The Galaxy Luminosity Function During the Reionization Epoch

The new Wide Field Camera 3/IR observations on the Hubble Ultra-Deep Field (HUDF) 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 (LF) measured at z = 5 and z = 4. We then predict the LF at z ⩾ 7 under the sole assumption of evolution in the underlying dark-matter halo mass function. Our model is consistent with the observed z ≳ 7 galaxy number counts in the HUDF survey and suggests a possible steepening of the faint-end slope of the LF: α( z ≳ 8) ≲ −1.9 compared to α = −1.74 at z = 6. Although we currently see only the brightest galaxies, a hidden population of lower luminosity objects ( L / L * ≳ 10 −4 ) might provide ≳75% of the total reionizing flux. Assuming escape fraction f esc ∼ 0.2, clumping factor C ∼ 5, top-heavy initial mass function (IMF), and low metallicity, galaxies below the detection limit produce complete 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 an optical depth consistent with the Wilkinson Microwave Anisotropy Probe 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 ⩾ 6 than today.