The intrinsic escape fraction of ionizing Lyman continuum photons ( f _ { { esc } } ) is crucial to understand whether galaxies are capable of reionizing the neutral hydrogen in the early universe at z > 6 .
Unfortunately , it is not possible to access f _ { { esc } } at z > 4 with direct observations and the handful of measurements from low redshift galaxies consistently find f _ { { esc } } < 10 \% , while at least f _ { { esc } } \sim 10 \% is necessary for galaxies to dominate reionization .
Here , we present the first empirical prediction of f _ { { esc } } at z > 6 by combining the ( sparsely populated ) relation between [ O III ] / [ O II ] and f _ { { esc } } with the redshift evolution of [ O III ] / [ O II ] as predicted from local high-z analogs selected by their H \alpha equivalent-width .
We find f _ { { esc } } = 5.7 _ { -3.3 } ^ { +8.3 } \% at z = 6 and f _ { { esc } } = 10.4 _ { -6.3 } ^ { +15.5 } \% at z = 9 for galaxies with \log ( M / { M } _ { \odot } ) \sim 9.0 ( errors given as 1 \sigma ) .
However , there is a negative correlation with stellar mass and we find up to 50 \% larger f _ { { esc } } per 0.5 { dex } decrease in stellar mass .
The population averaged escape fraction increases according to f _ { { esc } } = f _ { { esc, 0 } } \left ( ( 1 + z ) / 3 \right ) ^ { \alpha } , with f _ { { esc, 0 } } = 2.3 \pm 0.05 and \alpha = 1.17 \pm 0.02 at z > 2 for \log ( M / { M } _ { \odot } ) \sim 9.0 .
With our empirical prediction of f _ { { esc } } ( thus fixing an important previously unknown variable ) and further reasonable assumption on clumping factor and the production efficiency of Lyman continuum photons , we conclude that the average population of galaxies is just capable of reionizing the universe by z \sim 6 .