  The fraction of ionizing photons which escape their host galaxy and so are
able to ionize hydrogen in the inter-galactic medium (IGM) is a critical
parameter in studies of the reionization era and early galaxy formation. In
this paper we combine observations of Lyman-alpha absorption towards high
redshift quasars with the measured UV luminosity function of high redshift
galaxies to constrain the escape fraction (f_esc) of ionizing photons from
galaxies at z ~ 5.5-6. The observed Lyman-alpha transmission constrains the
escape fraction to lie in the range f_esc ~ 10-25 % (at z ~ 5.5-6). Excluding
halos with M< 10^10 M_sun (as might be expected if galaxy formation is
suppressed due to the reionization of the IGM) implies a larger escape fraction
of f_esc ~ 20-45 %. Using the numerical results to calibrate an analytic
relation between the escape fraction and minimum galaxy halo mass we also
extrapolate our results to a mass (M~10^8 M_sun) corresponding to the hydrogen
cooling threshold. In this case we find f_esc ~ 5-10 %, consistent with
observed estimates at lower redshift. We find that the escape fraction of high
redshift galaxies must be greater than 5 % irrespepctive of galaxy mass. Based
on these results we use a semi-analytic description to model the reionization
history of the IGM, assuming ionizing sources with escape fractions suggested
by our numerical simulations. We find that the IBG observed at z ~ 5.5-6
implies a sufficient number of ionizing photons to have reionized the Universe
by z ~ 6. However, if the minimum mass for star-formation were greater than
10^9 M_sun, the IBG would be over-produced at redshifts less than z ~ 5. In
summary, our results support a scenario in which the IGM was reionized by low
mass galaxies.
