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 pro file of the lensing object to be the singular isothermal sphere (SIS) or the Navarro-Frenk-White (NFW) pro file, 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 m a x) of the sources. We find that gravitational lensing enhances the number of galaxies with redshifts z greater than or similar to 13 detected in the angular region theta(E/2) <= theta <= 2 theta(E) (where theta(E) is the Einstein angle) by a factor of similar to 3 and 1.5 in the HUDF (df/d nu(0) similar to 9 nJy) and medium-deep JWST surveys (df/d nu(0) similar to 6 nJy). Furthermore, we find that even in cases where a negative magnification bias reduces t he 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 greater than or similar to 6 and z greater than or similar to 13 galaxies with JWST can be used to infer this cut-off magnitude for values as faint as M-max similar to -14.4 and -16.1 mag (L-min approximate to 2.5 x 10(26) and 1.2 x 10(27) erg s(-1) Hz(-1)) respectively, within the range bracketed by existing theoretical models. Gravitational lensing may therefore off er an effective way of constraining the low-luminosity cut-off of high-redshift galaxies.