Lensing Galaxy Research Articles

Witt’s Hyperbola Is Both Predicted and Observed to Pass Close to the Lensing Galaxies in Quadruple Quasars

When a rectangular hyperbola is constructed from the image positions of a quadruply lensed quasar, as proposed by Witt, it passes very close to the lensing galaxy. The median measured perpendicular offset between the observed light center of the lens and Witt’s hyperbola is 0.″013 for a sample for 39 systems lensed by a relatively isolated galaxy. The family of lens models adopted by Witt predicts that the lens lies on the hyperbola, but its position is not used for its construction. The median offset corresponds to roughly 1% of the Einstein ring radius and suggests that the centers of the lensing potential are close to the light centers of the lens. By putting a restrictive prior on the perpendicular distance to Witt’s hyperbola (or on the distance between the galaxy and the potential), one reduces by one the dimensionality of a model space when fitting data. Taking the brightest pixel of a lensing galaxy as its center avoids a shortcoming of using the average light center for a constraint.

Cosmology with shear ratios: a joint study of weak lensing and spectroscopic redshift datasets

The ratio of the average tangential shear signal of different weak lensing source populations around the same lens galaxies, also known as a shear ratio, provides an important test of lensing systematics and a potential source of cosmological information. In this paper we measure shear ratios of three current weak lensing surveys –KiDS, DES, and HSC– using overlapping data from the Baryon Oscillation Spectroscopic Survey. We apply a Bayesian method to reduce bias in shear ratio measurement, and assess the degree to which shear ratio information improves the determination of important astrophysical parameters describing the source redshift distributions and intrinsic galaxy alignments, as well as cosmological parameters, in comparison with cosmic shear and full 3x2-pt correlations (cosmic shear, galaxy-galaxy lensing, and galaxy clustering). We consider both Fisher matrix forecasts, as well as full likelihood analyses of the data. We find that the addition of shear ratio information to cosmic shear allows the mean redshifts of the source samples and intrinsic alignment parameters to be determined significantly more accurately. Although the additional constraining power enabled by the shear ratio is less than that obtained by introducing an accurate prior in the mean source redshift using photometric redshift calibration, the shear ratio allows for a useful cross-check. The inclusion of shear ratio data consistently benefits the determination of cosmological parameters such as S_8, for which we obtain improvements up to 34%. However these improvements are less significant when shear ratio is combined with the full 3x2-pt correlations. We conclude that shear ratio tests will remain a useful source of cosmological information and cross-checks for lensing systematics, whose application will be further enhanced by upcoming datasets such as the Dark Energy Spectroscopic Instrument.

The mass profiles of dwarf galaxies from Dark Energy Survey lensing

ABSTRACT We present a novel approach to extracting dwarf galaxies from photometric data to measure their average halo mass profile with weak lensing. We characterize their stellar mass and redshift distributions with a spectroscopic calibration sample. By combining the ${\sim} 5000\,\mathrm{deg}^2$ multiband photometry from the Dark Energy Survey and redshifts from the Satellites Around Galactic Analogs Survey with an unsupervised machine learning method, we select a low-mass galaxy sample spanning redshifts $z\lt 0.3$ and divide it into three mass bins. From low to high median mass, the bins contain [146 420, 330 146, 275 028] galaxies and have median stellar masses of $\log _{10}(M_*/\text{M}_\odot)=\left[8.52\substack{+0.57 -0.76},\, 9.02\substack{+0.50 -0.64},\, 9.49\substack{+0.50 -0.58}\right]$ . We measure the stacked excess surface mass density profiles, $\Delta \Sigma (R)$, of these galaxies using galaxy–galaxy lensing with a signal-to-noise ratio of [14, 23, 28]. Through a simulation-based forward-modelling approach, we fit the measurements to constrain the stellar-to-halo mass relation and find the median halo mass of these samples to be $\log _{10}(M_{\rm halo}/\text{M}_\odot)$ = [$10.67\substack{+0.2 -0.4}$, $11.01\substack{+0.14 -0.27}$, $11.40\substack{+0.08 -0.15}$]. The cold dark matter profiles are consistent with NFW (Navarro, Frenk, and White) profiles over scales ${\lesssim} 0.15 \, {h}^{-1}$ Mpc. We find that ${\sim} 20$ per cent of the dwarf galaxy sample are satellites. This is the first measurement of the halo profiles and masses of such a comprehensive, low-mass galaxy sample. The techniques presented here pave the way for extracting and analysing even lower mass dwarf galaxies and for more finely splitting galaxies by their properties with future photometric and spectroscopic survey data.

A Survey of Dynamical and Gravitational Lensing Tests in Scale Invariance: The Fall of Dark Matter?

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977). In the way that the geometry of space–time can be described by the coefficients gμν, a gauging condition given by a scale factor λ(xμ) is needed to express the scaling. In general relativity (GR), λ=1. The “Large Number Hypothesis” was taken by Dirac and by Canuto et al. to fix λ. The condition that the macroscopic empty space is scale-invariant was further preferred (Maeder 2017a), the resulting gauge is also supported by an action principle. Cosmological equations and a modified Newton equation were then derived. In short, except in extremely low density regions, the scale-invariant effects are largely dominated by Newtonian effects. However, their cumulative effects may still play a significant role in cosmic evolution. The theory contains no “adjustment parameter”. In this work, we gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 M⊙< M <1014M⊙) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc). Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3. Last but not least, we investigate the effect of scale invariance on gravitational lensing. We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample. Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale.

A novel high-z submm galaxy efficient line survey in ALMA Bands 3 through 8 – an ANGELS pilot

ABSTRACT We use the Atacama Large sub/Millimetre Array (ALMA) to efficiently observe spectral lines across Bands 3, 4, 5, 6, 7, and 8 at high-resolution (0.5–0.1 arcsec) for 16 bright southern Herschel sources at $1.5 \lt z \lt 4.2$. With only six and a half hours of observations, we reveal 66 spectral lines in 17 galaxies. These observations detect emission from CO (3−2) to CO(18−17), as well as atomic ([C i](1−0), (2−1), [O i] 145 $\mu$m and [N ii] 205 $\mu$m) lines. Additional molecular lines are seen in emission (${\rm H_2O}$ and ${\rm H_2O^+}$) and absorption (OH$^+$ and CH$^+$). The morphologies based on dust continuum ranges from extended sources to strong lensed galaxies with magnifications between 2 and 30. CO line transitions indicate a diverse set of excitation conditions with a fraction of the sources ($\sim 35$ per cent) showcasing dense, warm gas. The resolved gas to star formation surface densities vary strongly per source, and suggest that the observed diversity of dusty star-forming galaxies could be a combination of lensed, compact dusty starbursts and extended, potentially merging galaxies. The predicted gas depletion time-scales are consistent with 100 Myr to 1 Gyr, but require efficient fuelling from the extended gas reservoirs onto the more central starbursts, in line with the Doppler-shifted absorption lines that indicate inflowing gas for two out of six sources. This pilot paper explores a successful new method of observing spectral lines in large samples of galaxies, supports future studies of larger samples, and finds that the efficiency of this new observational method will be further improved with the planned ALMA Wideband Sensitivity Upgrade.

Observational Test of f(Q) Gravity with Weak Gravitational Lensing

In this article we confront a class of f(Q) gravity models with observational data of galaxy–galaxy lensing. Specifically, we consider f(Q) gravity models containing a small quadratic correction when compared with general relativity (GR), and quantify this correction by a model parameter, α. To derive the observational constraints, we start by extracting spherically symmetric solutions, which correspond to deviations from the Schwarzschild solution that depends on the model parameters in a twofold way, i.e., a renormalized mass and a new term proportional to r −2. Then, we calculate the effective lensing potential, the deflection angle, the shear component, and the effective excess surface density profile. After that, we employ a group catalog and a shape catalog from the Sloan Digital Sky Survey Data Release 7 for the lens and source samples, respectively. Moreover, we handle the off-center radius as a free parameter and constrain it using a Markov Chain Monte Carlo method. Concerning the deviation parameter from GR we derive α=1.202−0.179+0.277×10−6Mpc−2 at the 1σ confidence level, and then compare the fitting efficiency with the standard Λ cold dark matter paradigm by applying the Akaike information criterion and Bayesian information criterion. Our results indicate that the f(Q) corrections alongside the off-center effect yield a scenario that is slightly favored.

The SLACS strong lens sample, debiased

Strong gravitational lensing observations can provide extremely valuable information on the structure of galaxies, but their interpretation is made difficult by selection effects, which, if not accounted for, introduce a bias between the properties of strong lens galaxies and those of the general population. A rigorous treatment of the strong lensing bias requires, in principle, to fully forward model the lens selection process. However, doing so for existing lens surveys is prohibitively difficult. With this work we propose a practical solution to the problem: using an empirical model to capture the most complex aspects of the lens finding process, and constraining it directly from the data together with the properties of the lens population. We applied this method to real data from the SLACS sample of strong lenses. Assuming a power-law density profile, we recovered the mass distribution of the parent population of galaxies from which the SLACS lenses were drawn. We found that early-type galaxies with a stellar mass of log M*/M⊙ = 11.3 and average size have a median projected mass enclosed within a 5 kpc aperture of log M5/M⊙ = 11.332 ± 0.013, and an average logarithmic density slope of γ = 1.99 ± 0.03. These values are respectively 0.02 dex and 0.1 lower than inferred when ignoring selection effects. According to our model, most of the bias is due to the prioritisation of SLACS follow-up observations based on the measured velocity dispersion. As a result, the strong lensing bias in γ reduces to ∼0.01 when controlling for stellar velocity dispersion.

Selection functions of strong lens finding neural networks

ABSTRACT We show that convolution neural networks (CNNs) trained to find strong gravitational lens systems are biased towards systems with larger Einstein radii and large concentrated sources. This selection function is key to fully realizing the potential of the large samples of strong gravitational lens systems that will be found in upcoming wide-field surveys. In this paper, we use a CNN and three training data sets to quantify the network selection function and its implication for the many scientific applications of strong gravitational lensing. We use CNNs with similar architecture as is commonly found in the literature. The networks preferentially select systems with larger Einstein radii and larger sources with more concentrated source-light distributions. Increasing the detection significance threshold to 12$\sigma$ from 8$\sigma$ results in 50 per cent of the selected strong lens systems having Einstein radii $\theta _\mathrm{E}$$\ge$ 1.04 arcsec from $\theta _\mathrm{E}$$\ge$ 0.879 arcsec, source radii $R_S$$\ge$ 0.194 arcsec from $R_S$$\ge$ 0.178 arcsec, and source Sérsic indices $n_{\mathrm{Sc}}^{\mathrm{S}}$$\ge$ 2.62 from $n_{\mathrm{Sc}}^{\mathrm{S}}$$\ge$ 2.55. The model trained to find lensed quasars shows a stronger preference for higher lens ellipticities than those trained to find lensed galaxies. The selection function is independent of the slope of the power law of the mass profiles, hence measurements of this quantity will be unaffected. The lens finder selection function reinforces that of the lensing cross-section, and thus we expect our findings to be a general result for all galaxy–galaxy and galaxy–quasar lens finding neural networks.

DiffLense: a conditional diffusion model for super-resolution of gravitational lensing data

Abstract Gravitational lensing data is frequently collected at low resolution due to instrumental limitations and observing conditions. Machine learning-based super-resolution techniques offer a method to enhance the resolution of these images, enabling more precise measurements of lensing effects and a better understanding of the matter distribution in the lensing system. This enhancement can significantly improve our knowledge of the distribution of mass within the lensing galaxy and its environment, as well as the properties of the background source being lensed. Traditional super-resolution techniques typically learn a mapping function from lower-resolution to higher-resolution samples. However, these methods are often constrained by their dependence on optimizing a fixed distance function, which can result in the loss of intricate details crucial for astrophysical analysis. In this work, we introduce DiffLense, a novel super-resolution pipeline based on a conditional diffusion model specifically designed to enhance the resolution of gravitational lensing images obtained from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). Our approach adopts a generative model, leveraging the detailed structural information present in Hubble space telescope (HST) counterparts. The diffusion model, trained to generate HST data, is conditioned on HSC data pre-processed with denoising techniques and thresholding to significantly reduce noise and background interference. This process leads to a more distinct and less overlapping conditional distribution during the model’s training phase. We demonstrate that DiffLense outperforms existing state-of-the-art single-image super-resolution techniques, particularly in retaining the fine details necessary for astrophysical analyses.

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.

Redshift evolution and covariances for joint lensing and clustering studies with DESI Y1

ABSTRACT Galaxy–galaxy lensing (GGL) and clustering measurements from the Dark Energy Spectroscopic Instrument Year 1 (DESI Y1) data set promise to yield unprecedented combined-probe tests of cosmology and the galaxy–halo connection. In such analyses, it is essential to identify and characterize all relevant statistical and systematic errors. We forecast the covariances of DESI Y1 GGL + clustering measurements and the systematic bias due to redshift evolution in the lens samples. Focusing on the projected clustering and GGL correlations, we compute a Gaussian analytical covariance, using a suite of N-body and lognormal simulations to characterize the effect of the survey footprint. Using the DESI one percent survey data, we measure the evolution of galaxy bias parameters for the DESI luminous red galaxy (LRG) and bright galaxy survey (BGS) samples. We find mild evolution in the LRGs in $0.4 < z < 0.8$, subdominant to the expected statistical errors. For BGS, we find less evolution for brighter absolute magnitude cuts, at the cost of reduced sample size. We find that for a redshift bin width $\Delta z = 0.1$, evolution effects on DESI Y1 GGL is negligible across all scales, all fiducial selection cuts, all fiducial redshift bins. Galaxy clustering is more sensitive to evolution due to the bias squared scaling. Nevertheless the redshift evolution effect is insignificant for clustering above the 1-halo scale of $0.1h^{-1}$ Mpc. For studies that wish to reliably access smaller scales, additional treatment of redshift evolution is likely needed. This study serves as a reference for GGL and clustering studies using the DESI Y1 sample.

Gravitational lensing of gravitational waves: prospects for probing intermediate-mass black holes in galaxy lenses with global minima image

ABSTRACT This work studies microlensing effects in strongly lensed gravitational wave (GW) signals corresponding to global minima images in galaxy-scale lenses. We find that stellar microlenses alone are unable to introduce noticeable wave effects in the global minima GW signals at strong lensing magnification $( {\mu})\lt 50$ with match value between unlensed and lensed GW signals being above ${\sim }99.5~{{\ \rm per \, cent}}$ in ${\sim }90~{{\ \rm per \, cent}}$ of systems implying that GW signals corresponding to global minima can be treated as reference signal to determine the amount of microlensing in other strongly lensed counterparts. Since the stellar microlenses introduce negligible wave effects in global minima, they can be used to probe the intermediate-mass black hole (IMBH) lenses in the galaxy lens. We show that the presence of an IMBH lens with mass in the range $[50,10^3]~{\rm M_\odot }$ such that the global minima lies within five Einstein radius of it, the microlensing effects at $f\lt 10^2$ Hz are mainly determined by the IMBH lens for ${\mu} \lt 50$. Assuming that a typical strong lensing magnification of 3.8 and high enough signal-to-noise ratio (in the range ${\simeq }[10, 30]$) to detect the microlensing effect in GW signals corresponding to global minima, with non-detection of IMBH-led microlensing effects in ${\simeq }15~({\simeq }150)$ lensed GW signals, we can rule out dark matter fraction $\gt 10~{{\ \rm per \, cent}}~(\gt 1~{{\ \rm per \, cent}})$ made of IMBH population inside galaxy lenses with mass values $\gt 150~{\rm M_\odot }$ with ${\sim }$90 per cent confidence. Although we have specifically used IMBHs as an example, the same analysis applies to any subhalo (or compact objects) with lensing masses (i.e. the total mass inside Einstein radius) satisfying the above criterion.

Spectroscopic determination of velocity dispersion lens galaxies and their impact on the measurement of the post-Newtonian parameter

Este estudo se dedica a realizar medições precisas da dispersão de velocidades das galáxias lentes, utilizando dados obtidos pelo telescópio SOuthern Astrophysical Research (SOAR) durante o ano de 2022. A partir da análise de 10 espectros de galáxias, obtivemos estimativas fundamentais das suas dispersões de velocidade. Este trabalho oferece medições cruciais que serão utilizadas em colaboração com pesquisadores do Centro Brasileiro de Pesquisas Físicas para inferir o parâmetro pós-Newtoniano γ. Esta parceria visa aprimorar a precisão das futuras estimativas desse parâmetro, contribuindo significativamente para a compreensão das leis fundamentais da gravidade em escalas galácticas por meio do método de comparação de massas, ao comparar a massa dinâmica das lentes gravitacionais galácticas, independente de γ, com a massa obtida através da modelagem das lentes, a qual depende de γ.

X-Ray View of Little Red Dots: Do They Host Supermassive Black Holes?

The discovery of Little Red Dots (LRDs)—a population of compact, high-redshift, dust-reddened galaxies—is one of the most surprising results from JWST. However, the nature of LRDs is still debated: does the near-infrared emission originate from accreting supermassive black holes (SMBHs), or intense star formation? In this work, we utilize ultra-deep Chandra observations and study LRDs residing behind the lensing galaxy cluster, A2744. We probe the X-ray emission from individual galaxies but find that they remain undetected and provide SMBH mass upper limits of ≲(1.5–16) × 106 M ⊙ assuming Eddington limited accretion. To increase the signal-to-noise ratios, we conduct a stacking analysis of the full sample with a total lensed exposure time of ≈87 Ms. We also bin the galaxies based on their stellar mass, lensing magnification, and detected broad-line Hα emission. For the LRDs exhibiting broad-line Hα emission, there is a hint of a stacked signal (∼2.6σ), corresponding to an SMBH mass of ∼3.2 × 106 M ⊙. Assuming unobscured, Eddington-limited accretion, this black hole (BH) mass is at least 1.5 orders of magnitude lower than that inferred from virial mass estimates using JWST spectra. Given galaxy-dominated stellar mass estimates, our results imply that LRDs do not host overmassive SMBHs and/or accrete at a few percent of their Eddington limit. However, alternative stellar mass estimates may still support that LRDs host overmassive BHs. The significant discrepancy between the JWST and Chandra data hints that the scaling relations used to infer the SMBH mass from the Hα line and virial relations may not be applicable for high-redshift LRDs.

Galaxy–Galaxy Lensing Data: f(T) Gravity Challenges General Relativity

We use galaxy–galaxy lensing data to test general relativity and f(T) gravity at galaxy scales. We consider an exact spherically symmetric solution of f(T) theory, which is obtained from an approximate quadratic correction, and thus it is expected to hold for every realistic deviation from general relativity. Quantifying the deviation by a single parameter Q, and following the post-Newtonian approximation, we obtain the corresponding deviation in the gravitational potential, shear component, and effective excess surface density profile. We used five stellar mass samples and divided them into blue and red galaxies to test the model dependence on galaxy color, and we modeled the excess surface density profiles using the Navarro–Frenk–White profiles. Based on the group catalog from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) we finally extract Q=−2.138−0.516+0.952×10−5 Mpc−2 at 1σ confidence. This result indicates that f(T) corrections on top of general relativity are favored. Finally, we apply information criteria, such as the Akaike and Bayesian ones, and although the dependence of f(T) gravity on the off-center effect implies that its optimality needs to be carefully studied, our analysis shows that f(T) gravity is more efficient in fitting the data compared to general relativity and the ΛCDM paradigm, and thus it offers a challenge to the latter.

Unveiling lens light complexity with a novel multi-Gaussian expansion approach for strong gravitational lensing

ABSTRACT In a strong gravitational lensing system, the distorted light from a source is analysed to infer the properties of the lens. However, light emitted by the lens itself can contaminate the image of the source, introducing systematic errors in the analysis. We present a simple and efficient lens light model based on the well-tested multi-Gaussian expansion (MGE) method for representing galaxy surface brightness profiles, which we combine with a semi-linear inversion scheme for pixelized source modelling. Testing it against realistic mock lensing images, we show that our scheme can fit the lensed images to the noise level, with relative differences between the true input and best-fitting lens light model remaining below 5 per cent. We apply the MGE lens light model to 38 lenses from the HST SLACS sample. We find that the new scheme provides a good fit for the majority of the sample with only 3 exceptions – these show clear asymmetric residuals in the lens light. We examine the radial dependence of the ellipticity and position angles and confirm that it is common for a typical lens galaxy to exhibit twisting non-elliptical isophotes and boxy / disky isophotes. Our MGE lens light model will be a valuable tool for understanding the hidden complexity of the lens mass distribution.

Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.

Elucidating galaxy population properties using a model-free analysis of quadruply imaged quasar lenses from large surveys

ABSTRACT The population of strong lensing galaxies is a subset of intermediate-redshift massive galaxies, whose population-level properties are not yet well understood. In the near future, thousands of multiply imaged systems are expected to be discovered by wide-field surveys like Rubin Observatory’s Legacy Survey of Space and Time and Euclid. With the soon-to-be robust population of quadruply lensed quasars, or quads, in mind, we introduce a novel technique to elucidate the empirical distribution of the galaxy population properties. Our re-imagining of the prevailing strong lensing analysis does not fit mass models to individual lenses, but instead starts with parametric models of many galaxy populations, which include generally ignored mass distribution complexities and exclude external shear for now. We construct many mock galaxy populations with different properties and obtain populations of quads from each of them. The mock ‘observed’ population of quads is then compared to those from the mocks using a model-free analysis based on a three-dimensional subspace of directly observable quad image properties. The distance between two quad populations in the space of image properties is measured by a metric $\eta$, and the distance between their parent galaxy populations in the space of galaxy properties is measured by $\zeta$. We find a well-defined relation between $\eta$ and $\zeta$. The discovered relation between the space of image properties and the space of galaxy properties allows for the observed galaxy population properties to be estimated from the properties of their quads, which will be conducted in a future paper.

The dark energy survey: detection of weak lensing magnification of supernovae and constraints on dark matter haloes

ABSTRACT The residuals of the distance moduli of Type Ia supernovae (SNe Ia) relative to a Hubble diagram fit contain information about the inhomogeneity of the Universe, due to weak lensing magnification by foreground matter. By correlating the residuals of the Dark Energy Survey Year 5 SN Ia sample (DES-SN5YR) with extragalactic foregrounds from the DES Y3 Gold catalogue, we detect the presence of lensing at $6.0 \sigma$ significance. This is the first detection with a significance level above $5\sigma$. Constraints on the effective mass-to-light ratios and radial profiles of dark matter haloes surrounding individual galaxies are also obtained. We show that the scatter of SNe Ia around the Hubble diagram is reduced by modifying the standardization of the distance moduli to include an easily calculable de-lensing (i.e. environmental) term. We use the de-lensed distance moduli to recompute cosmological parameters derived from SN Ia, finding in Flat wcold dark matter a difference of $\Delta \Omega _{\rm M} = +0.036$ and $\Delta w = -0.056$ compared to the unmodified distance moduli, a change of $\sim 0.3\sigma$. We argue that our modelling of SN Ia lensing will lower systematics on future surveys with higher statistical power. We use the observed dispersion of lensing in DES-SN5YR to constrain $\sigma _8$, but caution that the fit is sensitive to uncertainties at small scales. Nevertheless, our detection of SN Ia lensing opens a new pathway to study matter inhomogeneity that complements galaxy–galaxy lensing surveys and has unrelated systematics.

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.