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 deep luminosity functions to <-18 AB mag and the star formation rate density at z~7 and z~8. The galaxy sample is derived using a sophisticated Lyman-Break technique 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) and the wider area ERS (~27.5 AB mag) ~40 arcmin**2). The application of strict optical non-detection criteria ensures the contamination fraction is kept low (just ~7% in the HUDF). This very low value includes a full assessment of the contamination from lower redshift sources, photometric scatter, AGN, spurious sources, low mass stars, and transients (e.g., SNe). From careful modelling of the selection volumes for each of our search fields we derive luminosity functions for galaxies at z~7 and z~8 to <-18 AB mag. The faint-end slopes alpha at z~7 and z~8 are uncertain but very steep at alpha = -2.01+/-0.21 and alpha=-1.91+/-0.32, respectively. Such steep slopes contrast to the local alpha<~-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 the galaxy luminosity density during the epoch of reionization. The star formation rate densities derived from these new z~7 and z~8 luminosity functions are consistent with the trends found at later times (lower redshifts). We find reasonable consistency, with the SFR densities implied from reported stellar mass densities, being only ~40% higher at z<7. This suggests that (1) the stellar mass densities inferred from the Spitzer IRAC photometry are reasonably accurate and (2) that the IMF at very high redshift may not be very different from that at later times.
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