z~2-9 Galaxies magnified by the Hubble Frontier Field Clusters I: Source Selection and Surface Density-Magnification Constraints from >2500 galaxies

Abstract

We assemble a large comprehensive sample of 2534 z ∼ 2, 3, 4, 5, 6, 7, 8, and 9 galaxies lensed by the six clusters from the Hubble Frontier Fields (HFF) program. Making use of the availability of multiple independent magnification models for each of the HFF clusters and alternatively treating one of the models as the "truth," we show that the median magnification factors from the v4 parametric models are typically reliable to values of 30 to 50, and in one case to 100. Using the median magnification factor from the latest v4 models, we estimate the UV luminosities of the 2534 lensed z ∼ 2-9 galaxies, finding sources as faint as −12.4 mag at z ∼ 3 and −12.9 mag at z ∼ 7. We explicitly demonstrate the power of the surface density-magnification relations Σ(z) vs. µ in the HFF clusters to constrain both distant galaxy properties and cluster lensing properties. Based on the Σ(z) vs. µ relations, we show that the median magnification estimates from existing public models must be reliable predictors of the true magnification µ to µ < 15 (95% confidence). We also use the observed Σ(z) vs. µ relations to derive constraints on the evolution of the luminosity function faint-end slope from z ∼ 7 to z ∼ 2, showing that faint-end slope results can be consistent with blank-field studies if, and only if, the selection efficiency shows no strong dependence on the magnification factor µ. This can only be the case if very low luminosity galaxies are very small, being unresolved in deep lensing probes.

z~2-9 Galaxies Magnified by the Hubble Frontier Field Clusters II: Luminosity Functions and Constraints on a Faint-End Turnover

“…We consider the systematic application of z = 2-9 Lyman-break galaxy selection criteria to the HFF near-UV, optical, and near-IR observations available over the six clusters that make up the HFF program. We describe our application of these criteria to the HFF observations in a companion paper (Bouwens et al 2022b), and it is very similar to what we previously performed in Bouwens et al (2015aBouwens et al ( , 2016aBouwens et al ( , and 2017b.…”

“…A second major source of error are uncertainties in the lensing models themselves and the impact this has on U V LF results (Bouwens et al 2017b;Atek et al 2018). Comparisons of different lensing models can show a wide range in the predicted magnifications for individual sources (∼0.3-0.5 dex scatter), with the position of high magnification critical lines varying by 1 from one model to another (Meneghetti et al 2017;Sebesta et al 2016;Bouwens et al 2017bBouwens et al , 2022b. The magnification factors for sources in the highest-magnification regions are accordingly the most uncertain and can have a particularly large impact on the recovered U V LF.…”

“…The small sizes of faint sources result in substantially smaller completeness correction than if these sources were more extended (Bouwens et al 2017b(Bouwens et al , 2022aKawamata et al 2018). Similarly, use of the median magnification from multiple public lensing models (Livermore et al 2017;Bouwens et al 2017b;Bhatawdekar et al 2019;Bouwens et al 2022b) and forward modeling (Bouwens et al 2017b;Atek et al 2018) provide us with a very effective way of accounting for the uncertainties in lensing models for specific clusters. By creating mock data sets on the basis of candidate LFs and specific lensing models and interpreting the observations using a median of the other magnification maps, one can replicate the LF recovery process and arrive at realistic uncertainties on the overall shape of the recovered LF.…”

“…Mapping out the extreme faint end of the UV LF is valuable for providing insight into the efficiency of star formation in lower mass galaxies and quantifying the total budget of ionizing photons available at z ≥ 6 to drive cosmic reionization. For this effort, we make use of the extremely large >2500-source sample of lensed galaxies recently identified at z ∼ 2-9 over all six HFF clusters in a companion paper (Bouwens et al 2022b).…”

“…All magnitudes are in the AB system (Oke & Gunn 1983). (Bouwens et al 2022b) a Sources are not selected at this redshift in the indicated cluster field, due to concerns about contamination from foreground galaxies from the cluster due to the similar position of the Lyman break and the 4000 Åbreak (see Figure 3 from Bouwens et al 2022b). b Oesch et al (2018a).…”