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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 â€˜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.