Constraining the Minimum Luminosity of High Redshift Galaxies through
  Gravitational Lensing
  We simulate the effects of gravitational lensing on the source count of high
redshift galaxies as projected to be observed by the Hubble Frontier Fields
program and the James Webb Space Telescope (JWST) in the near future. Taking
the mass density profile of the lensing object to be the singular isothermal
sphere (SIS) or the Navarro-Frenk-White (NFW) profile, we model a lens residing
at a redshift of z_L = 0.5 and explore the radial dependence of the resulting
magnification bias and its variability with the velocity dispersion of the
lens, the photometric sensitivity of the instrument, the redshift of the
background source population, and the intrinsic maximum absolute magnitude
(M_{max}) of the sources. We find that gravitational lensing enhances the
number of galaxies with redshifts z >= 13 detected in the angular region
\theta_E/2 <= \theta <= 2\theta_E (where \theta_E is the Einstein angle) by a
factor of ~ 3 and 1.5 in the HUDF (df/d\nu_0 ~ 9 nJy) and medium-deep JWST
surveys (df/d\nu_0 ~ 6 nJy). Furthermore, we find that even in cases where a
negative magnification bias reduces the observed number count of background
sources, the lensing effect improves the sensitivity of the count to the
intrinsic faint-magnitude cut-off of the Schechter luminosity function. In a
field centered on a strong lensing cluster, observations of z >= 6 and z >= 13
galaxies with JWST can be used to infer this cut-off magnitude for values as
faint as M_{max} ~ -14.4 and -16.1 mag (L_{min} ~ 2.5*10^{26} and 1.2*10^{27}
erg s^{-1} Hz^{-1}) respectively, within the range bracketed by existing
theoretical models. Gravitational lensing may therefore offer an effective way
of constraining the low-luminosity cut-off of high-redshift galaxies.
