Constraints on photoionization feedback from number counts of
  ultra-faint high-redshift galaxies in the Frontier Fields
  We exploit a sample of ultra-faint high-redshift galaxies (demagnified HST
$H_{160}$ magnitude $>30$) in the Frontier Fields clusters A2744 and M0416 to
constrain a theoretical model for the UV luminosity function (LF) in the
presence of photoionization feedback. The objects have been selected on the
basis of accurate photometric redshifts computed from multi-band photometry
including 7 HST bands and deep $K_s$ and IRAC observations. Magnification is
computed on an object-by-object basis from all available lensing models of the
two clusters. We take into account source detection completeness as a function
of luminosity and size, magnification effects and systematics in the lens
modeling of the clusters under investigation. We find that our sample of
high-$z$ galaxies constrain the cut-off halo circular velocity below which
star-formation is suppressed by photo-ionization feedback to $v_c^{\rm cut} <
50$ km s$^{-1}$. This circular velocity corresponds to a halo mass of
$\approx5.6\times10^9~M_\odot$ and $\approx2.3\times10^9~M_\odot$ at $z=5$ and
10 respectively: higher mass halos can thus sustain continuous star formation
activity without being quenched by external ionizing flux. More stringent
constraints are prevented by the uncertainty in the modeling of the cluster
lens, as embodied by systematic differences among the lens models available.
