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 zsim7 and zsim8 galaxies are combined with new LFs for zsim5-6 galaxies and the earlier zsim4 LF to reach to very faint limits (<0.05 L*(z=3)). The faint-end slopes alpha are steep: -1.79+/-0.12 (zsim5), -1.73+/-0.20 (zsim6), -2.01+/-0.21 (zsim7), and -1.91+/-0.32 (zsim8). Slopes alphalesssim-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 zsim6-8 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 zsim6, 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 zsim6-8), 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/dzsim-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.
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