The size-luminosity relation of lensed galaxies at $z=6-9$ in the Hubble Frontier Fields

We measure the size-luminosity relation of photometrically-selected galaxies within the redshift range $z\sim6-9$, using galaxies lensed by six foreground Hubble Frontier Fields (HFF) clusters. The power afforded by strong gravitational lensing allows us to observe fainter and smaller galaxies than in blank fields. We select our sample of galaxies and obtain their properties, e.g., redshift, magnitude, from the photometrically-derived ASTRODEEP catalogues. The intrinsic size is measured with the Lenstruction software, and completeness maps are created as a function of size and luminosity via the GLACiAR2 software. We perform a Bayesian analysis to estimate the intrinsic and incompleteness-corrected size-luminosity distribution, with parameterization $r_e \propto L^\beta$. We find slopes of $\beta\sim0.48\pm0.08$ at $z\sim6-7$ and $\beta\sim0.68\pm0.14$ at $z\sim8.5$, adopting the Bradac lens model. The slope derived by lensed galaxies is steeper than that obtained in blank fields and is consistent with other independent determinations of the size-luminosity relation from the HFF dataset. We also investigate the systematic uncertainties correlated with the choice of lens models, finding that the slopes of size-luminosity relations derived from different models are consistent with each other, i.e. the modeling errors are not a significant source of uncertainty in the size-luminosity relation.