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Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the 𝐸 𝐺 statistic

We derive new constraints on the 𝐸 𝐺 statistic as a test of gravity, combining the cosmic microwave background (CMB) lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS BOSS) CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the 𝐸 𝐺 statistic can distinguish Λ⁢ CDM from alternative models of gravity. We find 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢1$^{+0.06}_{−0.05}$ for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢9$^{+0.14}_{−0.11}$ for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in 𝐸 𝐺 ⁡(𝑧 eff = 0.555) = 0.3⁢4$^{+0.05}_{−0.05}$ with CMASS and 𝐸 𝐺 ⁡(𝑧 eff = 0.316) = 0.4⁢3$^{+0.11}_{−0.09}$ with LOWZ. These are consistent with predictions for the Λ⁢ CDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where 𝐸$^{GR}_{𝐺⁡}$(𝑧 eff =0.555) =0.401 ± 0.005 for CMB lensing combined with CMASS and 𝐸$^{GR}_{𝐺}$⁡(𝑧 eff = 0.316) = 0.452 ± 0.005 combined with LOWZ. We also find 𝐸 𝐺 to be scale independent, with probability to exceed >5%, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Quarknet Project: Simulating Double-Source Plane Lenses and Einstein Rings for Domain Adaptation

Double-Source Plane Lenses (DSPLs) are a form of strong gravitational lensing that can be used to uniquely constrain cosmological parameters like the dark energy equation of state. These objects are exceedingly rare: to date, only four have been discovered in astronomical surveys, like the Sloan Digital Sky Survey and the HyperSuprimeCam Survey. Additionally, the main features of these objects are typically co-located sets of arcs, which look like Einstein Rings of single-source galaxy-galaxy lenses. Larger astronomical surveys typically have low image resolution, which significantly exacerbates issues when trying to find DSPLs. Future surveys are likely to include many more of these objects and have higher image resolution. Traditional methods for finding strong lenses struggle to identify simple galaxy-galaxy lenses. Recently, neural networks have become the standard for lens identification, but these tools have not yet been used to search for DSPLs. In this work, we use the software deeplenstronomy to simulate varied images of DSPLs and Einstein Rings – with and without noise and artifacts of observational surveys, forming a comprehensive benchmark dataset of 40,000 images. We utilise this dataset to perform experiments with convolutional neural networks to discern between the two phenomena. Sofia Grimm and Jerry Zhou are co-first authors on this work.

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LensingETC: A Tool to Optimize Multifilter Imaging Campaigns of Galaxy-scale Strong Lensing Systems

Imaging data is the principal observable required to use galaxy-scale strong lensing in a multitude of applications in extragalactic astrophysics and cosmology. In this paper, we develop Lensing Exposure Time Calculator (LensingETC; to optimize the efficiency of telescope-time usage when planning multifilter imaging campaigns for galaxy-scale strong lenses. This tool simulates realistic data tailored to specified instrument characteristics and then automatically models them to assess the power of the data in constraining lens model parameters. We demonstrate a use case of this tool by optimizing a two-filter observing strategy (in the IR and ultraviolet-visual (UVIS)) within the limited exposure time per system allowed by a Hubble Space Telescope (HST) Snapshot program. We find that higher resolution is more advantageous to gain constraining power on the lensing observables, when there is a trade-off between signal-to-noise ratio and resolution; for example, between the UVIS and IR filters of the HST. We also find that, whereas a point-spread function (PSF) with sub-Nyquist sampling allows the sample mean for a model parameter to be robustly recovered for both galaxy–galaxy and point-source lensing systems, a sub-Nyquist-sampled PSF introduces a larger scatter than a Nyquist-sampled one in the deviation from the ground truth for point-source lens systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Joint Analysis of Small-scale Galaxy Clustering and Galaxy–Galaxy Lensing from BOSS Galaxies

We present a joint analysis of galaxy clustering and galaxy–galaxy lensing measurements from BOSS galaxies using a simulation-based emulation method combined with a halo occupation distribution model. Our emulators are constructed with the Aemulus ν simulations, a suite of wνCDM N-body simulations with massive neutrinos as independent particle species. We combine small-scale analysis of clustering from 0.1 to 60.2 h −1 Mpc and lensing from 1.7 to 60.2 h −1 Mpc to perform cosmological constraints. We split the BOSS galaxies into three redshift bins to measure their clustering and employ galaxies from Dark Energy Camera Legacy Survey and Hyper Suprime-Cam as source galaxies to measure lensing separately. We find that the addition of lensing significantly improves the constraining power on $S_8 = σ_8(Ω_m/0.3)^{0.5}$, with a weak improvement for fσ 8 . Our results of fσ 8 indicate tensions of around 1σ−4σ below the results of the cosmic microwave background observations of Planck. For S 8 , our results are also lower than Planck, and the tension can be mitigated when considering possible systematics in lensing measurement. As a by-product, our analysis prefers a nonzero neutrino mass but without strong significance, with the constraining power dominated by the clustering. Given the accuracy and precision of our model and the observational data, it is anticipated that larger and higher-quality spectroscopic data sets will improve the constraints on this fundamental property in the near future.

Gao, Wenhao [Shanghai Jiao Tong University (China)↗

Discovering Strong Gravitational Lenses in the Dark Energy Survey with Interactive Machine Learning and Crowd-sourced Inspection with Space Warps

We conduct a search for strong gravitational lenses in the Dark Energy Survey (DES) Year 6 imaging data. We implement a pre-trained Vision Transformer (ViT) for our machine learning (ML) architecture and adopt interactive machine learning to construct a training sample with multiple classes to address common types of false positives. Our ML model reduces ∼236 million DES cutout images to 22,564 targets of interest, including ∼85% of previously reported galaxy–galaxy lens candidates discovered in DES. These targets were visually inspected by citizen scientists, who ruled out ∼90% as false positives. Of the remaining 2618 candidates, 149 were expert-classified as “definite” lenses and 516 as “probable” lenses, for a total of 665 systems, with 147 of these candidates being newly identified. Additionally, we trained a second ViT to find double-source plane lens systems, finding at least one double-source system. Our main ViT excels at identifying galaxy–galaxy lenses, consistently assigning high scores to candidates with high expert assessments. The top 800 ViT-scored images include ∼100 of our “definite” lens candidates. This selection is an order of magnitude higher in purity than previous convolutional neural-network-based lens searches and demonstrates the feasibility of applying our methodology for discovering large samples of lenses in future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Finding Multiply Lensed and Binary Quasars in the DESI Legacy Imaging Surveys

The time delay between multiple images of strongly lensed quasars is a powerful tool for measuring the Hubble constant ( H 0 ). To achieve H 0 measurements with higher precision and accuracy using the time delay, it is crucial to expand the sample of lensed quasars. We conduct a search for strongly lensed quasars in the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys. The DESI Legacy Surveys comprise 19,000 deg 2 of the extragalactic sky observed in three optical bands ( g , r , and z ), making it well suited for the discovery of new strongly lensed quasars. We apply an autocorrelation algorithm to ~5 million objects classified as quasars in the DESI Quasar Sample. These systems are visually inspected and ranked. Here, we present 436 new multiply lensed and binary quasar candidates, 65 of which have redshifts from Sloan Digital Sky Survey Data Release 16. We provide redshifts for an additional 18 candidates from the SuperNova Integral Field Spectrograph.

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Strong Lensing Parameter Estimation on Ground-Based Imaging Data Using Simulation-Based Inference

Current ground-based cosmological surveys, such as the Dark Energy Survey (DES), are predicted to discover thousands of galaxy-scale strong lenses, while future surveys, such as the Vera Rubin Observatory Legacy Survey of Space and Time (LSST) will increase that number by 1-2 orders of magnitude. The large number of strong lenses discoverable in future surveys will make strong lensing a highly competitive and complementary cosmic probe. To leverage the increased statistical power of the lenses that will be discovered through upcoming surveys, automated lens analysis techniques are necessary. We present two Simulation-Based Inference (SBI) approaches for lens parameter estimation of galaxy-galaxy lenses. We demonstrate the successful application of Neural Posterior Estimation (NPE) to automate the inference of a 12-parameter lens mass model for DES-like ground-based imaging data. We compare our NPE constraints to a Bayesian Neural Network (BNN) and find that it outperforms the BNN, producing posterior distributions that are for the most part both more accurate and more precise; in particular, several source-light model parameters are systematically biased in the BNN implementation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Domain Adaptation for Measurements of Strong Gravitational Lenses

Upcoming surveys are predicted to discover galaxy-scale strong lenses on the magnitude of 105, making deep learning methods necessary in lensing data analysis. Currently, there is insufficient real lensing data to train deep learning algorithms, but training only on simulated data results in poor performance on real data. Domain adaptation can bridge the gap between simulated and real datasets. We adopt domain adaptation on the estimation of Einstein radius in simulated galaxy-scale gravitational lensing images. We evaluate two domain adaptation techniques - domain adversarial neural networks (DANN) and maximum mean discrepancy (MMD). We train on a source domain of simulated lenses and apply it to a target domain with emulation of DES survey conditions. We show that both domain adaptation techniques can significantly improve the model performance on the more complex target domain datasets. Our results show the potential of using domain adaptation to perform analysis on future survey data with a deep neural network trained on simulated data.

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Population-level Dark Energy Constraints from Strong Gravitational Lensing using Simulation-Based Inference

In this work, we present a scalable approach for inferring the dark energy equation-of-state parameter ($w$) from a population of strong gravitational lens images using Simulation-Based Inference (SBI). Strong gravitational lensing offers crucial insights into cosmology, but traditional Monte Carlo methods for cosmological inference are computationally prohibitive and inadequate for processing the thousands of lenses anticipated from future cosmic surveys. New tools for inference, such as SBI using Neural Ratio Estimation (NRE), address this challenge effectively. By training a machine learning model on simulated data of strong lenses, we can learn the likelihood-to-evidence ratio for robust inference. Our scalable approach enables more constrained population-level inference of $w$ compared to individual lens analysis, constraining $w$ to within $1\sigma$. Our model can be used to provide cosmological constraints from forthcoming strong lens surveys, such as the 4MOST Strong Lensing Spectroscopic Legacy Survey (4SLSLS), which is expected to observe 10,000 strong lenses.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Population-level Dark Energy Constraints from Strong Gravitational Lensing using Simulation-Based Inference

In this work, we present a scalable approach for inferring the dark energy equation-of-state parameter ($w$) from a population of strong gravitational lens images using Simulation-Based Inference (SBI). Strong gravitational lensing offers crucial insights into cosmology, but traditional Monte Carlo methods for cosmological inference are computationally prohibitive and inadequate for processing the thousands of lenses anticipated from future cosmic surveys. New tools for inference, such as SBI using Neural Ratio Estimation (NRE), address this challenge effectively. By training a machine learning model on simulated data of strong lenses, we can learn the likelihood-to-evidence ratio for robust inference. Our scalable approach enables more constrained population-level inference of $w$ compared to individual lens analysis, constraining $w$ to within 1$\sigma$. Our model can be used to provide cosmological constraints from forthcoming strong lens surveys, such as the 4MOST Strong Lensing Spectroscopic Legacy Survey (4SLSLS), which is expected to observe 10,000 strong lenses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A DECADE of dwarfs: first detection of weak lensing around spectroscopically confirmed low-mass galaxies

We present the first detection of weak gravitational lensing around spectroscopically confirmed dwarf galaxies, using the large overlap between DESI DR1 spectroscopic data and DECADE/DES weak lensing catalogs. A clean dwarf galaxy sample with well-defined redshift and stellar mass cuts enables excess surface mass density measurements in two stellar mass bins ($\log \rm{M}_*=[8.2, 9.2]~M_\odot$ and $\log \rm{M}_*=[9.2, 10.2]~M_\odot$), with signal-to-noise ratios of $5.6$ and $12.4$ respectively. This signal-to-noise drops to $4.5$ and $9.2$ respectively for measurements without applying individual inverse probability (IIP) weights, which mitigates fiber incompleteness from DESI's targeting. The measurements are robust against variations in stellar mass estimates, photometric shredding, and lensing calibration systematics. Using a simulation-based modeling framework with stellar mass function priors, we constrain the stellar mass-halo mass relation and find a satellite fraction of $\simeq 0.3$, which is higher than previous photometric studies but $1.5σ$ lower than $Λ$CDM predictions. We find that IIP weights have a significant impact on lensing measurements and can change the inferred $f_{\rm{sat}}$ by a factor of two, highlighting the need for accurate fiber incompleteness corrections for dwarf galaxy samples. Our results open a new observational window into the galaxy-halo connection at low masses, showing that future massively multiplexed spectroscopic observations and weak lensing data will enable stringent tests of galaxy formation models and $Λ$CDM predictions.

To, Chun-Hao [Chicago U., Astron. Astrophys. Ctr.;↗

Strong Lensing Cosmology with Population-level Calibrated Neural Ratio Estimation

Strong gravitational lensing contains key information about cosmic acceleration. Modern and next-generation galaxy imaging surveys are expected to provide high-quality data on $\mathcal{O}(10^5)$ galaxy-galaxy lensing systems. The plethora and complexity of the data are likely to present computational challenges for parameter inference methods for fitting high-dimensional likelihoods, which are often analytically intractable. Neural Ratio Estimation (NRE) efficiently computes individual likelihood ratios that can be combined into population-level posteriors. We use simulations to study the capacity of NRE to jointly predict the dark energy equation-of-state parameter $w$ and the total matter density $Ω_{m}$ from lensing images and companion spectroscopic information. We also introduce a post hoc posterior coverage calibration procedure that mitigates the model overconfidence that is typically found in neural density estimation applications. Our experiments show that the errors on both parameters decrease with increasing inference population sizes. In particular, for 100 lenses in a standard $Λ$CDM Universe, our calibrated NRE model achieves median fractional uncertainty of $22.8\%$ in $w$ and $2.9\%$ in $Ω_{m}$. This proof of concept demonstrates a potentially scalable approach for efficient cosmological parameter inference with large populations of galaxy-scale lenses observed in future surveys.

Jarugula, Sreevani [Fermilab] (ORCID:0000000253867↗

Cosmology from Planck CMB lensing and DESI DR1 quasar tomography

We present a measurement of the amplitude of matter fluctuations over the redshift range 0.8 ≤ z ≤ 3.5 from the cross correlation of over 1.2 million spectroscopic quasars selected by the Dark Energy Spectroscopic Instrument (DESI) across 7,200 deg 2 (∼ 170 quasars/deg 2 ) and Planck PR4 (NPIPE) cosmic microwave background (CMB) lensing maps. We perform a tomographic measurement in three bins centered at effective redshiftsz=1.44, 2.27 and 2.75, which have ample overlap with the CMB lensing kernel. From a joint fit using the angular clustering of all three redshift bins (auto and cross-spectra), and including an Q m prior from DESI DR1 baryon acoustic oscillations to break the $Ω_{m}-σ_{8}$ degeneracy, we constrain the amplitude of matter fluctuations in the matter-dominated regime to be $σ_{8}=0.929^{+0.059}_{-0.074}$ and $S_{8}≡σ_{8}(Ω_m/0.3)^{0.5} = 0.922^{+0.059}_{-0.073}$. We provide a growth of structure measurement with the largest spectroscopic quasar sample to date at high redshift, which is ∼ 1.5σ higher than predictions from ΛCDM fits to measurements of the primary CMB from Planck PR4. The cross-correlation between PR4 lensing maps and DESI DR1 quasars is detected with a signal-to-noise ratio of 21.7 and the quasar auto-correlation at 27.2 for the joint analysis of all redshift bins. We combine our measurement with the CMB lensing auto-spectrum from the ground-based Atacama Cosmology Telescope (ACT DR6) and Planck PR4 to perform a sound-horizon-free measurement of the Hubble constant, yielding $H_{0}=69.1^{+2.2}_{-2.6} {\rm \ km\ s}^{-1}{\rm Mpc}^{-1}$ through its sensitivity to the matter-radiation equality scale.

baryon acoustic oscillations↗

Dark energy survey year 3 results: likelihood-free, simulation-based w CDM inference with neural compression of weak-lensing map statistics

We present simulation-based cosmological wcold dark matter (wCDM) inference using dark energy survey year 3 weak-lensing maps, via neural data compression of weak-lensing map summary statistics: power spectra, peak counts, and direct map-level compression/inference with convolutional neural networks (CNN). Using simulation-based inference, also known as likelihood-free or implicit inference, we use forward-modelled mock data to estimate posterior probability distributions of unknown parameters. This approach allows all statistical assumptions and uncertainties to be propagated through the forward-modelled mock data; these include sky masks, non-Gaussian shape noise, shape measurement bias, source galaxy clustering, photometric redshift uncertainty, intrinsic galaxy alignments, non-Gaussian density fields, neutrinos, and non-linear summary statistics. We include a series of tests to validate our inference results. This paper also describes the Gower Street simulation suite: 791 full-sky pkdgrav3 dark matter simulations, with cosmological model parameters sampled with a mixed active-learning strategy, from which we construct over 3000 mock dark energy survey lensing data sets. For wCDM inference, for which we allow –1 < w < –$\frac{1}{3}$⁠, our most constraining result uses power spectra combined with map-level (CNN) inference. Using gravitational lensing data only, this map-level combination gives Ω m = 0.283$^{+0.020}_{–0.027}$⁠, S 8 = 0.804$^{+0.025}_{–0.017⁠}$, and w < –0.80 (with a 68 per cent credible interval); compared to the power spectrum inference, this is more than a factor of two improvement in dark energy parameter (Ω⁠ DE , w⁠) precision.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey Year 6 results: cell-based coadds and METADETECTION weak lensing shape catalogue

We present the metadetection weak lensing galaxy shape catalogue from the 6-yr Dark Energy Survey (DES Y6) imaging data. This data set is the final release from DES, spanning 4422 deg 2 of the southern sky. We describe how the catalogue was constructed, including the two new major processing steps, cell-based image coaddition, and shear measurements with metadetection. The DES Y6 M etadetection weak lensing shape catalogue consists of 151 922 791 galaxies detected over riz bands, with an effective number density of n eff = 8.22 galaxies per arcmin 2 and shape noise of σ e = 0.29. We carry out a suite of validation tests on the catalogue, including testing for point spread function (PSF) leakage, testing for the impact of PSF modelling errors, and testing the correlation of the shear measurements with galaxy, PSF, and survey properties. In addition to demonstrating that our catalogue is robust for weak lensing science, we use the DES Y6 image simulation suite to estimate the overall multiplicative shear bias of our shear measurement pipeline. We find no detectable multiplicative bias at the roughly half-per cent level, with m = (3.4 ± 6.1) x 10 –3 , at 3σ uncertainty. This is the first time both cell-based coaddition and Metadetection algorithms are applied to observational data, paving the way to the Stage-IV weak lensing surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Systematic Effects in Galaxy-Galaxy Lensing with DESI

The Dark Energy Spectroscopic Instrument (DESI) survey will measure spectroscopic redshifts for millions of galaxies across roughly $14,000 \, \mathrm{deg}^2$ of the sky. Cross-correlating targets in the DESI survey with complementary imaging surveys allows us to measure and analyze shear distortions caused by gravitational lensing in unprecedented detail. In this work, we analyze a series of mock catalogs with ray-traced gravitational lensing and increasing sophistication to estimate systematic effects on galaxy-galaxy lensing estimators such as the tangential shear $\gamma_{\mathrm{t}}$ and the excess surface density $\Delta\Sigma$ . We employ mock catalogs tailored to the specific imaging surveys overlapping with the DESI survey: the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) survey, and the Kilo-Degree Survey (KiDS). Among others, we find that fiber incompleteness can have significant effects on galaxy-galaxy lensing estimators but can be corrected effectively by up-weighting DESI targets with fibers by the inverse of the fiber assignment probability. Similarly, we show that intrinsic alignment and lens magnification are expected to be statistically significant given the precision forecasted for the DESI year-1 data set. Our study informs several analysis choices for upcoming cross-correlation studies of DESI with DES, HSC, and KiDS.

79 ASTRONOMY AND ASTROPHYSICS↗

Weak Gravitational Lensing around Low Surface Brightness Galaxies in the DES Year 3 Data

We present galaxy-galaxy lensing measurements using a sample of low surface brightness galaxies (LSBGs) drawn from the Dark Energy Survey Year 3 (Y3) data as lenses. LSBGs are diffuse galaxies with a surface brightness dimmer than the ambient night sky. These dark-matter-dominated objects are intriguing due to potentially unusual formation channels that lead to their diffuse stellar component. Given the faintness of LSBGs, using standard observational techniques to characterize their total masses proves challenging. Weak gravitational lensing, which is less sensitive to the stellar component of galaxies, could be a promising avenue to estimate the masses of LSBGs. Our LSBG sample consists of 23,790 galaxies separated into red and blue color types at g - i ≥ 0.60 and g - i < 0.60 , respectively. Combined with the DES Y3 shear catalog, we measure the tangential shear around these LSBGs and find signal-to-noise ratios of 6.67 for the red sample, 2.17 for the blue sample, and 5.30 for the full sample. We use the clustering redshifts method to obtain redshift distributions for the red and blue LSBG samples. Assuming all red LSBGs are satellites, we fit a simple model to the measurements and estimate the host halo mass of these LSBGs to be log(M host /M ⊙ ) = $12.98^{+0.10}_{-0.11}$. We place a 95% upper bound on the subhalo mass at log(M sub /M ⊙ ) < 11.51. By contrast, we assume the blue LSBGs are centrals, and place a 95% upper bound on the halo mass at log(M host /M ⊙ ) < 11.84. We find that the stellar-to-halo mass ratio of the LSBG samples is consistent with that of the general galaxy population. This work illustrates the viability of using weak gravitational lensing to constrain the halo masses of LSBGs.

79 ASTRONOMY AND ASTROPHYSICS↗

The z ∼ 1.03 Merging Cluster SPT-CL J0356–5337: New Strong Lensing Analysis with HST and MUSE

We present a strong lensing analysis and reconstruct the mass distribution of SPT-CL J0356−5337, a galaxy cluster at redshift z = 1.034. Our model supersedes previous models by making use of new multiband Hubble Space Telescope data and Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy. We identify two additional lensed galaxies to inform a more well-constrained model using 12 sets of multiple images in five separate lensed sources. The three previously known sources were spectroscopically confirmed by G. Mahler et al. at redshifts of z = 2.363, z = 2.364, and z = 3.048. We measured the spectroscopic redshifts of two of the newly discovered arcs using MUSE data, at z = 3.0205 and z = 5.3288. We increase the number of cluster member galaxies by a factor of 3 compared to previous work. We also report the detection of extended Lyα emission from several background galaxies. We measure the total projected mass density of the two major subcluster components, one dominated by the brightest cluster galaxy and the other by a compact group of luminous red galaxies. We find ${M}_{{\rm{B}}{\rm{C}}{\rm{G}}}(\lt 80\,\rm{kpc})=3.9{3}_{-0.14}^{+0.21}\times 1{0}^{13}$ M⊙ and ${M}_{{\rm{LRG}}}(\lt 80\,\rm{kpc})=2.9{2}_{-0.23}^{+0.16}\times 1{0}^{13}$ M⊙, yielding a mass ratio of $1.3{5}_{-0.08}^{+0.16}$ . The strong lensing constraints offer a robust estimate of the projected mass density regardless of modeling assumptions; allowing more substructure in this line of sight does not change the results or conclusions. Our results corroborate the conclusion that SPT-CL J0356−5337 is dominated by two mass components and is likely undergoing a major merger on the plane of the sky.

79 ASTRONOMY AND ASTROPHYSICS↗