They can ionize nearby halos, and even if their ionizing
photons are trapped by their own halos, their Lyman-Werner (LW) photons can
still escape and destroy H$_2$ in other halos, preventing them from cooling and
forming stars. LW escape fractions are thus a key parameter in cosmological
simulations of early reionization and star formation but have not yet been
parametrized for realistic halos by halo or stellar mass. To do so, we perform
radiation hydrodynamical simulations of LW UV escape from 9--120 M$_{\odot}$
Pop III stars in $10^5$ to $10^7$ M$_{\odot}$ halos with ZEUS-MP. We find that
photons in the LW lines (i.e. those responsible for destroying H$_{2}$ in
nearby systems) have escape fractions ranging from 0% to 85%. No LW photons
escape the most massive halo in our sample, even from the most massive star.
Escape fractions for photons elsewhere in the 11.18--13.6~eV energy range,
which can be redshifted into the LW lines at cosmological distances, are
generally much higher, being above 60% for all but the least massive stars in
the most massive halos. We find that shielding of H$_2$ by neutral hydrogen,
which has been neglected in most studies to date, produces escape fractions
that are up to a factor of three smaller than those predicted by H$_2$
self-shielding alone.
