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DOE OSTI2023

Retrospective Search for Strongly Lensed Supernovae in the DESI Legacy Imaging Surveys

The introduction of deep wide-field surveys in recent years and the adoption of machine-learning techniques have led to the discoveries of $\mathcal{O}$(10 4 ) strong gravitational lensing systems and candidates. However, the discovery of multiply-lensed transients remains a rarity. Lensed transients and especially lensed supernovae are invaluable tools to cosmology because they allow us to constrain cosmological parameters via lens modeling and the measurements of their time delays. In this paper, we develop a pipeline to perform a targeted lensed transient search. We apply this pipeline to 5807 strong lenses and candidates, which were identified in the literature, in the DESI Legacy Imaging Surveys Data Release 9 (DR9) footprint. For each system, we analyze every exposure in all of the observed bands (DECam g, r, and z). Our pipeline finds, groups, and ranks detections that are in sufficient proximity temporally and spatially. After the first round of inspection, for promising candidate systems, we further examine the newly available DR10 data (with additional i and Y bands). Here we present our targeted lensed supernova search pipeline and seven new lensed supernova candidates, including a very likely lensed supernova—probably a Type Ia—in a system with an Einstein radius of ~1$^{"}_{.}$5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Analytical noise bias correction for precise weak lensing shear inference

Noise bias is a significant source of systematic error in weak gravitational lensing measurements that must be corrected to satisfy the stringent standards of modern imaging surveys in the era of precision cosmology. This paper reviews the analytical noise bias correction method and provides analytical derivations demonstrating that we can recover shear to its second order using the ‘renoising’ noise bias correction approach introduced by METACALIBRATION. We implement this analytical noise bias correction within the AnaCal shear estimation framework and propose several enhancements to the noise bias correction algorithm. We evaluate the improved AnaCal using simulations designed to replicate Rubin Legacy Survey of Space and Time (LSST) imaging data. These simulations feature semi-realistic galaxies and stars, complete with representative distributions of magnitudes and Galactic spatial density. We conduct tests under various observational challenges, including cosmic rays, defective CCD columns, bright star saturation, bleed trails, and spatially variable point spread functions. Our results indicate a multiplicative bias in weak lensing shear recovery of less than a few tenths of a per cent, meeting LSST Dark Energy Science Collaboration requirements without requiring calibration from external image simulations. Additionally, our algorithm achieves rapid processing, handling one galaxy in less than a millisecond.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

COOL-LAMPS. IV. A Sample of Bright Strongly Lensed Galaxies at 3 < z < 4

We report the discovery of five bright, strong gravitationally lensed galaxies at 3 < z < 4: COOL J0101+2055 (z = 3.459), COOL J0104–0757 (z = 3.480), COOL J0145+1018 (z = 3.310), COOL J0516–2208 (z = 3.549), and COOL J1356+0339 (z = 3.753). These galaxies have magnitudes of r AB , z AB < 21.81 mag and are lensed by galaxy clusters at 0.26 < z < 1. This sample nearly doubles the number of known bright lensed galaxies with extended arcs at 3 < z < 4. We characterize the lensed galaxies using ground-based grz/giy imaging and optical spectroscopy. We report model-based magnitudes and derive stellar masses, dust content, and star formation rates via stellar population synthesis modeling. Building lens models based on ground-based imaging, we estimate source magnifications ranging from ~29 to ~180. Combining these analyses, we derive demagnified stellar masses in the range log 10 (M * /M ⊙ ) ~ 9.69 – 10.75 and star formation rates in the youngest age bin in the range log 10 (SFR/(M ⊙ yr -1 )) ~ 0.39 – 1.46, placing the sample galaxies on the massive end of the star-forming main sequence in this redshift interval. In addition, three of the five galaxies have strong Lyα emissions, offering unique opportunities to study Lyα emitters at high redshift in future work.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The intrinsic alignment of red galaxies in DES Y1 redMaPPer galaxy clusters

ABSTRACT Clusters of galaxies trace the most non-linear peaks in the cosmic density field. The weak gravitational lensing of background galaxies by clusters can allow us to infer their masses. However, galaxies associated with the local environment of the cluster can also be intrinsically aligned due to the local tidal gradient, contaminating any cosmology derived from the lensing signal. We measure this intrinsic alignment in Dark Energy Survey (DES) Year 1 redMaPPer clusters. We find evidence of a non-zero mean radial alignment of galaxies within clusters between redshifts 0.1–0.7. We find a significant systematic in the measured ellipticities of cluster satellite galaxies that we attribute to the central galaxy flux and other intracluster light. We attempt to correct this signal, and fit a simple model for intrinsic alignment amplitude (AIA) to the measurement, finding AIA = 0.15 ± 0.04, when excluding data near the edge of the cluster. We find a significantly stronger alignment of the central galaxy with the cluster dark matter halo at low redshift and with higher richness and central galaxy absolute magnitude (proxies for cluster mass). This is an important demonstration of the ability of large photometric data sets like DES to provide direct constraints on the intrinsic alignment of galaxies within clusters. These measurements can inform improvements to small-scale modelling and simulation of the intrinsic alignment of galaxies to help improve the separation of the intrinsic alignment signal in weak lensing studies.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2020

Measurement of the Cosmic Microwave Background Polarization Lensing Power Spectrum from Two Years of POLARBEAR Data

Here, we present a measurement of the gravitational lensing deflection power spectrum reconstructed with two seasons of cosmic microwave background polarization data from the Polarbear experiment. Observations were taken at 150 GHz from 2012 to 2014 and surveyed three patches of sky totaling 30 square degrees. We test the consistency of the lensing spectrum with a cold dark matter cosmology and reject the no-lensing hypothesis at a confidence of 10.9σ, including statistical and systematic uncertainties. We observe a value of A L = 1.33 ± 0.32 (statistical) ±0.02 (systematic) ±0.07 (foreground) using all polarization lensing estimators, which corresponds to a 24% accurate measurement of the lensing amplitude. Compared to the analysis of the first-year data, we have improved the breadth of both the suite of null tests and the error terms included in the estimation of systematic contamination.

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

Detecting low-mass perturbers in cluster lenses using curved arc bases

ABSTRACT Strong gravitationally lensed arcs produced by galaxy clusters have been observationally detected for several decades now. These strong lensing constraints provided high-fidelity mass models for cluster lenses that include substructure down to $10^{9{-}10}\, \mathrm{M}_\odot$. Optimizing lens models, where the cluster mass distribution is modelled by a smooth component and subhaloes associated with the locations of individual cluster galaxies, has enabled deriving the subhalo mass function, providing important constraints on the nature and granularity of dark matter. In this work, we explore and present a novel method to detect and measure individual perturbers (subhaloes, line-of-sight haloes, and wandering supermassive black holes) by exploiting their proximity to highly distorted lensed arcs in galaxy clusters, and by modelling the local lensing distortions with curved arc bases. This method offers the possibility of detecting individual low-mass perturber subhaloes in clusters and haloes along the line of sight down to a mass resolution of $10^8\, \mathrm{M}_\odot$. We quantify our sensitivity to low-mass perturbers ($M\sim 10^{7{-}9}\, \mathrm{M}_\odot$) in clusters (M ∼ 1014–15 M⊙), by creating realistic mock data. Using three lensed images of a background galaxy in the cluster SMACS J0723, taken by JWST, we study the retrieval of the properties of potential perturbers with masses $M=10^{7{-}9}\, \mathrm{M}_\odot$. From the derived posterior probability distributions for the perturber, we constrain its concentration, redshift, and ellipticity. By allowing us to probe lower mass substructures, the use of curved arc bases can lead to powerful constraints on the nature of dark matter as discrimination between dark matter models appears on smaller scales.

Astronomy & Astrophysics↗
DOE OSTI2024

Small-correlated-against-large estimator for the lensing of the cosmic microwave background

Weak gravitational lensing of the cosmic microwave background (CMB) carries imprints of the physics operating at redshifts much lower than that of recombination and serves as an important probe of cosmological structure formation, dark matter physics, and the mass of neutrinos. Reconstruction of the CMB lensing deflection field through use of quadratic estimators has proven successful with existing data but is known to be sub-optimal on small angular scales ($\ell > 3000$) for experiments with low noise levels. Future experiments will provide better observations in this regime, but these techniques will remain statistically limited by their approximations. We show that correlations between fluctuations of the large-scale temperature gradient power of the CMB sourced by $\ell < 2000$, and fluctuations of the local small-scale temperature power reveal a lensing signal which is prominent in even the real-space pixel statistics across a CMB temperature map. We present the development of the Small Correlated Against Large Estimator (SCALE), a novel estimator for the CMB lensing spectrum which offers promising complementary analysis alongside other reconstruction techniques in this regime. The SCALE method computes correlations between both the large/small-scale temperature gradient power in harmonic space, and it is able to quantitatively recover unbiased statistics of the CMB lensing field without the need for map-level reconstruction. SCALE can outperform quadratic estimator signal-to-noise by a factor of up to 1.5 in current and upcoming experiments for CMB lensing power spectra $C_{6000 < L < 8000}^{\phi\phi}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Deep inference of simulated strong lenses in ground-based surveys

The large number of strong lenses discoverable in future astronomical surveys will likely enhance the value of strong gravitational lensing as a cosmic probe of dark energy and dark matter. However, leveraging the increased statistical power of such large samples will require further development of automated lens modeling techniques. We show that deep learning and simulation-based inference (SBI) methods produce informative and reliable estimates of parameter posteriors for strong lensing systems in ground-based surveys. We present the examination and comparison of two approaches to lens parameter estimation for strong galaxy-galaxy lenses — Neural Posterior Estimation (NPE) and Bayesian Neural Networks (BNNs). We perform inference on 1-, 5-, and 12-parameter lens models for ground-based imaging data that mimics the Dark Energy Survey (DES). We find that NPE outperforms BNNs, producing posterior distributions that are more accurate, precise, and well-calibrated for most parameters. For the 12-parameter NPE model, the calibration is consistently within <10% of optimal calibration for all parameters, while the BNN is rarely within 20% of optimal calibration for any of the parameters. Similarly, residuals for most of the parameters are smaller (by up to an order of magnitude) with the NPE model than the BNN model. This work takes important steps in the systematic comparison of methods for different levels of model complexity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

DeepZipper: A Novel Deep-learning Architecture for Lensed Supernovae Identification

Large-scale astronomical surveys have the potential to capture data on large numbers of strongly gravitationally lensed supernovae (LSNe). To facilitate timely analysis and spectroscopic follow-up before the supernova fades, an LSN needs to be identified soon after it begins. To quickly identify LSNe in optical survey data sets, we designed ZipperNet, a multibranch deep neural network that combines convolutional layers (traditionally used for images) with long short-term memory layers (traditionally used for time series). We tested ZipperNet on the task of classifying objects from four categories—no lens, galaxy-galaxy lens, lensed Type-Ia supernova, lensed core-collapse supernova—within high-fidelity simulations of three cosmic survey data sets: the Dark Energy Survey, Rubin Observatory’s Legacy Survey of Space and Time (LSST), and a Dark Energy Spectroscopic Instrument (DESI) imaging survey. Among our results, we find that for the LSST-like data set, ZipperNet classifies LSNe with a receiver operating characteristic area under the curve of 0.97, predicts the spectroscopic type of the lensed supernovae with 79% accuracy, and demonstrates similarly high performance for LSNe 1–2 epochs after first detection. We anticipate that a model like ZipperNet, which simultaneously incorporates spatial and temporal information, can play a significant role in the rapid identification of lensed transient systems in cosmic survey experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

The DESI-Lensing Mock Challenge: large-scale cosmological analysis of 3x2-pt statistics

The current generation of large galaxy surveys will test the cosmological model by combining multiple types of observational probes. Realising the statistical promise of these new datasets requires rigorous attention to all aspects of analysis including cosmological measurements, modelling, covariance and parameter likelihood. In this paper we present the results of an end-to-end simulation study designed to test the analysis pipeline for the combination of the Dark Energy Spectroscopic Instrument (DESI) Year 1 galaxy redshift dataset and separate weak gravitational lensing information from the Kilo-Degree Survey, Dark Energy Survey and Hyper-Suprime-Cam Survey. Our analysis employs the 3x2-pt correlation functions including cosmic shear and galaxy-galaxy lensing, together with the projected correlation function of the spectroscopic DESI lenses. We build realistic simulations of these datasets including galaxy halo occupation distributions, photometric redshift errors, weights, multiplicative shear calibration biases and magnification. We calculate the analytical covariance of these correlation functions including the Gaussian, noise and super-sample contributions, and show that our covariance determination agrees with estimates based on the ensemble of simulations. We use a Bayesian inference platform to demonstrate that we can recover the fiducial cosmological parameters of the simulation within the statistical error margin of the experiment, investigating the sensitivity to scale cuts. This study is the first in a sequence of papers in which we present and validate the large-scale 3x2-pt cosmological analysis of DESI-Y1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Observation and confirmation of nine strong-lensing systems in Dark Energy Survey Year 1 data

ABSTRACT We describe the observation and confirmation of nine new strong gravitational lenses discovered in Year 1 data from the Dark Energy Survey (DES). We created candidate lists based on (i) galaxy group and cluster samples, and (ii) photometrically selected galaxy samples. We selected 46 candidates through visual inspection and then used the Gemini Multi-Object Spectrograph(GMOS) at the Gemini South telescope to acquire a spectroscopic follow-up of 21 of these candidates. Through an analysis of these spectroscopic follow-up data, we confirmed nine new lensing systems and rejected two candidates, and the analysis was inconclusive on 10 candidates. For each of the confirmed systems, our report measured spectroscopic properties, estimated source image–lens separations, and estimated enclosed masses as well. The sources that we targeted have an i-band surface brightness range of $i_{\rm SB} \sim 22\!-\!24\, {\rm mag}\,{\rm arcsec}^{-2}$ and a spectroscopic redshift range of zspec ∼ 0.8−2.6. The lens galaxies have a photometric redshift range of zlens ∼ 0.3−0.7. The lensing systems range in source image–lens separation from 2 to 9 arcsec and in enclosed mass from 1012 to 1013 M⊙.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Extending empirical constraints on the SZ–mass scaling relation to higher redshifts via HST weak lensing measurements of nine clusters from the SPT-SZ survey at z ≳ 1

We present a Hubble Space Telescope (HST) weak gravitational lensing study of nine distant and massive galaxy clusters with redshifts 1.0 ≲ z ≲ 1.7 (z median = 1.4) and Sunyaev Zel’dovich (SZ) detection significance ξ > 6.0 from the South Pole Telescope Sunyaev Zel’dovich (SPT-SZ) survey. We measured weak lensing galaxy shapes in HST/ACS F606W and F814W images and used additional observations from HST/WFC3 in F110W and VLT/FORS2 in U HIGH to preferentially select background galaxies at z ≳ 1.8, achieving a high purity. We combined recent redshift estimates from the CANDELS/3D-HST and HUDF fields to infer an improved estimate of the source redshift distribution. We measured weak lensing masses by fitting the tangential reduced shear profiles with spherical Navarro-Frenk-White (NFW) models. We obtained the largest lensing mass in our sample for the cluster SPT-CL J2040—4451, thereby confirming earlier results that suggest a high lensing mass of this cluster compared to X-ray and SZ mass measurements. Combining our weak lensing mass constraints with results obtained by previous studies for lower redshift clusters, we extended the calibration of the scaling relation between the unbiased SZ detection significance ζ and the cluster mass for the SPT-SZ survey out to higher redshifts. We found that the mass scale inferred from our highest redshift bin (1.2 < z < 1.7) is consistent with an extrapolation of constraints derived from lower redshifts, albeit with large statistical uncertainties. Thus, our results show a similar tendency as found in previous studies, where the cluster mass scale derived from the weak lensing data is lower than the mass scale expected in a PlanckνΛCDM (i.e. νΛ cold dark matter) cosmology given the SPT-SZ cluster number counts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Dark Energy Survey Year 3 results: Curved-sky weak lensing mass map reconstruction

ABSTRACT We present reconstructed convergence maps, mass maps, from the Dark Energy Survey (DES) third year (Y3) weak gravitational lensing data set. The mass maps are weighted projections of the density field (primarily dark matter) in the foreground of the observed galaxies. We use four reconstruction methods, each is a maximum a posteriori estimate with a different model for the prior probability of the map: Kaiser–Squires, null B-mode prior, Gaussian prior, and a sparsity prior. All methods are implemented on the celestial sphere to accommodate the large sky coverage of the DES Y3 data. We compare the methods using realistic ΛCDM simulations with mock data that are closely matched to the DES Y3 data. We quantify the performance of the methods at the map level and then apply the reconstruction methods to the DES Y3 data, performing tests for systematic error effects. The maps are compared with optical foreground cosmic-web structures and are used to evaluate the lensing signal from cosmic-void profiles. The recovered dark matter map covers the largest sky fraction of any galaxy weak lensing map to date.

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 OSTI2025

Analyzing line-of-sight selection biases in galaxy-scale strong lensing with external convergence and shear

The upcoming Vera Rubin Observatory Legacy Survey of Space and Time (LSST) will dramatically increase the number of strong gravitational lensing systems, requiring precise modeling of line-of-sight (LOS) effects to mitigate biases in lensing observations and cosmological inferences. We develop a method to construct joint distributions of external convergence (κ ext ) and shear (γ ext ) for strong lensing LOS by aggregating large-scale structure simulations with high-resolution halo renderings and non-linear correction. Our approach captures both smooth background matter and perturbations from halos, enabling accurate modeling of LOS effects. Here, we apply non-linear LOS corrections to κ ext and γ ext that address the non-additive lensing effects caused by objects along the LOS in strong lensing. We find that, with a minimum image separation of 1.0'', non-linear LOS correction due to the presence of a dominant deflector slightly increases the ratio of quadruple to double lenses; this non-linear LOS correction also introduces systematic biases of ∼ 0.1% for galaxy-AGN lens in the inferred Hubble constant (H 0 ) if not accounted for. We also observe a 0.66% bias for galaxy-galaxy lenses on H 0 , and even larger biases 1.02% for galaxy-AGN systems if LOS effects are not accounted for. These results highlight the importance of LOS for precision cosmology. The publicly available code and datasets provide tools for incorporating LOS effects in future analyses.

Hubble constant↗
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↗