Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Deriving a lens magnification map for a galaxy cluster is a classic inversion problem and many methods have been developed over the past two decades to solve it. Several research groups have developed techniques independently to map the predominantly dark matter distribution in cluster lenses. While these methods have all provided remarkably high precision mass maps, particularly with exquisite imaging data from the Hubble Space Telescope (HST), the reconstructions themselves have never been directly compared. In this paper, we report the results of comparing various independent lens modeling techniques employed by individual research groups in the community. Here we present for the first time a detailed and robust comparison of methodologies for fidelity, accuracy and precision. For this collaborative exercise, the lens modeling community was provided simulated cluster images -of two clusters Ares and Hera -that mimic the depth and resolution of the ongoing HST Frontier Fields. The results of the submitted reconstructions with the un-blinded true mass profile of these two clusters are presented here. Parametric, free-form and hybrid techniques have been deployed by the participating groups and we detail the strengths and trade-offs in accuracy and systematics that arise for each methodology. We note in conclusion that lensing reconstruction methods produce reliable mass distributions that enable the use of clusters as extremely valuable astrophysical laboratories and cosmological probes.

The deflection angles of lensed sources increase with their distance behind a given lens. We utilize this geometric effect to corroborate the z phot 9.8 photometric redshift estimate of a faint near-IR dropout, triply imaged by the massive galaxy cluster A2744 in deep Hubble Frontier Fields images. The multiple images of this source follow the same symmetry as other nearby sets of multiple images that bracket the critical curves and have well-defined redshifts (up to z spec 3.6), but with larger deflection angles, indicating that this source must lie at a higher redshift. Similarly, our different parametric and non-parametric lens models all require this object be at z 4, with at least 95% confidence, thoroughly excluding the possibility of lower-redshift interlopers. To study the properties of this source, we correct the two brighter images for their magnifications, leading to a star formation rate of ∼0.3 M yr −1 , a stellar mass of ∼4 × 10 7 M , and an age of 220 Myr (95% confidence). The intrinsic apparent magnitude is 29.9 AB (F160W), and the rest-frame UV (∼1500 Å) absolute magnitude is M UV,AB = −17.6. This corresponds to ∼0.1 L * z=8 (∼0.2 L * z=10 , adopting dM * /dz ∼ 0.45), making this candidate one of the least luminous galaxies discovered at z ∼ 10.

We provide the first observational constraints on the sizes of the faintest galaxies lensed by the Hubble Frontier Fields (HFF) clusters. Ionizing radiation from faint galaxies likely drives cosmic reionization, and the HFF initiative provides a key opportunity to find such galaxies. Yet, we cannot assess their ionizing emissivity without a robust measurement of their sizes, since this is key to quantifying both their prevalence and the faint-end slope to the U V luminosity function. Here we provide the first size constraints with two new techniques. The first utilizes the fact that the detectability of highlymagnified galaxies as a function of shear is very dependent on a galaxy's size. Only the most compact galaxies remain detectable in high-shear regions (vs. a larger detectable size range for low shear), a phenomenon we quantify using simulations. Remarkably, however, no correlation is found between the surface density of faint galaxies and the predicted shear, using 87 high-magnification (µ = 10-100) z ∼ 2-8 galaxies seen behind the first four HFF clusters. This can only be the case if faint (∼ −15 mag) galaxies have significantly smaller sizes than more luminous galaxies, i.e., 30 mas or 160-240 pc. As a second size probe, we rotate and stack 26 faint high-magnification sources along the major shear axis. Less elongation is found than even for objects with an intrinsic half-light radius of 10 mas. Together these results indicate that extremely faint z ∼ 2-8 galaxies have near point-source profiles (half-light radii <30 mas and perhaps 5-10 mas). These results suggest smaller completeness corrections and hence shallower faint-end slopes for the z ∼ 2-8 LFs than derived in some recent studies (by ∆α 0.1-0.3).

Large surveys of galaxy clusters with the Hubble and Spitzer Space Telescopes, including CLASH and the Frontier Fields, have demonstrated the power of strong gravitational lensing to efficiently deliver large samples of high-redshift galaxies. We extend this strategy through a wider, shallower survey named RELICS, the Reionization Lensing Cluster Survey. This survey, described here, was designed primarily to deliver the best and brightest high-redshift candidates from the first billion years after the Big Bang. RELICS observed 41 massive galaxy clusters with Hubble and Spitzer at 0.4-1.7µm and 3.0-5.0µm, respectively. We selected 21 clusters based on Planck PSZ2 mass estimates and the other 20 based on observed or inferred lensing strength. Our 188-orbit Hubble Treasury Program obtained the first high-resolution near-infrared images of these clusters to efficiently search for lensed highredshift galaxies. We observed 46 WFC3/IR pointings (∼200 arcmin 2 ) with two orbits divided among four filters (F105W, F125W, F140W, and F160W) and ACS imaging as needed to achieve single-orbit depth in each of three filters (F435W, F606W, and F814W). As previously reported by Salmon et al., we discovered 322 z ∼ 6 − 10 candidates, including the brightest known at z ∼ 6, and the most spatially-resolved distant lensed arc known at z ∼ 10. Spitzer IRAC imaging (945 hours awarded, plus 100 archival) has crucially enabled us to distinguish z ∼ 10 candidates from z ∼ 2 interlopers. For each cluster, two HST observing epochs were staggered by about a month, enabling us to discover 11 supernovae, including 3 lensed supernovae, which we followed up with 20 orbits from our program. We delivered reduced HST images and catalogs of all clusters to the public via MAST and reduced Spitzer images via IRSA. We have also begun delivering lens models of all clusters, to be completed before the JWST GO Cycle 1 call for proposals.

Strong gravitational lensing by galaxy clusters magnifies background galaxies, enhancing our ability to discover statistically significant samples of galaxies at z 6 > , in order to constrain the high-redshift galaxy luminosity functions. Here, we present the first five lens models out of the Reionization Lensing Cluster Survey (RELICS) Hubble Treasury Program, based on new HST WFC3/IR and ACS imaging of the clusters RXCJ0142.9+4438, Abell2537, Abell2163, RXCJ2211.7-0349, and ACT-CLJ0102-49151. The derived lensing magnification is essential for estimating the intrinsic properties of high-redshift galaxy candidates, and properly accounting for the survey volume. We report on new spectroscopic redshifts of multiply imaged lensed galaxies behind these clusters, which are used as constraints, and detail our strategy to reduce systematic uncertainties due to lack of spectroscopic information. In addition, we quantify the uncertainty on the lensing magnification due to statistical and systematic errors related to the lens modeling process, and find that in all but one cluster, the magnification is constrained to better than 20% in at least 80% of the field of view, including statistical and systematic uncertainties. The five clusters presented in this paper span the range of masses and redshifts of the clusters in the RELICS program. We find that they exhibit similar strong lensing efficiencies to the clusters targeted by the Hubble Frontier Fields within the WFC3/IR field of view. Outputs of the lens models are made available to the community through the Mikulski Archive for Space Telescopes.