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

Abstract

We measure the size-luminosity relation of photometrically-selected galaxies within the redshift range 𝑧 ∼ 6 − 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 ∝ 𝐿 𝛽 . We find slopes of 𝛽 ∼ 0.48 ± 0.08 at 𝑧 ∼ 6 − 7 and 𝛽 ∼ 0.68 ± 0.14 at 𝑧 ∼ 8.5, 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.

z ∼ 2–9 Galaxies Magnified by the Hubble Frontier Field Clusters. I. Source Selection and Surface Density–Magnification Constraints from >2500 Galaxies

“…Such a dependence is expected in the case of an especially steep sizeluminosity relation for z ∼ 2-9 galaxies, i.e., where r ∝ L 0.5 and there is no change in the surface brightness of sources versus luminosity or magnification factor at the faint end of the HFF probes. Interestingly enough, Bouwens et al (2017aBouwens et al ( , 2021a, Kawamata et al (2018), andYang et al (2022) all found steep size-luminosity relations at z  6, with radius depending on luminosity as L 0.50±0.07 , -+ L 0.46 0.09 0.08 , L 0.40±0.04 , and L 0.48±0.08 . As important context, a negative δ would be expected for the size-luminosity relations derived for brighter field galaxies in the intermediate-or high-redshift universe.…”

First Light And Reionisation Epoch Simulations (FLARES) IV: The size evolution of galaxies at $z\geq5$

“…The negative gradient in the intrinsic size-luminosity relation presented in Figure 5 is in direct conflict with observational results which necessarily include the effects of dust attenuation (e.g. Hathi et al 2008;Grazian et al 2011Grazian et al , 2012Shibuya et al 2015;Calvi et al 2016;Kawamata et al 2015Kawamata et al , 2018Morishita et al 2018;Bridge et al 2019;Bouwens et al 2021;Yang et al 2022). However, in Section 5.2.1 we have shown that the inclusion of dust attenuation can result in large increases in size for the most intrinsically compact galaxies.…”

“…Figure 9 shows a comparison of these fits (solid red lines) to fits from observed samples: Huang et al (2013) at 𝑧 = 5, Holwerda et al (2015) at 𝑧 = 7 and 𝑧 = 9, Kawamata et al (2018) at 𝑧 = 6 − 9, Bouwens et al (2021) at 𝑧 = 6 − 8, and Yang et al (2022) at 𝑧 = 6 − 7, the latter 3 of these including lensed sources. We also compare to two simulations: the M semi-analytic model (Liu et al 2016;Marshall et al 2019) at 𝑧 = 5 − 9, and the B T simulation (Marshall et al 2021) at 𝑧 = 7 − 9.…”

“…To perform the fits we use the entire complete galaxy sample. We include comparisons to observations without lensed galaxies (Huang et al 2013;Holwerda et al 2015), observations including lensed sources (Kawamata et al 2018;Bouwens et al 2021;Yang et al 2022) and simulations (Marshall et al 2019(Marshall et al , 2021. We denote F by a red solid line, observations by dashed lines and other simulations by dotted lines.…”

“…Recent lensing studies agree with the steeper slope of Kawamata et al (2018), itself using a sample including lensed sources. Bouwens et al (2021) find 𝛽 = 0.40 ± 0.04 for a galaxy sample in the redshift range 𝑧 ∼ 6 − 8, while Yang et al (2022) find 𝛽 = 0.48 ± 0.08 for 𝑧 ∼ 6 − 7 and 𝛽 = 0.68 ± 0.14 for 𝑧 ∼ 8.5 (assuming the Bradac lens model Bradač et al (2005)). This steeper slope is driven by compact dim galaxies which are better sampled in lensing studies.…”