Lyman break galaxies at z~6-9 from HFF

These are the largest samples hitherto and reach down to the faint ends of recently obtained deep luminosity functions. At faint magnitudes, however, these samples are highly incomplete for galaxies with large sizes, implying that derivation of the luminosity function sensitively depends on the intrinsic size-luminosity relation.

We thus conduct simultaneous maximum-likelihood estimation of luminosity function and size-luminosity relation parameters from the observed distribution of galaxies on the size-luminosity plane with the help of a completeness map as a function of size and luminosity. At z~6-7, we find that the intrinsic size-luminosity relation expressed as r_e_{propto}L^{beta}^ has a notably steeper slope of {beta}=0.46_-0.09_^+0.08^ than those at lower redshifts, which in turn implies that the luminosity function has a relatively shallow faint-end slope of {alpha}=-1.86_-0.18_^+0.17^.