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 the 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 similar to 5 per cent [log f(esc) = -1.35 +/- 0.15 (68 per cent)] for our fiducial model. This relatively small value of escape fraction follows from the slow evolution in the star formation rate density at z greater than or similar to 4 implied by the number counts of high-redshift GRBs. Our derived value is reasonably stable against uncertainties in the modelling, including the implementation of radiative feedback, the possibility of an evolving escape fraction and the unknown shape of the IMF, which in sum contribute similar to 0.2 dex of additional systematic uncertainty on the value of escape fraction.