Lensing Systems Research Articles

Reconciling concentration to virial mass relations

The concentration--virial mass (c-M) relation is a fundamental scaling relation within the standard cold dark matter (Lambda CDM) framework well established in numerical simulations. However, observational constraints of this relation are hampered by the difficulty of characterising the properties of dark matter haloes. Recent comparisons between simulations and observations have suggested a systematic difference of the c-M relation, with higher concentrations in the latter. In this work, we undertake detailed comparisons between simulated galaxies and observations of a sample of strong-lensing galaxies. We explore several factors of the comparison with strong gravitational lensing constraints, including the choice of the generic dark matter density profile, the effect of radial resolution, the reconstruction limits of observed versus simulated mass profiles, and the role of the initial mass function in the derivation of the dark matter parameters. Furthermore, we show the dependence of the c-M relation on reconstruction and model errors through a detailed comparison of real and simulated gravitational lensing systems. An effective reconciliation of simulated and observed c-M relations can be achieved if one considers less strict assumptions on the dark matter profile, for example, by changing the slope of a generic NFW profile or focusing on rather extreme combinations of stellar-to-dark matter distributions. A minor effect is inherent to the applied method: fits to the NFW profile on a less well-constrained inner mass profile yield slightly higher concentrations and lower virial masses.

The cosmic distance duality relation in light of the time-delayed strong gravitational lensing

Abstract The cosmic distance duality relation (DDR), which links the angular diameter distance and the luminosity distance, is a cornerstone in modern cosmology. Any deviation from DDR may indicate new physics beyond the standard cosmological model. In this paper, we use four high-precision time-delayed strong gravitational lensing (SGL) systems provided by the H0LiCOW to test the validity of DDR. To this end, we directly compare the angular diameter distances from these SGL systems and the luminosity distances from the latest Pantheon+ compilation of SNe Ia. In order to reduce the statistical errors arising from redshift matching, the Gaussian process method is applied to reconstruct the distance-redshift relation from the Pantheon+ dataset. We parameterize the possible violation of DDR in three different models. It is found that all results confirm the validity of DDR at 1$\sigma$ confidence level. Additionally, Monte Carlo simulations based on the future LSST survey indicate that the precision of DDR could reach $10^{-2}$ level with 100 SGL systems.

A targeted search for strongly lensed supernovae with the Las Cumbres Observatory

ABSTRACT Gravitationally lensed supernovae (glSNe) are of interest for time delay cosmology and SN physics. However, glSNe detections are rare, owing to the intrinsic rarity of SN explosions, the necessity of alignment with a foreground lens, and the relatively short window of detectability. We present the Las Cumbres Observatory Lensed Supernova Search, LCOLSS, a targeted survey designed for detecting glSNe in known strong lensing systems. Using cadenced $r^\prime$-band imaging, LCOLSS targeted 114 galaxy–galaxy lensing systems with high expected SN rates, based on estimated star formation rates. No plausible glSN was detected by LCOLSS during our two year observing program. We carry out an analysis here to measure a detection efficiency for these observations. We then perform Monte Carlo simulations using the predicted supernova rates to determine the expected number of glSN detections. The results of the simulation suggest an expected number of detections and 68 per cent Poisson confidence intervals, $N_{\mathrm{ SN}} = 0.20, [0,2.1]$, $N_{\mathrm{ Ia}} = 0.08, [0,2.0]$, $N_{\mathrm{ CC}} = 0.12, [0,2.0]$, for all SNe, Type Ia SNe, and core-collapse (CC) SNe, respectively. These results are broadly consistent with the absence of a detection in our survey. Analysis of the survey strategy can provide insights for future efforts to develop targeted glSN discovery programs, especially considering the large anticipated yields of upcoming surveys.

New Strong Gravitational Lenses from the DESI Legacy Imaging Surveys Data Release 9

We have conducted a search for strong gravitational lensing systems in the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9. This is the third paper in a series. These surveys together cover ∼19,000 deg2 visible from the Northern Hemisphere, reaching a z-band AB magnitude of ∼22.5. We use a deep residual neural network, trained on a compilation of known lensing systems and high-grade candidates as well as nonlenses in the same footprint. After applying our trained neural network to the survey data, we visually inspect and rank images with probabilities above a threshold which has been chosen to balance precision and recall. We have found 1895 lens candidates, of which 1512 are identified for the first time. Combining the discoveries from this work with those from Papers I (335) and II (1210), we have discovered a total of 3057 new candidates in the Legacy Surveys.

Inverse distance ladder method for determining H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} from angular diameter distances of time-delay lenses and supernova observations

Time-delay measurements from strong lensing systems combined with spectroscopic measurements of stellar kinematics in deflecting galaxies provide a natural way to infer absolute distances (lensing distances). This means that it can be used to anchor the relative distances of Type Ia supernovae (SNe Ia), and further infer the Hubble constant H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} in a cosmological model-independent way, while avoiding the assumptions of curvature and the equation of state of dark energy. Indeed, observations based on gravitational lensing time delays can measure H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} directly, but usually require assumptions about the specific cosmological models. Meanwhile, this method suffers the mass-sheet degeneracy obstacle. These factors may induce the bias on determination of H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}. However, the inverse distance ladder method we use avoids these assumptions altogether. In this study, we seek for the Pantheon and Pantheon plus datasets and use Gaussian process regression to reconstruct the unanchored distance to match the distance at the redshift of the lens to determine H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}, respectively. Based on the four H0LiCOW lenses, the unanchored distances reconstructed by combining the Pantheon and Pantheon plus datasets yielded H0=80.1-6.9+7.0km/s/Mpc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0=80.1^{+7.0}_{-6.9} \\mathrm {~km/s/Mpc}$$\\end{document} and H0=81.2-7.0+7.1km/s/Mpc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0=81.2^{+7.1}_{-7.0} \\mathrm {~km/s/Mpc}$$\\end{document} with 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\sigma $$\\end{document} observational uncertainty, respectively. All the lenses show the measured H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} is in good agreement with the local measurement results reported by the SH0ES collaboration within ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim $$\\end{document}1.3σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.3 \\sigma $$\\end{document} confidence level.

Robust test of general relativity at the galactic scales by combining strong lensing systems and gravitational wave standard sirens

Robust test of general relativity at the galactic scales by combining strong lensing systems and gravitational wave standard sirens

The CluMPR galaxy cluster-finding algorithm and DESI legacy survey galaxy cluster catalogue

ABSTRACT Galaxy clusters enable unique opportunities to study cosmology, dark matter, galaxy evolution, and strongly lensed transients. We here present a new cluster-finding algorithm, CluMPR (Clusters from Masses and Photometric Redshifts), that exploits photometric redshifts (photo-z’s) as well as photometric stellar mass measurements. CluMPR uses a 2D binary search tree to search for overdensities of massive galaxies with similar redshifts on the sky and then probabilistically assigns cluster membership by accounting for photo-z uncertainties. We leverage the deep DESI Legacy Survey grzW1W2 imaging over one-third of the sky to create a catalogue of $\sim 300\, 000$ galaxy cluster candidates out to z = 1, including tabulations of member galaxies and estimates of each cluster’s total stellar mass. Compared to other methods, CluMPR is particularly effective at identifying clusters at the high end of the redshift range considered (z = 0.75–1), with minimal contamination from low-mass groups. These characteristics make it ideal for identifying strongly lensed high-redshift supernovae and quasars that are powerful probes of cosmology, dark matter, and stellar astrophysics. As an example application of this cluster catalogue, we present a catalogue of candidate wide-angle strongly lensed quasars in Appendix C. The nine best candidates identified from this sample include two known lensed quasar systems and a possible changing-look lensed QSO with SDSS spectroscopy. All code and catalogues produced in this work are publicly available (see Data Availability).

Probing a scale dependent gravitational slip with galaxy strong lensing systems

Probing a scale dependent gravitational slip with galaxy strong lensing systems

Determining cosmological-model-independent H0 and post-Newtonian parameter with time-delay lenses and supernovae

ABSTRACT Strong gravitational lensing provides a natural opportunity to test general relativity (GR). We propose a model-independent method for simultaneous constraining on Hubble constant (H0) and post-Newtonian parameter (γPPN) using strong lensing systems and observational Type Ia supernovae. The time-delay measurements from strong lensing can directly determine the Hubble constant, and the lens distance inferred from the spectroscopic measurement of the stellar kinematics of the deflector galaxy can help us to constrain the post-Newtonian parameter. We seek the Pantheon data set and reconstruct unanchored distances using Gaussian process regression to achieve the cosmological-model-independent GR testing instead of assuming a specific model, which can reduce possible bias on GR testing and measurement of Hubble constant. Combining the reconstructed unanchored distances and the four H0LiCOW lens data sets, our results are $H_0=72.9^{+2.0}_{-2.3} \, \mathrm{km \, s^{-1} \, Mpc^{-1}}$ and $\gamma _{\rm {PPN}}=0.89^{+0.17}_{-0.15}$. All the lenses show that there is no obvious evidence to support GR deviation within observational uncertainties. In the subsequent analysis, we consider a ratio of distance ${D_{\Delta t}}/{D^{^{\prime }}_{\mathrm{ d}}}$ method to further avoid the influence of H0 on GR testing. The results show that, except J1206 within the ∼1.2σ observational uncertainty, the remaining three lenses support that GR holds within the 1σ observational uncertainties.

A Model-independent Method to Determine H 0 Using Time-delay Lensing, Quasars, and Type Ia Supernovae

Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia) at cosmological distances giving a model-independent inference of the Hubble constant (H 0). Future observations could provide strong lensing time-delay distances with source redshifts up to z ≃ 4, which are much higher than the maximum redshift of SNe Ia observed so far. In order to make full use of time-delay distances measured at higher redshifts, we use quasars as a complementary cosmic probe to measure cosmological distances at redshifts beyond those of SNe Ia and provide a model-independent method to determine H 0. In this work, we demonstrate a model-independent, joint constraint of SNe Ia, quasars, and time-delay distances from strong lensed quasars. We first generate mock data sets of SNe Ia, quasar, and time-delay distances based on a fiducial cosmological model. Then, we calibrate the quasar parameters model independently using Gaussian process (GP) regression with mock SNe Ia data. Finally, we determine the value of H 0 model-independently using GP regression from mock quasars and time-delay distances from strong lensing systems. As a comparison, we also show the H 0 results obtained from mock SNe Ia in combination with time-delay lensing systems whose redshifts overlap with SNe Ia. Our results show that quasars at higher redshifts show great potential to extend the redshift coverage of SNe Ia and thus enable the full use of strong lens time-delay distance measurements from ongoing cosmic surveys and improve the accuracy of the estimation of H 0 from 2.1% to 1.3% when the uncertainties of the time-delay distances are 5% of the distance values.

Cosmology from large populations of galaxy–galaxy strong gravitational lenses

ABSTRACT We present a forecast analysis on the feasibility of measuring the cosmological parameters with a large number of galaxy–galaxy scale strong gravitational lensing systems. Future wide-area surveys like Euclid and 4MOST are expected to discover and measure the properties of more than 10 000 strong lensing systems. We develop a hierarchical model that can simultaneously constrain the lens population and cosmological parameters by combining Einstein radius measurements with stellar dynamical mass estimates for every lens. Marginalizing over the lens density profiles and stellar orbital anisotropies, we find that w can be constrained, at 68 per cent confidence, to a precision of 0.11 with 10 000 galaxy–galaxy lens systems, which would be better than any existing single-probe constraint. We test our method on 161 existing lenses from various surveys (LSD, SL2S, SLACS, and S4TM), finding w = −0.96 ± 0.46. We also show how to mitigate against the potential systematic of redshift evolution in the mean lens density profile of the population.

Constraining the Spatial Curvature of the Local Universe with Deep Learning

We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161 strong gravitational lensing systems, whose distances are calibrated from the Pantheon compilation of type Ia supernovae using deep learning. To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameter Ω k , we consider three different lens models. Results show that a flat Universe is supported in the singular isothermal sphere (SIS) model with the parameter . While in the power-law (PL) model, a closed Universe is preferred at the ∼3σ confidence level, with the parameter . In the extended PL model, the 95% confidence level upper limit of Ω k is <0.011. As for the parameters of the lens models, constraints on the three models indicate that the mass profile of the lens galaxy could not be simply described by the standard SIS model.

Forecasts analysis on varying-[formula omitted] theories from gravitational wave standard sirens

Motivated by future gravitational waves observations, we perform forecasts analysis to constrain a possible time variation of the fine structure constant (α) within the context of the so-called runaway dilaton model. For this purpose, some gravitational-wave standard sirens mock data within the perspective of Einstein Telescope and LISA mission were considered jointly with current strong gravitational lensing systems observations. We find that future standard sirens observations can also play an important role in the search for possible variations of α within the methodology presented in this work.

Searching for strong galaxy-scale lenses in galaxy clusters with deep networks

Strong galaxy-scale lenses in galaxy clusters provide a unique tool with which to investigate the inner mass distribution of these clusters and the subhalo density profiles in the low-mass regime, which can be compared with predictions from ΛCDM cosmological simulations. We search for galaxy–galaxy strong-lensing systems in theHubbleSpace Telescope (HST) multi-band imaging of galaxy cluster cores by exploring the classification capabilities of deep learning techniques. Convolutional neural networks (CNNs) are trained utilising highly realistic simulations of galaxy-scale strong lenses injected into the HST cluster fields around cluster members (CLMs). To this aim, we take advantage of extensive spectroscopic information available in 16 clusters and accurate knowledge of the deflection fields in half of these from high-precision strong-lensing models. Using observationally based distributions, we sample the magnitudes (down toF814W = 29 AB), redshifts, and sizes of the background galaxy population. By placing these sources within the secondary caustics associated with the cluster galaxies, we build a sample of approximately 3000 strong galaxy–galaxy lenses, which preserve the full complexity of real multi-colour data and produce a wide diversity of strong-lensing configurations. We study two deep learning networks, processing a large sample of image cutouts, in three bands, acquired by HST Advanced Camera for Survey (ACS), and we quantify their classification performance using several standard metrics. We find that both networks achieve a very good trade-off between purity and completeness (85%–95%), as well as a good stability, with fluctuations within 2%–4%. We characterise the limited number of false negatives (FNs) and false positives (FPs) in terms of the physical properties of the background sources (magnitudes, colours, redshifts, and effective radii) and CLMs (Einstein radii and morphology). We also demonstrate the high degree of generalisation of the neural networks by applying our method to HST observations of 12 clusters with previously known galaxy-scale lensing systems.

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 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.

Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems Using Recurrent Inference Machines

Modeling strong gravitational lenses in order to quantify distortions in the images of background sources and to reconstruct the mass density in foreground lenses has been a difficult computational challenge. As the quality of gravitational lens images increases, the task of fully exploiting the information they contain becomes computationally and algorithmically more difficult. In this work, we use a neural network based on the recurrent inference machine to reconstruct simultaneously an undistorted image of the background source and the lens mass density distribution as pixelated maps. The method iteratively reconstructs the model parameters (the image of the source and a pixelated density map) by learning the process of optimizing the likelihood given the data using the physical model (a ray-tracing simulation), regularized by a prior implicitly learned by the neural network through its training data. When compared to more traditional parametric models, the proposed method is significantly more expressive and can reconstruct complex mass distributions, which we demonstrate by using realistic lensing galaxies taken from the IllustrisTNG cosmological hydrodynamic simulation.

Investigating Gravitationally Lensed Quasars Observable by Nancy Grace Roman Space Telescope

In this work, we investigate the possibility of observing quasars, particularly lensed quasars, by the Nancy Grace Roman Space Telescope (Roman). To this aim, based on the capabilities of the Roman Space Telescope and the results from the quasar luminosity function (QLF) in the infrared band of the Spitzer Space Telescope imaging survey, we calculated the number of quasars expected to be in its field of view. In order to estimate the number of lensed quasars, we develop a Monte Carlo simulation to estimate the probability that a quasar is lensed once or more times by foreground galaxies. Using the mass–luminosity distribution function of galaxies and the redshift distributions of galaxies and quasars, we find that 1 per 180 observed quasars will be lensed by foreground galaxies. Further on, adopting a singular isothermal sphere (SIS) model for lens galaxies, we calculate the time delay between lensed images for single and multiple lensing systems and present their distributions. We emphasize that detailed studies of these lensing systems will provide a powerful probe of the physical properties of quasars and may allow testing the mass distribution models of galaxies in addition to being extremely helpful for constraining the cosmological parameters.

Strong gravitational lensing by AGNs as a probe of the quasar–host relations in the distant Universe

The tight correlations found between the mass of supermassive black holes and the luminosities, stellar masses and velocity dispersions of their host galaxies are often interpreted as a sign of their co-evolution. Studying these correlations across redshift provides a powerful insight into the evolutionary path followed by the quasar and its host galaxy. While the mass of the black hole is accessible from single-epoch spectra, measuring the mass of its host galaxy is challenging as the active nucleus largely overshines its host. Here we present a technique to probe quasar–host relations beyond the local Universe with strong gravitational lensing, hence overcoming the use of stellar population models or velocity dispersion measurements, both prone to degeneracies. We study in detail one of the three known cases of strong lensing by a quasar to accurately measure the mass of its host and to infer a total lensing mass within the Einstein radius. The lensing measurement is more precise than any other alternative technique and compatible with the local scaling relation between the mass of the black hole and the stellar mass. The sample of such quasar–galaxy or quasar–quasar lensing systems should reach a few hundred with Euclid and the Rubin-Large Synoptic Survey Telescope, thus enabling the application of such a method with statistically significant sample sizes. A rare case of a quasar acting as a gravitational lens allows a precise determination of the mass of the quasar’s host galaxy and offers a new path to studying the connections between supermassive black holes and their host galaxies.

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

Context. 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 H0, 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). Aims. 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). Methods. 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. Results. 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.

Revealing the Nature of Strong Lensing System J1436+4943 with Only the MaNGA Data

Strong gravitational lensing is a powerful tool for probing the mass content of the Universe. Both high-resolution imaging and spectroscopy observations are important for identifying and measuring the properties of the lensing object. The strong lensing system J1436+4943 was discovered in the SDSS-IV MaNGA survey and further observed with the FOCAS IFU spectrograph on the Subaru Telescope. We investigate whether comparable properties, e.g., the Einstein radius can be obtained using only MaNGA data cubes. The result shows that the general properties of the lens system can be recovered but the Einstein radius is different from the result with FOCAS IFU data by less than 25%. The MaNGA data cubes are helpful for fast analysis of large samples and to study the statistical properties of gravitational lensing systems.