New Constraints on the Faint-end of the UV Luminosity Function at z~7-8
  using the Gravitational Lensing of the Hubble Frontier Fields Cluster A2744
  Exploiting the power of gravitational lensing, the Hubble Frontier Fields
(HFF) program aims at observing six massive galaxy clusters to explore the
distant Universe far beyond the depth limits of blank field surveys. Using the
complete Hubble Space Telescope observations of the first HFF cluster Abell
2744, we report the detection of 50 galaxy candidates at $z \sim 7$ and eight
candidates at $z \sim 8$ in a total survey area of 0.96 arcmin$^{2}$ in the
source plane. Three of these galaxies are multiply-imaged by the lensing
cluster. Using an updated model of the mass distribution in the cluster we were
able to calculate the magnification factor and the effective survey volume for
each galaxy in order to compute the ultraviolet galaxy luminosity function at
both redshifts 7 and 8. Our new measurements extend the $z \sim 7$ UV LF down
to an absolute magnitude of $M_{UV} \sim -15.5$. We find a characteristic
magnitude of $M^{\star}_{UV}=-20.63^{+0.69}_{-0.56}$ mag and a faint-end slope
$\alpha = -1.88^{+0.17}_{-0.20}$ close to previous determinations in blank
fields. We show here for the first time that this slope remains steep down to
very faint luminosities of 0.01$L^{\star}$. Although prone to large
uncertainties, our results at $z \sim 8$ also seem to confirm a steep faint-end
slope below 0.1$L^{\star}$. The HFF program is therefore providing an extremely
efficient way to study the faintest galaxy populations at $z > 7$ that would
otherwise be inaccessible with current instrumentation. The full sample of six
galaxy clusters will provide yet better constraints on the build-up of galaxies
at early epochs and their contribution to cosmic reionization.
