Gravitational lensing modification of the high-redshift galaxy luminosity function

The bright end of the rest-frame ultraviolet luminosity function (UVLF) of high-redshift galaxies is modified by gravitational lensing magnification bias. Motivated by recent discoveries of very high-z galaxies with JWST, we study the dependence of magnification bias on the finite size of sources at 6 < z < 14. We calculate the magnification probability distributions and use these to calculate the magnification bias assuming a rest-frame Schechter UVLF for galaxies at redshift 6 < z < 14. We find that the finite size of bright high-redshift galaxies together with lens ellipticity significantly suppresses magnification bias, producing an observed bright end which declines more sharply than the power law resulting from assumption of point sources. By assuming a luminosity-size relation for the source population and comparing with the observed z = 6 galaxy luminosity function from Harikane et al. (2022), we show that the UVLF can be used to set mild constraints on the galaxies intrinsic size, favouring smaller galaxies compared to the fiducial luminosity-size relation. In the future, wide surveys using Euclid and Roman Space Telescope will place stronger constraints. We also tabulate the maximum magnification possible as a function of source size and lens ellipticity.