  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.
