SIMBAD references

We construct z ∼ 6-7, 8, and 9 faint Lyman break galaxy samples (334, 61, and 37 galaxies, respectively) with accurate size measurements with the software glafic from the complete Hubble Frontier Fields (HFF) cluster and parallel fields data. 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 ∝ L^β has a notably steeper slope of β=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 α=-1.86_–0.18^+0.17. This steep β can be reproduced by a simple analytical model in which smaller galaxies have lower specific angular momenta. The β and α values for the z ∼ 8 and 9 samples are consistent with those for z ∼ 6-7 but with larger errors. For all three samples, there is a large, positive covariance between β and α, implying that the simultaneous determination of these two parameters is important. We also provide new strong lens mass models of Abell S1063 and Abell 370, as well as updated mass models of Abell 2744 and MACS J0416.1-2403.