A Physical Model for the Evolving Ultraviolet Luminosity Function of High Redshift Galaxies and their Contribution to the Cosmic Reionization

We present a physical model for the evolution of the ultraviolet (UV) luminosity function of high-redshift galaxies, taking into account in a self-consistent way their chemical evolution and the associated evolution of dust extinction. Dust extinction is found to increase fast with halo mass. A strong correlation between dust attenuation and halo/stellar mass for UV selected high-z galaxies is thus predicted. The model yields good fits of the UV and Lyman-alpha (Lyalpha) line luminosity functions at all redshifts at which they have been measured. The weak observed evolution of both luminosity functions between z = 2 and z = 6 is explained as the combined effect of the negative evolution of the halo mass function; of the increase with redshift of the star formation efficiency due to the faster gas cooling; and of dust extinction, differential with halo mass. The slope of the faint end of the UV luminosity function is found to steepen with increasing redshift, implying that low luminosity galaxies increasingly dominate the contribution to the UV background at higher and higher redshifts. The observed range of the UV luminosities at high z implies a minimum halo mass capable of hosting active star formation M crit <~ 109.8 M &sun;, which is consistent with the constraints from hydrodynamical simulations. From fits of Lyalpha line luminosity functions, plus data on the luminosity dependence of extinction, and from the measured ratios of non-ionizing UV to Lyman-continuum flux density for samples of z ~= 3 Lyman break galaxies and Lyalpha emitters, we derive a simple relationship between the escape fraction of ionizing photons and the star formation rate. It implies that the escape fraction is larger for low-mass galaxies, which are almost dust-free and have lower gas column densities. Galaxies already represented in the UV luminosity function (M UV <~ -18) can keep the universe fully ionized up to z ~= 6. This is consistent with (uncertain) data pointing to a rapid drop of the ionization degree above z ~= 6, such as indications of a decrease of the comoving emission rate of ionizing photons at z ~= 6, a decrease of sizes of quasar near zones, and a possible decline of the Lyalpha transmission through the intergalactic medium at z > 6. On the other hand, the electron scattering optical depth, taues, inferred from cosmic microwave background (CMB) experiments favor an ionization degree close to unity up to z ~= 9-10. Consistency with CMB data can be achieved if M crit ~= 108.5 M &sun;, implying that the UV luminosity functions extend to M UV ~= -13, although the corresponding taues is still on the low side of CMB-based estimates