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 \sim 5 \% [ \log { f _ { esc } } = -1.35 \pm 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 \sim 0.2 dex of additional systematic uncertainty on the value of escape fraction .