  We present a catalog of high redshift star-forming galaxies selected to lie
within the redshift range z ~ 7-8 using the Ultra Deep Field 2012 (UDF12), the
deepest near-infrared (near-IR) exposures yet taken with the Hubble Space
Telescope. As a result of the increased near-infrared exposure time compared to
previous HST imaging in this field, we probe 0.65 (0.25) mag fainter in
absolute UV magnitude, at z ~ 7 (8), which increases confidence in a
measurement of the faint end slope of the galaxy luminosity function. Through a
0.7 mag deeper limit in the key F105W filter that encompasses or lies just
longward of the Lyman break, we also achieve a much-refined color-color
selection that balances high redshift completeness and a low expected
contamination fraction. We improve the number of drop-out selected UDF sources
to 47 at z ~ 7 and 27 at z ~ 8. Incorporating brighter archival and
ground-based samples, we measure the z ~ 7 UV luminosity function to an
absolute magnitude limit of M_UV = -17 and find a faint end Schechter slope of
\alpha = -1.87+/- 0.18. Using a similar color-color selection at z ~ 8 that
takes account of our newly-added imaging in the F140W filter, and incorporating
archival data from the HIPPIES and BoRG campaigns, we provide a robust estimate
of the faint end slope at z ~ 8, \alpha = -1.94 +/- 0.23. We briefly discuss
our results in the context of earlier work and that derived using the same
UDF12 data but with an independent photometric redshift technique (McLure et al
2012).
