Size-luminosity relations at z=6-9 from HFF data and their implications for the fraction of undetected galaxies

Ryota Kawamata

We construct z~6-7, 8, 9 LBG samples (194, 41, 22 galaxies, respectively) with accurate size measurements from four Hubble Frontier Fields (HFF, Lotz et al. 2016) clusters and their parallel-fields data. These samples reach down to the faint ends of recently obtained deep luminosity functions (LFs) at similar redshifts (Atek et al. 2015). Our size measurements by ‘glafic' (Oguri 2010) properly deal with the gravitational lensing effects by fitting galaxy images with lensing-distorted Sersic profiles calculated using our precise mass models.The observed size-luminosity relations at all redshifts turn out to be steep, but our careful completeness analysis on the size-luminosity plane reveals that they are artificially steepened because detection completeness drops rapidly with size at faint magnitudes. By extrapolating the size distribution over -19.7 < Muv < -18.7, where the distribution is reliably fitted by a log-normal distribution thanks to the large sample size, to fainter magnitudes according to three reasonable size-luminosity relations of Re \propto L^m with m=1/3, 1/4, 1/5, we find, for the first time, that as many as 99% of galaxies at Muv = -15 are concealed at z=6-7 even in our deep sample. These three m values correspond to simple modeling of feedback (no feedback and momentum- and energy-conserving SN feedback), and m=1/4 is also the value for z=5 LBGs (Huang et al. 2013). With these concealed galaxies taken into account, the LF faint-end slope alpha will largely steepen, giving significant impacts on the discussions of cosmic reionization and cosmic star-formation history. We also find that we can constrain alpha reasonably well using our sample with the systematic variation in alpha over 1/5 < m < 1/3 being only ~0.02.