Abstract
The HUDF09 data are the deepest near-IR observations ever, reaching to ~29.5
mag. The recent sample of 132 z~7 and z~8 galaxies from the HUDF09 data are
complemented here by new large samples at z~5 and z~6 galaxies (507 and 203,
respectively) and prior results at z~4. The luminosity functions we derive at
these redshifts reach to very faint limits of <0.05L*(z=3). The faint-end
slopes alpha are steep: -1.79+/-0.12 (z~5), -1.73+/-0.20 (z~6), -2.01+/-0.21
(z~7), and -1.91+/-0.32 (z~8). The results are consistent with a slope that
increases systematically to earlier times, with slopes close to -2 at z~7-8.
Slopes alpha ~-2 lead to formally divergent UV fluxes, though galaxies are not
expected to form below ~-10 AB mag. These results have major implications for
reionization. For such steep slopes, and a faint-end limit of -10 AB mag,
galaxies provide a very large UV ionizing photon flux. Adopting typical
parameters and extrapolating the current LF and faint-end slope evolution from
z~4-8 to z>8, we derive Thomson optical depths of 0.079, in excellent agreement
with the seven-year 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 are large and depend
critically on the trend to steeper faint-end slopes at z>=6. We show that
deeper, and realistic, WFC3/IR+ACS observations can substantially lessen the
uncertainties on the z~5-8 slopes and further constrain this key parameter in
determining the UV ionizing flux from galaxies.
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