On the faint-end of the high-$z$ galaxy luminosity function
  Recent measurements of the Luminosity Function (LF) of galaxies in the Epoch
of Reionization (EoR, $z\gsim6$) indicate a very steep increase of the number
density of low-mass galaxies populating the LF faint-end. However, as star
formation in low-mass halos can be easily depressed or even quenched by
ionizing radiation, a turnover is expected at some faint UV magnitudes. Using a
physically-motivated analytical model, we quantify reionization feedback
effects on the LF faint-end shape. We find that if reionization feedback is
neglected, the power-law Schechter parameterization characterizing the LF
faint-end remains valid up to absolute UV magnitude $\sim -9$. If instead
radiative feedback is strong enough that quenches star formation in halos with
circular velocity smaller than 50 km s$^{-1}$, the LF starts to drop at
absolute UV magnitude $\sim -15$, i.e. slightly below the detection limits of
current (unlensed) surveys at $z\sim5$. The LFs may rise again at higher
absolute UV magnitude, where, as a result of interplay between reionization
process and galaxy formation, most of the galaxy light is from relic stars
formed before the EoR. We suggest that the galaxy number counts data,
particularly in lensed fields, can put strong constraints on reionization
feedback. In models with stronger reionization feedback, stars in galaxies with
absolute UV magnitude higher than $\sim -13$ and smaller than $\sim - 8$ are
typically older. Hence, the stellar age - UV magnitude relation can be used as
an alternative feedback probe.
