The part played by stars in the ionization of the intergalactic medium remains an open question. A key issue is the proportion of the stellar ionizing radiation that escapes the galaxies in which it is produced. Spectroscopy of gamma-ray burst afterglows can be used to determine the neutral hydrogen column-density in their host galaxies and hence the opacity to extreme ultra-violet radiation along the lines-of-sight to the bursts. Thus, making the reasonable assumption that long-duration GRB locations are representative of the sites of massive stars that dominate EUV production, one can calculate an average escape fraction of ionizing radiation in a way that is independent of galaxy size, luminosity or underlying spectrum. Here we present a sample of NH measures for 138 GRBs in the range 1.6<z<6.7 and use it to establish an average escape fraction at the Lyman limit of <fesc>~0.005, with a 98% confidence upper limit of ~0.015. This analysis suggests that stars provide a small contribution to the ionizing radiation budget of the IGM at z<5, where the bulk of the bursts lie. At higher redshifts, z>5, firm conclusions are limited by the small size of the GRB sample, but any decline in average HI column-density seems to be modest. We also find no indication of a significant correlation of NH with galaxy UV luminosity or host stellar mass, for the subset of events for which these are available. We discuss in some detail a number of selection effects and potential biases. Drawing on a range of evidence we argue that such effects, while not negligible, are unlikely to produce systematic errors of more than a factor ~2, and so would not affect the primary conclusions. Given that many GRB hosts are low metallicity, high specific star-formation rate, dwarf galaxies, these results present a particular problem for the hypothesis that such galaxies dominated the reionization of the universe.
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