Gravitational lensing modification of the high redshift galaxy luminosity function

The bright end of the rest-frame UV 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+(2022), we show that the UVLF can be used to set mild constraints on the galaxies intrinsic size, favoring 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.