The new Wide Field Camera 3/IR observations on the Hubble Ultra-Deep Field started investigating the properties of galaxies during the reionization epoch .
To interpret these observations , we present a novel approach inspired by the conditional luminosity function method .
We calibrate our model to observations at z = 6 and assume a non-evolving galaxy luminosity versus halo mass relation .
We first compare model predictions against the luminosity function measured at z = 5 and z = 4 .
We then predict the luminosity function at z \geqslant 7 under the sole assumption of evolution in the underlying dark-matter halo mass function .
Our model is consistent with the observed z \gtrsim 7 galaxy number counts in the HUDF survey and suggests a possible steepening of the faint-end slope of the luminosity function : \alpha ( z \gtrsim 8 ) \lesssim - 1.9 compared to \alpha = -1.74 at z = 6 .
Although we currently see only the brightest galaxies , a hidden population of lower luminosity objects ( L / L _ { * } \gtrsim 10 ^ { -4 } ) might provide \gtrsim 75 \% of the total reionizing flux .
Assuming escape fraction f _ { esc } \sim 0.2 , clumping factor C \sim 5 , top heavy-IMF and low metallicity , galaxies below the detection limit produce complete reionization at z \gtrsim 8 .
For solar metallicity and normal stellar IMF , reionization finishes at z \gtrsim 6 , but a smaller C / f _ { esc } is required for an optical depth consistent with the WMAP measurement .
Our model highlights that the star formation rate in sub- L _ { * } galaxies has a quasi-linear relation to dark-matter halo mass , suggesting that radiative and mechanical feedback were less effective at z \geq 6 than today .