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We identify 73 z~7 and 59 z~8 candidate galaxies in the reionization epoch,and use this large 26-29.4 AB mag sample of galaxies to derive very deepluminosity functions to <-18 AB mag and the star formation rate density at z~7and z~8. The galaxy sample is derived using a sophisticated Lyman-Breaktechnique on the full two-year WFC3/IR and ACS data available over the HUDF09(~29.4 AB mag, 5 sigma), two nearby HUDF09 fields (~29 AB mag, 14 arcmin) andthe wider area ERS (~27.5 AB mag) ~40 arcmin**2). The application of strictoptical non-detection criteria ensures the contamination fraction is kept low(just ~7% in the HUDF). This very low value includes a full assessment of thecontamination from lower redshift sources, photometric scatter, AGN, spurioussources, low mass stars, and transients (e.g., SNe). From careful modelling ofthe selection volumes for each of our search fields we derive luminosityfunctions for galaxies at z~7 and z~8 to <-18 AB mag. The faint-end slopesalpha at z~7 and z~8 are uncertain but very steep at alpha = -2.01+/-0.21 andalpha=-1.91+/-0.32, respectively. Such steep slopes contrast to the localalpha<~-1.4 and may even be steeper than that at z~4 where alpha=-1.73+/-0.05.With such steep slopes (alpha<~-1.7) lower luminosity galaxies dominate thegalaxy luminosity density during the epoch of reionization. The star formationrate densities derived from these new z~7 and z~8 luminosity functions areconsistent with the trends found at later times (lower redshifts). We findreasonable consistency, with the SFR densities implied from reported stellarmass densities, being only ~40% higher at z<7. This suggests that (1) thestellar mass densities inferred from the Spitzer IRAC photometry are reasonablyaccurate and (2) that the IMF at very high redshift may not be very differentfrom that at later times.

UV Luminosity Functions from 132 z~7 and z~8 Lyman-Break Galaxies in the ultra-deep HUDF09 and wide-area ERS WFC3/IR Observations