Lower-Luminosity Galaxies could reionize the Universe: Very Steep
  Faint-End Slopes to the UV Luminosity Functions at z>=5-8 from the HUDF09
  WFC3/IR Observations
  The HUDF09 data are the deepest near-IR observations ever, reaching to 29.5
mag. Luminosity functions (LF) from these new HUDF09 data for 132 z\sim7 and
z\sim8 galaxies are combined with new LFs for z\sim5-6 galaxies and the earlier
z\sim4 LF to reach to very faint limits (<0.05 L*(z=3)). The faint-end slopes
alpha are steep: -1.79+/-0.12 (z\sim5), -1.73+/-0.20 (z\sim6), -2.01+/-0.21
(z\sim7), and -1.91+/-0.32 (z\sim8). Slopes alpha\lesssim-2 lead to formally
divergent UV fluxes, though galaxies are not expected to form below \sim-10 AB
mag. These results have important implications for reionization. The weighted
mean slope at z\sim6-8 is -1.87+/-0.13. For such steep slopes, and a faint-end
limit of -10 AB mag, galaxies provide a very large UV ionizing photon flux.
While current results show that galaxies can reionize the universe by z\sim6,
matching the Thomson optical depths is more challenging. Extrapolating the
current LF evolution to z>8, taking alpha to be -1.87+/-0.13 (the mean value at
z\sim6-8), and adopting typical parameters, we derive Thomson optical depths of
0.061_{-0.006}^{+0.009}. However, this result will change if the faint-end
slope alpha is not constant with redshift. We test this hypothesis and find a
weak, though uncertain, trend to steeper slopes at earlier times
(dalpha/dz\sim-0.05+/-0.04), that would increase the Thomson optical depths to
0.079_{-0.017}^{+0.063}, consistent with recent WMAP estimates
(tau=0.088+/-0.015). It may thus not be necessary to resort to extreme
assumptions about the escape fraction or clumping factor. Nevertheless, the
uncertainties remain large. Deeper WFC3/IR+ACS observations can further
constrain the ionizing flux from galaxies.
