  Using new Keck DEIMOS spectroscopy, we examine the origin of the steep number
counts of ultra-faint emission-line galaxies recently reported by Dressler et
al. (2011). We confirm six Lyman Alpha emitters (LAEs), three of which have
significant asymmetric line profiles with prominent wings extending 300-400
km/s redward of the peak emission. With these six LAEs, we revise our previous
estimate of the number of faint LAEs in the Dressler et al. survey. Combining
these data with the density of bright LAEs in the Cosmic Origins Survey and
Subaru Deep Field provides the best constraints to date on the redshift 5.7 LAE
luminosity function (LF). Schechter function parameters, phi^* = 4.5 x 10^{-4}
Mpc^{-3}, L^* = 9.1 x 10^{42} erg s^{-1}, and alpha= -1.70, are estimated using
a maximum likelihood technique with a model for slit losses. To place this
result in the context of the UV-selected galaxy population, we investigate how
various parameterizations of the Lyman Alpha equivalent width distribution,
along with the measured UV-continuum LF, affect shape and normalization of the
Lyman Alpha LF. The nominal model, which uses z~6 equivalent widths from the
literature, falls short of the observed space density of LAEs at the bright
end, possibly indicating a need for higher equivalent widths. This
parameterization of the equivalent width distribution implies that as many as
50% of our faintest LAEs should have M_{UV} > -18.0, rendering them
undetectable in even the deepest Hubble Space Telescope surveys at this
redshift. Hence, ultra-deep emission-line surveys find some of the faintest
galaxies ever observed at the end of the reionization epoch. Such faint
galaxies likely enrich the intergalactic medium with metals and maintain its
ionized state. Observations of these objects provide a glimpse of the building
blocks of present-day galaxies at an early time.
