  We model the latest HST WFPC3/IR observations of > 100 galaxies at redshifts
z=7-8 in terms of a hierarchical galaxy formation model with starburst
activity. Our model provides a distribution of UV luminosities per dark matter
halo of a given mass and a natural explanation for the fraction of halos
hosting galaxies. The observed luminosity function is best fit with a minimum
halo mass per galaxy of 10^{9.4+0.3-0.9} Msun, corresponding to a virial
temperature of 10^{4.9+0.2-0.7} K. Extrapolating to faint, undetected galaxies,
the total production rate of ionizing radiation depends critically on this
minimum mass. Future measurements with JWST should determine whether the entire
galaxy population can comfortably account for the UV background required to
keep the intergalactic medium ionized.
