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DOE OSTI2022

COOL-LAMPS. II. Characterizing the Size and Star Formation History of a Bright Strongly Lensed Early-type Galaxy at Redshift 1.02

We present COOL J1323+0343, an early-type galaxy at z = 1.0153 ± 0.0006, strongly lensed by a cluster of galaxies at z = 0.353 ± 0.001. This object was originally imaged by DECaLS and noted as a gravitational lens by COOL-LAMPS, a collaboration initiated to find strong-lensing systems in recent public optical imaging data, and confirmed with follow-up data. With ground-based grzH imaging and optical spectroscopy from the Las Campanas Observatory and the Nordic Optical Telescope, we derive a stellar mass, metallicity, and star formation history from stellar-population synthesis modeling. The lens modeling implies a total magnification, summed over the three images in the arc, of μ ~ 113. The stellar mass in the source plane is M * ~ 10.64 M ⊙ and the 1σ upper limit on the star formation rate (SFR) in the source plane is SFR ~ 3.75 × 10 -2 M ⊙ yr -1 (log sSFR = -12.1 yr -1 ) in the youngest two age bins (0–100 Myr), closest to the epoch of observation. Our measurements place COOL J1323+0343 below the characteristic mass of the stellar mass function, making it an especially compelling target that could help clarify how intermediate-mass quiescent galaxies evolve. We reconstruct COOL J1323+0343 in the source plane and fit its light profile. This object is below the expected size evolution of an early-type galaxy at this mass with an effective radius r e ~ 0.5 kpc. This extraordinarily magnified and bright lensed early-type galaxy offers an exciting opportunity to study the morphology and star formation history of an intermediate-mass early-type galaxy in detail at z ~ 1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

A Natural ≳100× Telescope: Discovery of the Strongly Lensed Type II SN 2025mkn at z = 1.37

We present the discovery of SN 2025mkn, a gravitationally lensed Type II supernova. First detected as a blue transient in Zwicky Transient Facility (ZTF), 0. "83 from a z = 0.42 elliptical galaxy, the follow-up SNIFS/UH2.2 m and LRIS/Keck spectra revealed absorption lines at z = 1.371. Later JWST NIRCam imaging shows that the bright transient is a close pair of point sources separated by 0. "07, and a 30 times fainter counterimage opposite the lens, for which NIRSpec reveals strong Hα emission also at z = 1.371. The lightcurves and spectra are consistent with the Type II supernova source being magnified ≳100 times, with ∼250 required to reconcile its luminosity with that of nearby events such as SN 2023ixf. Lens models are consistent with such high magnifications, and always show that the faint image arrived first (undetected in earlier ZTF imaging), consistent with the later spectral phase of this fainter image. A fourth image is also predicted and possibly detected in the NIRSpec data. Lightcurve-based time-delay measurements are not possible due to the first image being the faintest; however, the resolved NIRSpec spectra offer a future opportunity for time-delay cosmography through supernova phase measurements.

Strong gravitational lensing↗
DOE OSTI2023

LensWatch. I. Resolved HST Observations and Constraints on the Strongly Lensed Type Ia Supernova 2022qmx (“SN Zwicky”)

Supernovae (SNe) that have been multiply imaged by gravitational lensing are rare and powerful probes for cosmology. Each detection is an opportunity to develop the critical tools and methodologies needed as the sample of lensed SNe increases by orders of magnitude with the upcoming Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope. The latest such discovery is of the quadruply imaged Type Ia SN 2022qmx (aka, "SN Zwicky") at z = 0.3544. SN Zwicky was discovered by the Zwicky Transient Facility in spatially unresolved data. Here we present follow-up Hubble Space Telescope observations of SN Zwicky, the first from the multicycle "LensWatch (www.lenswatch.org)" program. We measure photometry for each of the four images of SN Zwicky, which are resolved in three WFC3/UVIS filters (F475W, F625W, and F814W) but unresolved with WFC3/IR F160W, and present an analysis of the lensing system using a variety of independent lens modeling methods. We find consistency between lens-model-predicted time delays (≲1 day), and delays estimated with the single epoch of Hubble Space Telescope colors (≲3.5 days), including the uncertainty from chromatic microlensing (~1–1.5 days). Our lens models converge to an Einstein radius of ${\theta }_{{\rm{E}}}=({0.168}_{-0.005}^{+0.009})^{\prime\prime} $, the smallest yet seen in a lensed SN system. The "standard candle" nature of SN Zwicky provides magnification estimates independent of the lens modeling that are brighter than predicted by $\sim {1.7}_{-0.6}^{+0.8}$ mag and $\sim {0.9}_{-0.6}^{+0.8}$ mag for two of the four images, suggesting significant microlensing and/or additional substructure beyond the flexibility of our image-position mass models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Self-interacting Dark Matter, Core Collapse, and the Galaxy–Galaxy Strong-lensing Discrepancy

Abstract Gravitational lensing by galaxy clusters has emerged as a powerful tool to probe the standard cold dark matter (CDM) paradigm of structure formation in the Universe. Despite the remarkable explanatory power of CDM on large scales, tensions with observations on small scales have been reported. Recent studies find that the observational cross section for galaxy–galaxy strong lensing (GGSL) in clusters exceeds the CDM prediction by more than an order of magnitude and persists even after rigorous examination of various possible systematics. We investigate the impact of modifying the internal structure of cluster dark matter subhalos on GGSL and report that altering the inner density profile, given by r γ , to steeper slopes with γ > 2.5 can alleviate the GGSL discrepancy. This is steeper than slopes obtained with the inclusion of the contribution of baryons to the inner regions of these subhalos. Deviating from the γ ~ 1.0 cusps that CDM predicts, these steeper slopes could arise in models of self-interacting dark matter undergoing core collapse. Our results motivate additional study of subhalo core collapse in dense cluster environments.

Dutra, Isaque (ORCID:0000000170404930)↗
DOE OSTI2022

The Dark Energy Survey Bright Arcs Survey: Candidate Strongly Lensed Galaxy Systems from the Dark Energy Survey 5000 Square Degree Footprint

We report the combined results of eight searches for strong gravitational lens systems in the full 5000 square degrees of Dark Energy Survey (DES) observations. The observations accumulated by the end of the third observing season fully covered the DES footprint in five filters (grizY), with an i-band limiting magnitude (at 10σ) of 23.44. In four searches, a list of potential candidates was identified using a color and magnitude selection from the object catalogs created from the first three observing seasons. Three other searches were conducted at the locations of previously identified galaxy clusters. Cutout images of potential candidates were then visually scanned using an object viewer. An additional set of candidates came from a data-quality check of a subset of the color–coadd tiles created from the full DES six-season data set. A short list of the most promising strong-lens candidates was then numerically ranked according to whether or not we judged them to be bona fide strong gravitational lens systems. These searches discovered a diverse set of 247 strong-lens candidate systems, of which 81 are identified for the first time. We provide the coordinates, magnitudes, and photometric properties of the lens and source objects, and an estimate of the Einstein radius for 81 new systems and 166 previously reported systems. This catalog will be of use for selecting interesting systems for detailed follow up, studies of galaxy cluster and group mass profiles, as well as a training/validation set for automated strong-lens searches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Large-scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant

We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time delay gravitational lenses for Hubble constant (H 0 ) determination. Here, our BNN was trained on synthetic Hubble Space Telescope quality images of strongly lensed active galactic nuclei with lens galaxy light included. The BNN can accurately characterize the posterior probability density functions (PDFs) of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into an ensemble H 0 inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of 9.3% per lens in the inferred H 0 . A simple combination of a set of 200 test lenses results in a precision of 0.5 km s –1 Mpc –1 (0.7%), with no detectable bias in this H 0 recovery test. The computation time for the entire pipeline—including the generation of the training set, BNN training and H0 inference—translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for H 0 inference.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

DESI-253.2534+26.8843: A New Einstein Cross Spectroscopically Confirmed with Very Large Telescope/MUSE and Modeled with GIGA-Lens

Gravitational lensing provides unique insights into astrophysics and cosmology, including the determination of galaxy mass profiles and constraining cosmological parameters. We present spectroscopic confirmation and lens modeling of the strong lensing system DESI-253.2534+26.8843, discovered in the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys data. This system consists of a massive elliptical galaxy surrounded by four blue images forming an Einstein Cross pattern. We obtained spectroscopic observations of this system using the Multi Unit Spectroscopic Explorer on ESO's Very Large Telescope and confirmed its lensing nature. The main lens, which is the elliptical galaxy, has a redshift of z L1 = 0.636 ± 0.001, while the spectra of the background source images are typical of a starburst galaxy and have a redshift of z s = 2.597 ± 0.001. Additionally, we identified a faint galaxy foreground of one of the lensed images, with a redshift of z L2 = 0.386. We employed the GIGA-Lens modeling code to characterize this system and determined the Einstein radius of the main lens to be ${\theta }_{{\rm{E}}}=2\buildrel{\prime\prime}\over{.} {520}_{-0.031}^{+0.032}$, which corresponds to a velocity dispersion of σ = 379 ± 2 km s –1 . Our study contributes to a growing catalog of this rare kind of strong lensing system and demonstrates the effectiveness of spectroscopic integral field unit observations and advanced modeling techniques in understanding the properties of these systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

COOL–LAMPS. III. Discovery of a 25."9 Separation Quasar Lensed by a Merging Galaxy Cluster*

In the third paper from the COOL–LAMPS Collaboration, we report the discovery of COOL J0542-2125, a gravitationally lensed quasar at z = 1.84, observed as three images due to an intervening massive galaxy cluster at z = 0.61. The lensed quasar images were identified in a search for lens systems in recent public optical imaging data and have separations on the sky up to 25farcs9, wider than any previously known lensed quasar. The galaxy cluster acting as a strong lens appears to be in the process of merging, with two subclusters separated by ~1 Mpc in the plane of the sky, and their central galaxies showing a radial velocity difference of ~1000 km s-1. Both cluster cores show strongly lensed images of an assortment of background sources, as does the region between them. A preliminary strong lens model implies masses of $M_{<250kpc} = 1.79^{+0.16}_{-0.01}$ x $10^{14} M_⊙$ and $M_{<250kpc} = 1.48^{+0.04}_{-0.10}$ x $10^{14} M_⊙$ for the east and west subclusters, respectively. This line of sight is also coincident with an ROSAT ALL-sky Survey source, centered between the two confirmed cluster halos reminiscent of other major cluster-scale mergers. Archival and new follow-up imaging show flux variability in the quasar images of up to 0.4 mag within ~1 yr, and new multicolor imaging data reveal a 2σ detection of the underlying quasar host. A lens system with this configuration offers rare opportunities for a range of future studies of both the lensed quasar and its host and the foreground cluster merger causing the lensing.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Be It Unresolved: Measuring Time Delays from Lensed Supernovae

Gravitationally lensed Type Ia supernovae (SNe Ia) may be the next frontier in cosmic probes, able to deliver independent constraints on dark energy, spatial curvature, and the Hubble constant. Measurements of time delays between the multiple images become more incisive due to the standardized candle nature of the source, monitoring for months rather than years, and partial immunity to microlensing. While currently extremely rare, hundreds of such systems should be detected by upcoming time domain surveys. Others will have the images spatially unresolved, with the observed lightcurve a superposition of time-delayed image fluxes. We investigate whether unresolved images can be recognized as lensed sources given only lightcurve information, and whether time delays can be extracted robustly. We develop a method that we show can identify these systems for the case of lensed SNe Ia with two images and time delays exceeding ten days. When tested on such an ensemble, without microlensing, the method achieves a false-positive rate of ≲5%, and measures the time delays with a completeness of ≳93% and with a bias of ≲0.5% for Δt fit ≳ 10 days. Since the method does not assume a template of any particular type of SN, the method has the (untested) potential to work on other types of lensed SNe systems and possibly on other transients as well.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Efficient Mass Estimate at the Core of Strong Lensing Galaxy Clusters Using the Einstein Radius

In the era of large surveys, yielding thousands of galaxy clusters, efficient mass proxies at all scales are necessary in order to fully utilize clusters as cosmological probes. At the cores of strong lensing clusters, the Einstein radius can be turned into a mass estimate. This efficient method has been routinely used in literature, in lieu of detailed mass models; however, its scatter, assumed to be similar to 30%, has not yet been quantified. Here, we assess this method by testing it against ray-traced images of cluster-scale halos from the Outer RimN-body cosmological simulation. We measure a scatter of 13.9% and a positive bias of 8.8% in M (<θ E ), with no systematic correlation with total cluster mass, concentration, or lens or source redshifts. We find that increased deviation from spherical symmetry increases the scatter; conversely, where the lens produces arcs that cover a large fraction of its Einstein circle, both the scatter and the bias decrease. While spectroscopic redshifts of the lensed sources are critical for accurate magnifications and time delays, we show that for the purpose of estimating the total enclosed mass, the scatter introduced by source redshift uncertainty is negligible compared to other sources of error. Finally, we derive and apply an empirical correction that eliminates the bias, and reduces the scatter to 10.1% without introducing new correlations with mass, redshifts, or concentration. Our analysis provides the first quantitative assessment of the uncertainties in M (<θ E ), and enables its effective use as a core mass estimator of strong lensing galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

High- z Universe probed via Lensing by QSOs (HULQ)

Galaxies and their central supermassive black holes are known to coevolve, but the physical background for this is unknown as of yet. The High-z Universe probed via Lensing by QSOs (HULQ) project aims to investigate this coevolution by using quasi-stellar object (QSO) host galaxies acting as gravitational lenses (QSO lenses). We present the results of the spectroscopic observation of the first QSO lens candidate from the HULQ project, HULQ J0002+0239, which consists of a QSO host galaxy at z d = 1.455 and four seemingly lensed objects in a cross-like configuration. Deep optical spectra of two of the possibly lensed objects with z ~ 24.5 mag were obtained with the Gemini Multi-Object Spectrograph on the Gemini North Telescope. Their spectra reveal that the objects are newly discovered galaxies at z = 0.29 and z = 1.11, and we conclude that HULQ J0002+0239 is not a QSO lens. Our QSO lens search results are so far in agreement with the predicted number of QSO lenses, and we discuss how the future investigation of additional QSO lens candidates could tell us more about the evolution of the black hole mass and host galaxy scaling relations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

On the detectability of strong lensing in near-infrared surveys

We present new lensing frequency estimates for existing and forthcoming deep near-infrared surveys, including those from JWST and VISTA. The estimates are based on the JAdes extragalactic Ultradeep Artificial Realisations (JAGUAR) galaxy catalogue accounting for the full photometry and morphologies for each galaxy. Due to the limited area of the JAGUAR simulations, they are less suited to wide-area surveys; however, we also present extrapolations to the surveys carried out by Euclid and the Nancy Grace Roman Space Telescope. The methodology does not make assumptions about the nature of the lens itself and probes a wide range of lens masses. The lenses and sources are selected from the same catalogue and extend the analysis from the visible bands into the near-infrared. After generating realistic simulated lensed sources and selecting those that are detectable with SNR > 20, we verify the lensing frequency expectations against published lens samples selected in the visible, finding them to be broadly consistent. We find that JWST could yield ~65 lensed systems in COSMOS-Web, of which ~25 per cent have source redshifts >4. Deeper, narrower programs (e.g. JADES-Medium) will probe more typical source galaxies (in flux and mass) but will find fewer systems (~25). Of the surveys we investigate, we find 55–80 per cent have detectable multiple imaging. Forthcoming NIR surveys will likely reveal new and diverse strong lens systems including lensed sources that are at higher redshift (JWST) and dustier, more massive and older (Euclid NISP) than those typically detected in the corresponding visible surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Core Mass Estimates in Strong Lensing Galaxy Clusters Using a Single-halo Lens Model

The core mass of galaxy clusters is an important probe of structure formation. Here we evaluate the use of a single-halo model (SHM) as an efficient method to estimate the strong lensing cluster core mass, testing it with ray-traced images from the Outer Rim simulation. Unlike detailed lens models, the SHM represents the cluster mass distribution with a single halo and can be automatically generated from the measured lensing constraints. In this work we find that the projected core mass estimated with this method, $M_{\text{SHM}}$, has a scatter of 8.52% and a bias of 0.90% compared to the "true" mass within the same aperture. Our analysis shows no systematic correlation between the scatter or bias and the lens-source system properties. The bias and scatter can be reduced to 3.26% and 0.34%, respectively, by excluding models that fail a visual inspection test. We find that the SHM success depends on the lensing geometry, with single giant arc configurations accounting for most of the failed cases due to their limiting constraining power. When excluding such cases, we measure a scatter and bias of 3.88% and 0.84%, respectively. Finally, we find that when the source redshift is unknown, the model-predicted redshifts are overestimated, and the $M_{\text{SHM}}$ is underestimated by a few percent, highlighting the importance of securing spectroscopic redshifts of background sources. Our analysis provides a quantitative characterization of $M_{\text{SHM}}$, enabling its efficient use as a tool to estimate the strong lensing cluster core masses in the large samples, expected from current and future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Core Mass Estimates in Strong Lensing Galaxy Clusters: A Comparison between Masses Obtained from Detailed Lens Models, Single-halo Lens Models, and Einstein Radii

The core mass of galaxy clusters is both an important anchor of the radial mass distribution profile and probe of structure formation. With thousands of strong lensing galaxy clusters being discovered by current and upcoming surveys, timely, efficient, and accurate core mass estimates are needed. Here, we assess the results of two efficient methods to estimate the core mass of strong lensing clusters: the mass enclosed by the Einstein radius (M(<θ E ) where θ E is approximated from arc positions; Remolina González et al. 2020), and single-halo lens model (M SHM ; Remolina González et al. 2021), against measurements from publicly available detailed lens models (M DLM ) of the same clusters. We use data from the Sloan Giant Arc Survey, the Reionization Lensing Cluster Survey, the Hubble Frontier Fields, and the Cluster Lensing and Supernova Survey with Hubble. We find a scatter of 18.2% (8.2%) with a bias of -7.1% (1.0%) between M corr (<θ arcs ) (M SHM ) and M DLM . Last, we compare the statistical uncertainties measured in this work to those from simulations. This work demonstrates the successful application of these methods to observational data. As the effort to efficiently model the mass distribution of strong lensing galaxy clusters continues, we need fast, reliable methods to advance the field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Discovering strongly lensed quasar candidates with catalogue-based methods from DESI Legacy Surveys

The Hubble tension, revealed by a ~5σ discrepancy between measurements of the Hubble-Lemaitre constant among observations of the early and local Universe, is one of the most significant problems in modern cosmology. In order to better understand the origin of this mismatch, independent techniques to measure H 0 , such as strong lensing time delays, are required. Notably, the sample size of such systems is key to minimising the statistical uncertainties and cosmic variance, which can be improved by exploring the datasets of large-scale sky surveys such as Dark Energy Spectroscopic Instrument (DESI). We identify possible strong lensing time-delay systems within DESI by selecting candidate multiply imaged lensed quasars from a catalogue of 24 440 816 candidate QSOs contained in the ninth data release of the DESI Legacy Imaging Surveys (DESI-LS). Using a friend-of-friends-like algorithm on spatial co-ordinates, our method generates an initial list of compact quasar groups. This list is subsequently filtered using a measure of the similarity of colours among a group’s members and the likelihood that they are quasars. A visual inspection finally selects candidate strong lensing systems based on the spatial configuration of the group members. We identified 620 new candidate multiply imaged lensed quasars (101 grade-A, 214 grade-B, 305 grade-C). This number excludes 53 known spectroscopically confirmed systems and existing candidate systems identified in other similar catalogues. When available, these new candidates will be further checked by combining the spectroscopic and photometric data from DESI.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Effects of Subhalos on Interpreting Highly Magnified Sources Near Lensing Caustics

Large magnification factors near gravitational lensing caustics of galaxy-cluster lenses allow the study of individual stars or compact stellar associations at cosmological distances. We study how the presence of sub-galactic subhalos, an inevitable consequence of cold dark matter, can alter the property of caustics and hence change the interpretation of highly magnified sources that lie atop them. First, we consider a galaxy-cluster halo populated with subhalos sampled from a realistic subhalo mass function calibrated to N-body simulations. Then, we compare a semianalytical approximation and an adaptive ray-shooting method that we employ to quantify the property of the caustics. As a case study, we investigate Earendel, a z = 6.2 candidate of magnified single- or multiple-star system with a lone lensed image atop the critical curve in the Sunrise Arc. We find that the source size constraint (≲0.3 pc) previously derived from macrolens models should be relaxed by a factor of a few to 10 when subhalos are accounted for, therefore allowing the possibility of a compact star cluster. The subhalos could introduce an astrometric perturbation that is ≲0$^{"}_{.}$5, which does not contradict observation. These conclusions are largely robust to changes in the subhalo population. Subhalos therefore should be seriously accounted for when interpreting the astrophysical nature of similar highly magnified sources uncovered in recent high-z observations.

Caustic curve↗
DOE OSTI2024

Detectability of Supermassive Dark Stars with the Roman Space Telescope

Abstract Supermassive dark stars (SMDS) are luminous stellar objects formed in the early Universe at redshift z ∼ 10–20, made primarily of hydrogen and helium, yet powered by dark matter. We examine the capabilities of the Roman Space Telescope (RST), and find it able to identify ∼10 6 M ⊙ SMDSs at redshifts up to z ≃ 14. With a gravitational lensing factor of μ ∼ 100, RST could identify SMDS as small as ∼10 4 M ⊙ at z ∼ 12 with ∼10 6 s exposure. Differentiating SMDSs from early galaxies containing zero metallicity stars at similar redshifts requires spectral, photometric, and morphological comparisons. With only RST, the differentiation of SMDS, particularly those formed via adiabatic contraction with M ≳ 10 5 M ⊙ and lensed by μ ≳ 100, is possible due to their distinct photometric signatures from the first galaxies. Those formed via dark matter capture can be differentiated only by image morphology: i.e., point object (SMDSs) versus extended object (sufficiently magnified galaxies). By additionally employing James Webb Space Telescope (JWST) spectroscopy, we can identify the He ii λ 1640 absorption line, a smoking gun for SMDS detection. Although RST does not cover the required wavelength band (for z emi ≳ 10), JWST does; hence, the two can be used in tandem to identify SMDS. The detection of SMDS would confirm a new type of star powered by dark matter and may shed light on the origins of the supermassive black holes powering bright quasars observed at z ≳ 6.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

TDCOSMO. XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy

Strong-lensing time delays enable measurement of the Hubble constant ($H_{0}$) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the $H_0$ measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131$-$1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate $H_0$, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy $D_{\rm d} = 865_{-81}^{+85}$ Mpc and the time-delay distance $D_{\Delta t} = 2180_{-271}^{+472}$ Mpc, giving $H_0 = 77.1_{-7.1}^{+7.3}$ km s$^{-1}$ Mpc$^{-1}$ - for a flat $\Lambda$ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and the line-of-sight effects, and those related to the mass-anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ($H_0 = 78.3^{+3.4}_{-3.3}$ km s$^{-1}$ Mpc$^{-1}$) and for seven lenses ($H_0 = 74.2_{-1.6}^{+1.6}$ km s$^{-1}$ Mpc$^{-1}$), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ($H_0 = 73.3^{+5.8}_{-5.8}$ km s$^{-1}$ Mpc$^{-1}$). This agreement corroborates the methodology of time-delay cosmography.

79 ASTRONOMY AND ASTROPHYSICS↗