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The new Wide Field Camera 3/IR observations on the Hubble Ultra-Deep Fieldstarted investigating the properties of galaxies during the reionization epoch.To interpret these observations, we present a novel approach inspired by theconditional luminosity function method. We calibrate our model to observationsat z=6 and assume a non-evolving galaxy luminosity versus halo mass relation.We first compare model predictions against the luminosity function measured atz=5 and z=4. We then predict the luminosity function at z>=7 under the soleassumption of evolution in the underlying dark-matter halo mass function. Ourmodel is consistent with the observed z>6.5 galaxy number counts in the HUDFsurvey and suggests a possible steepening of the faint-end slope of theluminosity function: alpha(z>8)< -1.9 compared to alpha=-1.74 at z=6. Althoughwe currently see only the brightest galaxies, a hidden population of lowerluminosity objects (L/L_{*}> 10^{-4}) might provide >75% of the totalreionizing flux. Assuming escape fraction f_{esc}~0.2, clumping factor C~5, topheavy-IMF and low metallicity, galaxies below the detection limit producecomplete reionization at z>8. For solar metallicity and normal stellar IMF,reionization finishes at z>6, but a smaller C/f_{esc} is required for anoptical depth consistent with the WMAP measurement. Our model highlights thatthe star formation rate in sub-L_* galaxies has a quasi-linear relation todark-matter halo mass, suggesting that radiative and mechanical feedback wereless effective at z>6 than today.

The Galaxy Luminosity Function during the Reionization Epoch