Galaxy-scale strong lensing is a powerful tool in Astrophysics and Cosmology, enabling studies of massive galaxies’ internal structure, their formation and evolution, stellar initial mass function, and cosmological parameters. In this conference proceeding, we highlight key findings from the past decade in astrophysical applications of strong lensing at the galaxy scale. We then briefly summarize the present status of discovery and analyses of new samples from recent or ongoing surveys. Finally, we offer insights into anticipated developments in the upcoming era of big data shaping the future of this field, thanks to the Rubin, Euclid, and Roman observatories.

The distribution of mass in galaxy-scale strong gravitational lenses is often modelled as an elliptical power law plus ‘external shear’, which notionally accounts for line-of-sight galaxies and cosmic shear. We argue that it does not, using three lines of evidence from the analysis of 54 galaxy-scale strong lenses: (i) strong lensing external shears do not correlate with weak lensing; (ii) the measured shear magnitudes in strong lenses (which are field galaxies) are too large (exceeding 0.05) for their environment and; (iii) the external shear position angle preferentially aligns or anti-aligns with the mass model position angle, indicating an internal origin. We argue the measured strong lensing shears are therefore systematically accounting for missing complexity in the canonical elliptical power-law mass model. If we can introduce this complexity into our lens models, this will further lensing studies of galaxy formation, dark matter and Cosmology.

Current searches for galaxy-scale strong lenses focus on massive Luminous Red Galaxies but tend to overlook late-type lenses, in part because of their smaller Einstein radii. We take advantage of the superb seeing of the UNIONS survey in the r-band to perform an imaging search for edge-on late-type lenses. We use Convolutional Neural Networks trained with simulated observations composed of images of real galaxies from UNIONS and real sources from HST. Using 3600 square degrees of the survey we test ∼7 million galaxies and find 56 systems with obvious signs of lensing. In addition, we empirically estimate the true prevalence of lenses in UNIONS by visually inspecting 120,000 randomly chosen images in the survey. We find that the number of edge-on lenses we discover with CNNs is compatible with these estimates.

From various lensing and non-lensing observations, the total density profile in elliptical galaxies is well approximated by a power law mass distribution. However, as neither the dark matter nor the baryons individually follow the power law, this observational result has been referred to as the “bulge–halo conspiracy”. We investigate the consistency of this conspiracy with higher precision than previous studies with the largest ever sample of galaxy–galaxy lenses assembled from archival Hubble Space Telescope (HST) data. By performing lens modelling with power law profiles and combining them with stellar dynamics using the mass-sheet transformation, we can constrain the profile’s deviation from the power law model over a redshift range of 0.1 to 0.8. To uniformly model such a large sample of lens models, we use the automated modelling pipeline dolphin. We also investigate the evolutionary trend of the total mass density slope of the lensing galaxies.

Upcoming large-scale surveys like LSST are expected to uncover approximately 105 strong gravitational lenses within massive datasets. Traditional manual techniques are too time-consuming and impractical for such volumes of data. Consequently, machine learning methods have emerged as an alternative. In our prior work (Thuruthipilly et al. 2022), we introduced a self-attention-based machine learning model (transformers) for detecting strong gravitational lenses in simulated data from the Bologna Lens Challenge. These models offer advantages over simpler convolutional neural networks (CNNs) and competitive performance compared to state-of-the-art CNN models. We applied this model to the datasets from Bologna Lens Challenge 1 and 2 and simulated data on Euclid.

Galaxy-galaxy strong lensing (SL) systems provide a unique opportunity to test modified gravity theories. Deviations from General Relativity are encoded in the post-Newtonian parameter (γ). As a preparation for the upcoming data from the Vera Rubin Observatory Legacy Survey of Space and Time (LSST), our research group collected imaging data of SL systems from ground-based telescopes and conducted spectroscopic observations of 21 systems on the Southern Astrophysical Research (SOAR) Telescope to measure the lens velocity dispersions, σv. We briefly describe the semi-automated SL modelling of the systems in this sample and combine the results with σv from SOAR to derive an estimate for γ. Our preliminary results yield a value of $$\gamma= 1.17_{ - 0.33}^{ + 0.29}$$, which is consistent with General Relativity. Although the error bars are limited by the sample size, this result represents the first constraint on modified gravity obtained purely from ground-based data, with a sample completely independent from previous studies, and which allows for a self consistent end-to-end analysis.

Forthcoming data from the Vera Rubin Observatory, Euclid and Roman telescopes are expected to increase the number of strong lenses by two orders of magnitude. With current discovery methods these would be accompanied by an even greater number of false positives. In that context we find that using an ensemble of classifiers would provide a more complete sample of high-purity lenses and present methods to post-process the outputs of such classifiers to give reliable probabilities that a given image contains a lens.

The gravitational lensing signal produced by a galaxy or a galaxy cluster is determined by its total matter distribution, providing us with a way to directly constrain their dark matter content. State-of-the-art numerical simulations successfully reproduce many observed properties of galaxies and can be used as a source of mock observations and predictions. Many gravitational lensing studies aim at constraining the nature of dark matter, discriminating between cold dark matter and alternative models. However, many past results are based on the comparison to simulations that did not include baryonic physics. Here we show that the presence of baryons can significantly alter the predictions: we look at the structural properties (profiles and shapes) of elliptical galaxies and at the inner density slope of subhaloes. Our results demonstrate that future simulations must model the interplay between baryons and alternative dark matter, to generate realistic predictions that could significantly modify the current constraints.

Strong gravitational lensing by galaxies provides us with a powerful laboratory for testing dark matter models. Various particle models for dark matter give rise to different small-scale distributions of mass in the lens galaxy, which can be differentiated with sensitive observations. Th. The sensitivity of a gravitational lens observation to the presence (or absence) of low-mass dark structures in the lens galaxy is determined mainly by the angular resolution of the instrument and the spatial structure of the source. Here, I discuss results from the analysis of a global VLBI observation of a gravitationally lensed radio jet. With an angular resolution better than 5 milli-arcseconds and a highly extended, spatially resolved source, we are able to place competitive constraints on the particle mass in fuzzy dark matter models using this single observation. I also discuss preliminary results from our analysis of warm dark matter models using this lens system.

While the direct detection of the dark-matter particle remains very challenging, the physical properties of dark matter could potentially be constrained indirectly – by comparing the population characteristics of substructures in real galaxies with predictions from the phenomenological dark-matter models, such as cold, warm or self-interacting dark matter. Whereas these models are practically indistinguishable with respect to the expected abundance and statistical properties of massive galactic substructures, the critical difference lies in the low-mass regime ≲ 108M⊙. Galaxy-galaxy strong gravitational lensing provides a unique opportunity to search for gravitational signatures of such low-mass substructures in galaxies acting as a strong gravitational lens on a more distant background galaxy, serendipitously located along the same line of sight. In [Bayer et∼al.(2023)Bayer, Chatterjee, Koopmans, Vegetti, McKean, Treu, Fassnacht, and Glazebrook, Bayer et∼al.(2023)Bayer, Koopmans, McKean, Vegetti, Treu, Fassnacht, and Glazebrook, Bayer et∼al.(2023)Bayer, Vernardos, and Koopmans], we have recently introduced a novel approach to investigate the collective perturbative effect of low-mass substructures in the inner regions of massive elliptical lens galaxies and observationally constrain their power spectrum (on 1-10 kpc scales) based on the Fourier analysis of the associated surface-brightness anomalies in the lensed images (i.e., Einstein rings and gravitational arcs) observed with the Hubble Space Telescope. Here, we present a concise summary of the methodology, the encountered modelling challenges and the inferred observational constraints on the sub-galactic matter power spectrum. The future comparison of these results with predictions from hydrodynamical simulations might either verify the cold-dark-matter paradigm or require its substantial revision. Moreover, we demonstrate that the grid-based smooth lens modelling might model away surface-brightness anomalies caused by the presence of substructures in the lens galaxy and incorrectly interpret them as surface-brightness structure in the lensed background galaxy itself. If not properly understood and accounted for, such signal suppression might lead to severely biased constraints on the properties of substructures in galactic haloes.

In gravitational imaging, the mass model for the main lensing galaxy is one of the main sources of systematic uncertainty. We use subhalo detection models with increasing levels of angular complexity in the lens mass model to analyse 100 HST mock observations. We find that perturbations of just 1% are enough to cause a 20% false positive subhalo detection rate, with order 3 multipoles having the strongest effect. The area in an observation where a substructure can be detected drops by a factor of 10 if multipoles up to 3 per cent amplitude are included in the lens model. The mass of the smallest detectable substructure however is not affected. We find a detection limit of M>108.2 M⊙ at 5σ in all models. In order for strong lensing searches for dark matter objects to remain reliable in the future, angular structure beyond the elliptical power-law must be included.

Over the last two decades, strong gravitational lensing has emerged as a potential method for studying the nature and distribution of dark matter on sub-galactic scales. In addition to the main lens substructure, line-of-sight dark matter haloes contribute greatly to the subtle perturbations of lensed images. Line-of-sight haloes, unlike dark matter subhaloes, imprint distinct anisotropic and quadrupole signatures in the maps that depict the divergence and curl of the effective deflection field, respectively, giving rise to quadrupole moments of the image-plane averaged two-point correlation function of these maps. In terms of central density evolution and dark matter halo distribution, the shapes and amplitudes of the two-point function multipoles alter dramatically in the presence of warm dark matter and self-interacting dark matter. This method, in conjunction with upcoming large-scale surveys, provides the prospect of improving the constraints on dark matter at a critical time in strong gravitational lensing research.

We present high-precision strong lensing models for the galaxy clusters MACS J0416.1–0403 at z=0.396 and Abell 2744 at z=0.307. The models are constrained by two of the largest data-sets of secure multiple images ever used in lensing. These are identified from the photometric images observed by the Hubble space telescope and JWST in combination with spectroscopic data obtained by the Multi-Unit Spectroscopic Explorer at the Very Large Telescope. The same spectro-photometric data are used to create pure and complete samples of cluster member galaxies. Our models allow an extremely precise estimation of the cluster total mass distribution and produce accurate magnification maps that are fundamental to study the physical properties (mass, size, luminosity, etc.) of the lensed high-redshift galaxies.

Gravitational lensing in clusters of galaxies is one of the most powerful methods to probe the dark matter mass distribution inside such systems, after mapping the baryonic component, and test the currently accepted ɅCDM cosmological paradigm. With the advent of new high-resolution facilities such as the JWST, strong lensing (SL) is capable of providing extremely accurate mass measurements in the densest regions of such structures. Weak lensing (WL) provides complementary information by measuring the total mass distribution in the outskirts of galaxy clusters, where no multiple images of background sources are produced.

In my talk, I will present updates on the WL mass reconstruction of the Frontier Fields galaxy cluster Abell 2744 (z = 0.308) based on Subaru, Magellan, and JWST data, and I will show how the results obtained, combined with accurate SL modeling of this lens, provide a consistent picture of the cluster total mass distribution. I will discuss the pipeline used for this work, the extensive checks performed on the different datasets and the scientific results obtained. Being composed of several substructures undergoing a merging process, the complex geometry of this cluster makes it an ideal laboratory to verify the consistency and reliability of the results obtained with the two methods. I will compare the predictions of the SL models extrapolated in the outer regions of the cluster with the non-parametric WL mass reconstruction to look for potential systematic effects affecting the SL analysis.

Galaxy-galaxy strong lensing in galaxy clusters is a unique tool for studying the subhalo mass distribution, as well as for testing predictions from cosmological simulations. We describe a novel method that simulates realistic lensed features embedded inside the complexity of observed data by exploiting high-precision cluster lens models. Such methodology is used to build a large dataset with which Convolutional Neural Networks have been trained to identify strong lensing events in galaxy clusters. In particular, we inject lensed sources around cluster members using the images acquired by the Hubble Space Telescope. The resulting simulated mock data preserve the complexity of observation by taking into account all the physical components that could affect the morphology and the luminosity of the lensing events. The trained networks achieve a purity-completeness level of ∼ 91% in detecting such events. The methodology presented can be extended to other data-intensive surveys carried out with the next-generation facilities.

Strong lensing galaxy clusters provide a powerful observational test of Cold Dark Matter (CDM) structure predictions derived from simulation. Specifically, the shape and relative alignments of the dark matter halo, stars, and hot intracluster gas tells us the extent to which theoretical structure predictions hold for clusters in various dynamical states. We measure the position angles, ellipticities, and locations/centroids of the brightest cluster galaxy (BCG), intracluster light (ICL), the hot intracluster medium (ICM), and the core lensing mass for a sample of strong lensing galaxy clusters from the SDSS Giant Arcs Survey (SGAS). We use iterative elliptical isophote fitting methods and GALFIT modeling on HST WFC3/IR imaging data to extract ICL and BCG information and use CIAO’s Sherpa modeling on Chandra ACIS-I X-ray data to make measurements of the ICM. Using this multicomponent approach, we attempt to constrain the physical state of these strong lensing clusters and evaluate the different observable components in terms of their ability to trace out the gravitational potential of the cluster.

The MAximum-entropy ReconStruction (MARS) method is a free-form strong-lensing (SL) reconstruction algorithm, which adopts the maximum cross-entropy as a regularization. MARS shows remarkable convergence of multiple images in both source (∼0.”02) and image planes (∼0.”05 – 0.”1) while suppressing spurious fluctuations. Although the reconstruction requires a large number of free parameters exceeding ∼19,000, our implementation through PyTorch can obtain the reconstruction within hours. From our test using the publicly available synthetic clusters, we have verified that the reconstructed radial mass profiles are consistent with the truth within 1 percent. This makes MARS one of the best-performing SL reconstruction methods. We apply MARS to the six Hubble Frontier Fields clusters and present new mass reconstruction results. We also reconstruct a mass model of Abell 2744 using both weak-lensing (WL) and SL data from the JWST observations, with the largest dataset of Abell 2744, including 286 SL multiple images and ∼350 arcmin−2 WL constraints.

Gravitationally lensed supernovae (SNe) are rare and valuable probes of astrophysics and cosmology. While only seven lensed SNe have currently been discovered, these numbers are predicted to increase by orders of magnitudes with future transient surveys such as the Legacy Survey of Space and Time (LSST). These proceedings describe the ongoing live search with the Zwicky Transient Facility (ZTF), including the discovery of SN ‘Zwicky’: a lensed SN found in a remarkably low-mass lens galaxy. Finally, we look ahead at predictions for detecting lensed SNe with LSST.

Rare systems with multiple sources strongly lensed by a single galaxy provide the most robust way to explore the geometry of the Universe and to study the inner mass structure of lens galaxies. We present here a study of the SDSS J0100+1818 deflector, analyzing its total and baryonic mass distributions. The system comprises an ultra-massive early-type galaxy, surrounded by ten multiple images of three background sources. Exploiting high-resolution HST photometry and VLT/X-shooter spectroscopy we conduct a strong lensing analysis with the software GLEE to reconstruct the complex surface brightness distributions of the background sources over approximately 7200 HST pixels. These results are presented in our recent paper, Bolamperti et al. (2023). Finally, we present some preliminary results from new VLT/MUSE observations, that will allow us to build a new strong lensing+dynamics joint model and measure the values of the total matter density and of the cosmological constant parameters, Ωm and ΩΛ.

Thanks to forthcoming large-scale surveys, a tremendous number of strong lenses will be discovered in the coming years. The gain in accuracy on H0 from such a large population of lensed quasars is a key question for the future of time-delay cosmography. In such context, lensed systems will have to be modeled in an automated way, with models that are sufficiently generic to apply to every lens. I explore the biases that may arise from unaccounted-for azimuthal structures in mass models. The non-modeled twists in lensing galaxies are expected to bias the shear inference but not H0. Disregarded ellipticity gradients, boxyness and discyness may impact the cosmological inference on a lens-by-lens basis. Nevertheless, the diversity of azimuthal mass profile in lenses balances the bias at a population level and the H0 inference can thus benefits from such large surveys.