Determining the escape fraction of ionizing photons during reionization
  with the GRB derived star-formation rate
  The fraction of ionizing photons that escape their host galaxies and so are
able to ionize hydrogen in the inter-galactic medium (IGM) is a critical
parameter in analyses of the reionization era and early galaxy formation.
Studies of the reionization history normally suffer from a degeneracy between
the unknown values for the efficiency with which high redshift galaxies turn
mass into stars and the escape fraction of ionizing photons. Recent gamma-ray
burst (GRB) measurements of the star formation rate density during reionization
provide the first opportunity to break this degeneracy. We confront a
semi-analytic model for reionization with the GRB-derived star formation rate,
as well as observations of the Ly-alpha forest and the CMB. Assuming that UV
photons produced in star-forming galaxies dominate the reionization process, we
show that the escape fraction of ionizing photons from high redshift galaxies
is ~5% [log(f_esc)=-1.35+/-0.15 (68%)] for our fiducial model. This value is
reasonably stable against uncertainties in the modeling, including the
implementation of radiative feedback, the possibility of an evolving escape
fraction, and the unknown shape of the IMF, which in sum contribute ~0.2 dex of
additional systematic uncertainty on the value of escape fraction.
