Mass-sheet Degeneracy Research Articles

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.

Breaking the mass-sheet degeneracy in strong lensing mass modelling with weak lensing observations

ABSTRACT The Hubble constant ($H_0$), a crucial parameter in cosmology, quantifies the expansion rate of the universe so its precise measurement is important to understand the fundamental dynamics of our evolving universe. One of the major limitations of measuring $H_0$ using time-delay cosmography is the presence of the mass-sheet degeneracy (MSD) in the lens mass modelling. We propose and quantitatively assess the use of galaxy–galaxy shear measurements to break the MSD in the strong lensing mass modelling. We use stacked galaxy–galaxy lensing profiles and corresponding covariance matrices from Huang et al. to constrain the MSD in lens mass modelling with a highly flexible mass profile. Our analyses show that if ideally all galaxy–galaxy lensing measurements from the Hyper Suprime-Cam survey can be used to constrain the MSD, we can achieve $\sim 10~{{\ \rm per\ cent}}$ precision on the MSD constraint. We forecast that galaxy–galaxy lensing measurements from Legacy Survey of Space and Time (LSST)-like surveys can in general constrain the MSD with $\sim 1\,\mathrm{ per\,cent}-3~{{\ \rm per\ cent}}$ precision. Furthermore, if we push weak lensing measurements to a lower angular scale of $\sim 0.04\,\rm Mpc$, a survey like LSST can provide $\sim 1~{{\ \rm per\ cent}}$ precision on the MSD constraint, enabling a measurement of $H_0$ at the 1 per cent level. We demonstrate that galaxy–galaxy weak lensing can robustly constrain the MSD independent of stellar kinematics of the deflector, with wide-field survey data alone.

How to break the mass sheet degeneracy with the light curves of microlensed Type Ia supernovae

ABSTRACT The standardizable nature of gravitationally lensed Type Ia supernovae (glSNe Ia) makes them an attractive target for time-delay cosmography, since a source with known luminosity breaks the mass sheet degeneracy. It is known that microlensing by stars in the lensing galaxy can add significant stochastic uncertainty to the unlensed luminosity, which is often much larger than the intrinsic scatter of the Type Ia population. In this work, we show how the temporal microlensing variations as the supernova (SN) disc expands can be used to improve the standardization of glSNe Ia. We find that SNe are standardizable if they do not cross caustics as they expand. We estimate that this will be the case for ≈6 doubly imaged systems and ≈0.3 quadruply imaged systems per year from the Vera Rubin Observatory (LSST). At the end of the 10 yr LSST survey, these systems should enable us to test for systematics in H0 due to the mass sheet degeneracy at the $1.00^{+0.07}_{-0.06}$ per cent level, or 1.8 ± 0.2 per cent if we can only extract time delays from the third of systems with counter-images brighter than i = 24 mag.

Sp1149. II. Spectroscopy of H ii Regions near the Critical Curve of MACS J1149 and Cluster Lens Models

Galaxy-cluster gravitational lenses enable the study of faint galaxies even at large lookback times, and, recently, time-delay constraints on the Hubble constant. There have been few tests, however, of lens model predictions adjacent to the critical curve (≲8″) where the magnification is greatest. In a companion paper, we use the GLAFIC lens model to constrain the Balmer L–σ relation for H ii regions in a galaxy at redshift z = 1.49 strongly lensed by the MACS J1149 galaxy cluster. Here we perform a detailed comparison between the predictions of 10 cluster lens models that employ multiple modeling assumptions with our measurements of 11 magnified, giant H ii regions. We find that that the models predict magnifications an average factor of 6.2 smaller, a ∼2σ tension, than that inferred from the H ii regions under the assumption that they follow the low-redshift L–σ relation. To evaluate the possibility that the lens model magnifications are strongly biased, we next consider the flux ratios among knots in three images of Sp1149, and find that these are consistent with model predictions. Moreover, while the mass-sheet degeneracy could in principle account for a factor of ∼6 discrepancy in magnification, the value of H 0 inferred from SN Refsdal’s time delay would become implausibly small. We conclude that the lens models are not likely to be highly biased, and that instead the H ii regions in Sp1149 are substantially more luminous than the low-redshift Balmer L–σ relation predicts.

Extrapolating the projected potential of gravitational lens models: property-preserving degeneracies

ABSTRACT While gravitational lens inversion holds great promise to reveal the structure of the light-deflecting mass distribution, both light and dark, the existence of various kinds of degeneracies implies that care must be taken when interpreting the resulting lens models. This article illustrates how thinking in terms of the projected potential helps to gain insight into these matters. Additionally it is shown explicitly how, when starting from a discretized version of the projected potential of one particular lens model, the technique of quadratic programming can be used to create a multitude of equivalent lens models that preserve all or a subset of lens properties. This method is applied to a number of scenarios, showing the lack of grasp on the mass outside the strong lensing region, revisiting mass redistribution in between images, and applying this to a recent model of the SDSS J1004+4112 cluster, as well as illustrating the generalized mass sheet degeneracy and source-position transformation. In the case of J1004, we show that this mass redistribution did not succeed at completely eliminating a dark mass clump recovered by grale near one of the quasar images.

TDCOSMO

Time-delay distance measurements of strongly lensed quasars have provided a powerful and independent probe of the current expansion rate of the Universe (H0). However, in light of the discrepancies between early- and late-time cosmological studies, current efforts revolve around the characterisation of systematic uncertainties in the methods. In this work we focus on the mass-sheet degeneracy (MSD), which is commonly considered a significant source of systematics in time-delay strong lensing studies, and aim to assess the constraining power provided by integral field unit (IFU) stellar kinematics. To this end, we approximated the MSD with a cored, two-parameter extension to the adopted lensing mass profiles (with core radius rc and mass-sheet parameter λint), which introduces a full degeneracy between λint and H0 from lensing data alone. In addition, we utilised spatially resolved mock IFU stellar kinematics of time-delay strong lenses, given the prospects of obtaining such high-quality data with the James Webb Space Telescope (JWST) in the near future. We constructed joint strong lensing and generalised two-integral axisymmetric Jeans models, where the time delays, mock imaging, and IFU observations are used as input to constrain the mass profile of lens galaxies at the individual galaxy level and consequently yield joint constraints on the time-delay distance (DΔt) and the angular diameter distance (Dd) to the lens. We find that mock JWST-like stellar kinematics constrain the amount of internal mass sheet that is physically associated with the lens galaxy and limit its contribution to the uncertainties of DΔt and Dd, each at the ≤4% level, without assumptions on the background cosmological model. Incorporating additional uncertainties due to external mass sheets associated with mass structures along the lens line of sight, these distance constraints would translate to a ≲4% precision measurement on H0 in flat Λ cold dark matter cosmology for a single lens. Our study shows that future IFU stellar kinematics of time-delay lenses will be key in lifting the MSD on a per lens basis, assuming reasonable and physically motivated core sizes. However, even in the limit of infinite rc, where DΔt is fully degenerate with λint and is thus not constrained, stellar kinematics of the deflector, time delays, and imaging data will provide powerful constraints on Dd, which becomes the dominant source of information in the cosmological inference.

TDCOSMO

Strong-lensing time delays enable the measurement of the Hubble constant (H0) 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 H0 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 H0, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy Dd = 865−81+85 Mpc and the time-delay distance DΔt = 2180−271+472 Mpc, giving H0 = 77.1−7.1+7.3 km s−1 Mpc−1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and 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 (H0 = 78.3−3.3+3.4 km s−1 Mpc−1) and for seven lenses (H0 = 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 (H0 = 73.3−5.8+5.8 km s−1 Mpc−1). This agreement corroborates the methodology of time-delay cosmography.

Comments on the mass sheet degeneracy in cosmography analyses

We make a number of comments regarding modeling degeneracies in strong lensing measurements of the Hubble parameter H 0. The first point concerns the impact of weak lensing associated with different segments of the line of sight. We show that external convergence terms associated with the lens-source and observer-lens segments need to be included in cosmographic modeling, in addition to the usual observer-source term, to avoid systematic bias in the inferred value of H 0. Specifically, we show how an incomplete account of some line of sight terms biases stellar kinematics as well as ray tracing simulation methods to alleviate the mass sheet degeneracy.The second point concerns the use of imaging data for multiple strongly-lensed sources in a given system.We show that the mass sheet degeneracy is not fully resolved by the availability of multiple sources: some degeneracy remains because of differential external convergence between the different sources.Similarly, differential external convergence also complicates the use of multiple sources in addressing the approximate mass sheet degeneracy associated with a local (“internal”) core component in lens galaxies. This internal-external degeneracy is amplified by the non-monotonicity of the angular diameter distance as a function of redshift.For a rough assessment of the weak lensing effects, we provide estimates of external convergence using the nonlinear matter power spectrum, paying attention to non-equal time correlators.

Gravitational lensing H0 tension from ultralight axion galactic cores

Gravitational lensing time delays offer an avenue to measure the Hubble parameter ${H}_{0}$, with some analyses suggesting a tension with early-type probes of ${H}_{0}$. The lensing measurements must mitigate systematic uncertainties due to the mass modeling of lens galaxies. In particular, a core component in the lens density profile would form an approximate local mass sheet degeneracy and could bias ${H}_{0}$ in the right direction to solve the lensing tension. We consider ultralight dark matter as a possible mechanism to generate such galactic cores. We show that cores of roughly the required properties could arise naturally if an ultralight axion of mass $m\ensuremath{\sim}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{eV}$ makes up a fraction of order 10% of the total cosmological dark matter density. A relic abundance of this order of magnitude could come from vacuum misalignment. Stellar kinematics measurements of well-resolved massive galaxies (including the Milky Way) may offer a way to test the scenario. Kinematics analyses aiming to test the core hypothesis in massive elliptical lens galaxies should not, in general, adopt the perfect mass sheet limit, as ignoring the finite extent of an actual physical core could lead to significant systematic errors.

Weak-lensing Mass Reconstruction of Galaxy Clusters with a Convolutional Neural Network

Abstract We introduce a novel method for reconstructing the projected matter distributions of galaxy clusters with weak-lensing (WL) data based on a convolutional neural network (CNN). Training data sets are generated with ray-tracing through cosmological simulations. We control the noise level of the galaxy shear catalog such that it mimics the typical properties of the existing ground-based WL observations of galaxy clusters. We find that the mass reconstruction by our multilayered CNN with the architecture of alternating convolution and trans-convolution filters significantly outperforms the traditional reconstruction methods. The CNN method provides better pixel-to-pixel correlations with the truth, restores more accurate positions of the mass peaks, and more efficiently suppresses artifacts near the field edges. In addition, the CNN mass reconstruction lifts the mass-sheet degeneracy when applied to our projected cluster mass estimation from sufficiently large fields. This implies that this CNN algorithm can be used to measure the cluster masses in a model-independent way for future wide-field WL surveys.

“Worst-case” Microlensing in the Identification and Modeling of Lensed Quasars

Abstract Although microlensing of macrolensed quasars and supernovae provides unique opportunities for several kinds of investigations, it can add unwanted and sometimes substantial noise. While microlensing flux anomalies may be safely ignored for some observations, they severely limit others. “Worst-case” estimates can inform the decision whether or not to undertake an extensive examination of microlensing scenarios. Here, we report “worst-case” microlensing uncertainties for point sources lensed by singular isothermal potentials, parameterized by a convergence equal to the shear and by the stellar fraction. The results can be straightforwardly applied to nonisothermal potentials by utilizing the mass sheet degeneracy. We use microlensing maps to compute the fluctuations in image micromagnifications and estimate the stellar fraction at which the fluctuations are greatest for a given convergence. We find that the worst-case fluctuations happen at the stellar fraction κ ⋆ = 1 ∣ μ macro ∣ . For macrominima, the fluctuations in both magnification and demagnification appear to be bounded (1.5 > Δm > −1.3, where Δm is the magnitude relative to the average macromagnification). Magnifications for macrosaddles are bounded as well (Δm > −1.7). In contrast, demagnifications for macrosaddles appear to have unbounded fluctuations as 1/μ macro → 0 and κ ⋆ → 0.

Bridging the Gap Between Simply Parametrized and Free-Form Pixelated Models of Galaxy Lenses: The Case of WFI 2033-4723 Quad

We study the radial and azimuthal mass distribution of the lensing galaxy in WFI2033-4723. Mindful of the fact that modeling results depend on modeling assumptions, we examine two very different recent models: simply parametrized (SP) models from the H0LiCOW collaboration, and pixelated free-form (FF) GLASS models. In addition, we fit our own models which are a compromise between the astrophysical grounding of SP, and the flexibility of FF approaches. Our models consist of two offset parametric mass components, and generate many solutions, all fitting the quasar point image data. Among other results, we show that to reproduce point image properties the lensing mass must be lopsided, but the origin of this asymmetry can reside in the main lens plane or along the line of sight. We also show that there is a degeneracy between the slope of the density profile and the magnitude of external shear, and that the models from various modeling approaches are connected not by the mass sheet degeneracy, but by a more generalized transformation. Finally, we discuss interpretation degeneracy which afflicts all mass modeling: inability to correctly assign mass to the main lensing galaxy vs. nearby galaxies or line of sight structures. While this may not be a problem for the determination of $H_0$, interpretation degeneracy may become a major issue for the detailed study of galaxy structure.

TDCOSMO

Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, H0, independent of traditional distance ladder methodology. A current potential limitation of time-delay distance measurements is the mass-sheet transformation (MST), which leaves the lensed imaging unchanged but changes the distance measurements and the derived value of H0. In this work we show that the standard method of addressing the MST in time-delay cosmography, through a combination of high-resolution imaging and the measurement of the stellar velocity dispersion of the lensing galaxy, depends on the assumption that the ratio, Ds/Dds, of angular diameter distances to the background quasar and between the lensing galaxy and the quasar can be constrained. This is typically achieved through the assumption of a particular cosmological model. Previous work (TDCOSMO IV) addressed the mass-sheet degeneracy and derived H0 under the assumption of the ΛCDM model. In this paper we show that the mass-sheet degeneracy can be broken without relying on a specific cosmological model by combining lensing with relative distance indicators such as supernovae Type Ia and baryon acoustic oscillations, which constrain the shape of the expansion history and hence Ds/Dds. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological model-independent way. Hence model-independent distance measurements in time-delay cosmography under MSTs can be obtained.

Breaking the mass-sheet degeneracy with gravitational wave interference in lensed events

The mass-sheet degeneracy is a well-known problem in gravitational lensing that limits our capability to infer astrophysical lens properties or cosmological parameters from observations. As the number of gravitational wave observations grows, detecting lensed events will become more likely, and to assess how the mass-sheet degeneracy may affect them is crucial. Here, we study both analytically and numerically how the lensed waveforms are affected by the mass-sheet degeneracy, computing the amplification factor from the diffraction integral. In particular, we differentiate between the geometrical optics, wave optics, and interference regimes, focusing on ground-based gravitational waves detectors. In agreement with expectations of gravitational lensing of electromagnetic radiation, we confirm how, in the geometrical optics scenario, the mass-sheet degeneracy cannot be broken with only one lensed image. However, we find that in the interference regime, and, in part, in the wave-optics regime, the mass-sheet degeneracy can be broken with only one lensed waveform, thanks to the characteristic interference patterns of the signal. Finally, we quantify, through template matching, how well the mass-sheet degeneracy can be broken. We find that, within present GW detector sensitivities and considering signals as strong as those that have been detected so far, the mass-sheet degeneracy can lead to a $1\ensuremath{\sigma}$ uncertainty on the lens mass of $\ensuremath{\sim}12%$. With these values, the MSD might still be a problematic issue, but in case of signals with higher signal-to-noise ratio, the uncertainty can drop to $\ensuremath{\sim}2%$, which is less than the current indeterminacy achieved by dynamical mass measurements.

Improved time-delay lens modelling and H0 inference with transient sources

ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of H0 precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which, in turn plays a key role in breaking the mass-sheet degeneracy and constraining H0.

TDCOSMO

Strong lensing time delays can measure the Hubble constant H0 independently of any other probe. Assuming commonly used forms for the radial mass density profile of the lenses, a 2% precision has been achieved with seven Time-Delay Cosmography (TDCOSMO) lenses, in tension with the H0 from the cosmic microwave background. However, without assumptions on the radial mass density profile – and relying exclusively on stellar kinematics to break the mass-sheet degeneracy – the precision drops to 8% with the current data obtained using the seven TDCOSMO lenses, which is insufficient to resolve the H0 tension. With the addition of external information from 33 Sloan Lens ACS (SLACS) lenses, the precision improves to 5% if the deflectors of TDCOSMO and SLACS lenses are drawn from the same population. We investigate the prospect of improving the precision of time-delay cosmography without relying on mass profile assumptions to break the mass-sheet degeneracy. Our forecasts are based on a previously published hierarchical framework. With existing samples and technology, 3.3% precision on H0 can be reached by adding spatially resolved kinematics of the seven TDCOSMO lenses. The precision improves to 2.5% with the further addition of kinematics for 50 nontime-delay lenses from SLACS and the Strong Lensing Legacy Survey. Expanding the samples to 40 time-delay and 200 nontime-delay lenses will improve the precision to 1.5% and 1.2%, respectively. Time-delay cosmography can reach sufficient precision to resolve the Hubble tension at 3–5σ, without assumptions on the radial mass profile of lens galaxies. By obtaining this precision with and without external datasets, we will test the consistency of the samples and enable further improvements based on even larger future samples of time-delay and nontime-delay lenses (e.g., from the Rubin, Euclid, and Roman Observatories).

Galaxy-lens determination of H0: constraining density slope in the context of the mass sheet degeneracy

Gravitational lensing offers a competitive method to measure H0 with the goal of 1% precision. A major obstacle comes in the form of lensing degeneracies, such as the mass sheet degeneracy (MSD), which make it possible for a family of density profiles to reproduce the same lensing observables but return different values of H0. The modeling process artificially selects one choice from this family, potentially biasing H0. The effect is more pronounced when the profile of a given lens is not perfectly described by the lens model, which will always be the case to some extent. To explore this, we quantify the bias and spread in H0 by creating quads from two-component mass models and fitting them with a power-law ellipse+shear model. We find that the bias does not correspond to the estimate one would calculate by transforming the profile into a power law near the image radius. We also emulate the effect of including stellar kinematics by performing fits where the slope is constrained to the true value. Informing the fit using the true value near the image radius can introduce substantial bias (0–23% depending on the model). We confirm using Jeans arguments that kinematic constraints can result in a biased value of H0, though the degree of bias depends on the region kinematic modeling probes in specific lenses. We conclude that lensing degeneracies manifest through commonplace modeling approaches in a more complicated way than is assumed in the literature. If stellar kinematics incorrectly break the MSD, their inclusion may introduce more bias than their omission.

Extended lens reconstructions with grale: exploiting time-domain, substructural, and weak lensing information

ABSTRACT The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to ‘overfocusing’ the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspired by previous reconstructions of the cluster of galaxies MACS J1149.6+2223, where a multiply imaged background galaxy contained a supernova, SN Refsdal, of which four additional images were produced by the presence of a smaller cluster galaxy. The inversion for the cluster as a whole was not able to recover sufficient detail interior to this quad. We show how constraints on such different scales, from the entire cluster to a single member galaxy, can now be used, allowing such small-scale substructures to be resolved. Finally, the addition of weak lensing information to this method is investigated. While this clearly helps recover the environment around the strong lensing region, the mass sheet degeneracy may make a full strong and weak inversion difficult, depending on the quality of the ellipticity information at hand. We encounter ring-like structure at the boundary of the two regimes, argued to be the result of combining strong and weak lensing constraints, possibly affected by degeneracies.

Lessons from a blind study of simulated lenses: image reconstructions do not always reproduce true convergence

ABSTRACT In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind tests of lens reconstruction with simulated data are needed for validation. In this paper, we present a systematic blind study of a sample of 15 simulated strong gravitational lenses from the EAGLE suite of hydrodynamic simulations. We model these lenses with a free-form technique and evaluate reconstructed mass distributions using criteria based on shape, orientation, and lensed image reconstruction. Especially useful is a lensing analogue of the Roche potential in binary star systems, which we call the lensing Roche potential. This we introduce in order to factor out the well-known problem of steepness or mass-sheet degeneracy. Einstein radii are on average well recovered with a relative error of ${\sim }5{{\ \rm per\ cent}}$ for quads and ${\sim }25{{\ \rm per\ cent}}$ for doubles; the position angle of ellipticity is on average also reproduced well up to ±10°, but the reconstructed mass maps tend to be too round and too shallow. It is also easy to reproduce the lensed images, but optimizing on this criterion does not guarantee better reconstruction of the mass distribution.

The Projected Dark and Baryonic Ellipsoidal Structure of 20 CLASH Galaxy Clusters*

Abstract We reconstruct the two-dimensional (2D) matter distributions in 20 high-mass galaxy clusters selected from the CLASH survey by using the new approach of performing a joint weak gravitational lensing analysis of 2D shear and azimuthally averaged magnification measurements. This combination allows for a complete analysis of the field, effectively breaking the mass-sheet degeneracy. In a Bayesian framework, we simultaneously constrain the mass profile and morphology of each individual cluster, assuming an elliptical Navarro–Frenk–White halo characterized by the mass, concentration, projected axis ratio, and position angle (PA) of the projected major axis. We find that spherical mass estimates of the clusters from azimuthally averaged weak-lensing measurements in previous work are in excellent agreement with our results from a full 2D analysis. Combining all 20 clusters in our sample, we detect the elliptical shape of weak-lensing halos at the 5σ significance level within a scale of 2 . The median projected axis ratio is 0.67 ± 0.07 at a virial mass of , which is in agreement with theoretical predictions from recent numerical simulations of the standard collisionless cold dark matter model. We also study misalignment statistics of the brightest cluster galaxy, X-ray, thermal Sunyaev–Zel’dovich effect, and strong-lensing morphologies with respect to the weak-lensing signal. Among the three baryonic tracers studied here, we find that the X-ray morphology is best aligned with the weak-lensing mass distribution, with a median misalignment angle of . We also conduct a stacked quadrupole shear analysis of the 20 clusters assuming that the X-ray major axis is aligned with that of the projected mass distribution. This yields a consistent axis ratio of 0.67 ± 0.10, suggesting again a tight alignment between the intracluster gas and dark matter.