Strong Lensing Research Articles

Revealing dark matter dress of primordial black holes by cosmological lensing

Stellar-mass primordial black holes (PBHs) from the early Universe can directly contribute to the gravitational wave (GW) events observed by LIGO, but can only comprise a subdominant component of the dark matter (DM). The primary DM constituent will generically form massive halos around seeding stellar-mass PBHs. We demonstrate that gravitational lensing of sources at cosmological (≳Gpc) distances can directly explore DM halo dresses engulfing PBHs, challenging for lensing of local sources in the vicinity of Milky Way. Strong lensing analysis of fast radio bursts detected by CHIME survey already starts to probe parameter space of dressed stellar-mass PBHs, and upcoming searches can efficiently explore dressed PBHs over ∼10−105M⊙ mass-range and provide a stringent test of the PBH scenario for the GW events. Our findings establish a general test for a broad class of DM models with stellar-mass PBHs, including those where QCD axions or WIMP-like particles comprise predominant DM. The results open a new route for exploring dressed PBHs with various types of lensing events at cosmological distances, such as supernovae and caustic crossings.

Apparent luminosity and pulsed fraction affected by gravitational lensing of accretion columns in bright X-ray pulsars

ABSTRACT The luminosity of X-ray pulsars is their key parameter determining the geometry and physical conditions of the accretion flow both on the spatial scales of a binary system and on much smaller scales of emitting regions located close to the stellar surface. Traditionally, the luminosity of X-ray pulsars is estimated out of the X-ray energy flux averaged over the pulsed period and the estimated distance to the source. Due to the anisotropy of X-ray emission, the luminosity estimated on the base of the observed pulse profile can differ from the actual one. Super-cw2ritical X-ray pulsars with accretion columns are of particular interest because the X-ray flux from columns is a matter of strong gravitational lensing by a neutron star. Using toy model of an accretion column, we simulate beam patterns in super-critical X-ray pulsars, construct theoretical pulse profiles for different geometries and mutual orientations of pulsars and distant observers and show that despite strong light bending, the typical deviation of the apparent luminosity from the actual one is $\sim 20~{{\ \rm per \, cent}}$ only, and in $\sim 90~{{\ \rm per \, cent}}$ of cases, the apparent luminosity 0.8L ≲ Lapp ≲ 1.25L. However, the shape of the pulse profiles is strongly affected by the geometry of the emitting region. We show that the appearance and growth of accretion columns tend to be accompanied by an increase of observed pulsed fraction, which is in agreement with the recent observations of bright X-ray transients.

Anisotropic strong lensing as a probe of dark matter self-interactions

ABSTRACT Galaxy-scale strongly lensed systems have been shown to provide a unique technique for exploring the underlying physics of dark matter at sub-galactic scales. In the past, much attention was given to detecting and studying individual haloes in a strong lens system. In addition to the subhaloes, line-of-sight haloes contribute significantly to the small perturbations in lensed images. In prior work, we demonstrated that these line-of-sight haloes imprint a distinctive anisotropic signature and hence give rise to a detectable non-zero parity-even quadrupole moment in the effective convergence field’s two-point correlation function. In this study, we show that these line-of-sight haloes also produce a non-zero curl component of the effective deflection field with a parity-odd quadrupole moment of the two-point function. These multipole moments have the ability to statistically separate line-of-sight haloes from dark matter substructure. In this paper, we examine how these multipole moments evolve in the presence of warm dark matter and self-interacting dark matter in terms of central density evolution and dark matter halo abundance. Importantly, we show that these different multipole moments display exquisite sensitivity to both the amplitude and the velocity dependence of the dark matter self-interaction cross-section. Our approach opens the door for strong lensing observations to probe dark matter self-interaction over a broad range of relative velocities.

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.

Probing the faint-end luminosity function of Lyman-alpha emitters at 3 <z< 7 behind 17 MUSE lensing clusters

Context.This paper presents a study of the galaxy Lyman-alpha luminosity function (LF) using a large sample of 17 lensing clusters observed by the Multi Unit Spectroscopic Explorer (MUSE) at the ESO Very Large Telescope (VLT). The magnification resulting from strong gravitational lensing by clusters of galaxies and MUSE spectroscopic capabilities allows for blind detections of LAEs without any photometric pre-selection, reaching the faint luminosity regime.Aims.The present work aims to constrain the abundance of Lyman-alpha emitters (LAEs) and quantify their contribution to the total cosmic reionization budget.Methods.We selected 600 lensed LAEs behind these clusters in the redshift range of 2.9 <z< 6.7, covering four orders of magnitude in magnification-corrected Ly-αluminosity (39.0 < log(L)[erg s−1] < 43.0). These data were collected behind lensing clusters, indicating an increased complexity in the computation of the LF to properly account for magnification and dilution effects. We applied a non-parametricVmaxmethod to compute the LF to carefully determine the survey volume where an individual source could have been detected. The method used in this work follows the recipes originally developed in previous works, with some improvements to better account for the effects of lensing when computing the effective volume.Results.The total co-moving volume at 2.9 < z < 6.7 in the present survey is ∼50 103Mpc3. Our LF points in the bright end (log(L) [erg s−1] > 42) are consistent with those obtained from blank field observations. In the faint luminosity regime, the density of sources is well described by a steep slope,α ∼ −2 for the global redshift range. Up to log(L) [erg s−1] ∼ 41, the steepening of the faint end slope with redshift, suggested in earlier works, is observed, but the uncertainties are still large. A significant flattening is observed towards the faintest end, for the highest redshift bins, namely, log(L)[erg s−1] < 41.Conclusions.When taken at face value, the steep slope at the faint-end causes the star formation rate density (SFRD) to dramatically increase with redshift, implying that LAEs could play a major role in the process of cosmic reionization. The flattening observed towards the faint end for the highest redshift bins still requires further investigation. This turnover is similar to the one observed for the UV LF atz ≥ 6 in lensing clusters, with the same conclusions regarding the reliability of current results. Improving the statistical significance of the sample in this low-luminosity high-redshift regime is a difficult endeavour that may lead to potentially valuable leads in understanding the process of reionization.

Exotic image formation in strong gravitational lensing by clusters of galaxies – IV. Elliptical NFW lenses and hyperbolic umbilics

ABSTRACT A source lying near a hyperbolic umbilic (HU) singularity leads to a ring-like image formation, constituting four images with high magnification factors and lying in a small region of the lens plane. Since (based on our earlier work) the observed number of HU image formations in cluster lenses is expected to increase in the future, it is timely to investigate them in more detail. Like fold and cusp singularities, HU also satisfies the magnification relation, i.e. the signed magnification sum of the four images equals zero. This work presents a detailed study of the HU magnification relation (Rhu) considering the elliptical Navarro–Frenk–White (eNFW) lens profile suitable for cluster scale dark matter haloes. Our results show that for an isolated eNFW lens, Rhu is more sensitive to ellipticity than its mass or concentration parameter. An ellipticity greater than 0.3 results in Rhu lying close to zero with a small scatter around it. A substructure near the HU image formation causes the average Rhu value to deviate from zero and increases the scatter, with the amount of deviation depending on the image type near which the substructure lies. However, a population of substructures in the lens plane (equivalent to the galaxies inside the cluster) does not significantly shift the average Rhu value from zero but increases the scatter around it. We find that Rhu ≃ 0 for HU image formation in the Abell 1703 cluster. Repeating this test in other clusters with HU formations can be a useful indicator of substructure in cluster haloes.

Research Progress of Galaxy-Galaxy Strong Lensing Observed by (Sub)millimeter Interferometer

The magnification effect provided by gravitational lensing overcomes the limitations of current observation instruments, allowing researchers to study faint objects at high redshift (z≈4). Over the last decades, the sample of strong lenses has been mostly confined to optical bands. With the advent of (sub)millimeter wide field extragalactic surveys, about 200 strong lenses have been discovered in (sub)millimeter bands. Observations with high resolution and sensitivity from ALMA, NOEMA, and SMA, coupled with the flux boost from strong lensing, provide new windows to study galaxies at high redshift. Many works have investigated topics such as star formation, interstellar medium, and dynamic properties. The main objective of this paper is to review the current research status of galaxy-galaxy lensing in (sub)millimeter bands from the perspectives of observation samples, modeling methods, and scientific applications.

Varstrometry for Off-nucleus and Dual Subkiloparsec Active Galactic Nuclei (VODKA): Investigating the Nature of SDSS J0823+2418 at z = 1.81, A Likely Lensed Quasar

Dual quasars at small physical separations are an important precursor phase of galaxy mergers, ultimately leading to the coalescence of the two supermassive black holes. Starting from a sample of dual and/or lensed quasar candidates discovered using astrometric jitter in Gaia data, we present a pilot case study of one of the most promising yet puzzling candidate dual quasars at cosmic noon (z ∼ 1.8). Using multiwavelength imaging and spectroscopy from X-ray to radio, we test whether the SDSS J0823+2418 system is two individual quasars in a bound pair at separation ∼0.″64, or instead a single quasar being gravitationally lensed by a foreground galaxy. We find consistent flux ratios (∼1.25−1.45) between the two sources in optical, near-IR (NIR), UV, and radio, and thus similar spectral energy distributions, suggesting a strong-lensing scenario. However, differences in the radio spectral index, as well as changing X-ray fluxes, hint at either a dual quasar with otherwise nearly identical properties or perhaps lensing-based time lag of ∼3 days paired with intrinsic variability. We find with lens mass modeling that the relative NIR positions and magnitudes of the two quasars and a marginally detected central galaxy are consistent with strong lensing. Archival Sloan Digital Sky Survey spectra likewise suggest a foreground absorber via Mg ii absorption lines. We conclude that SDSS J0823+2418 is likely a lensed quasar, and therefore that the VODKA sample contains a population of these lensed systems (perhaps as high as 50%) as well as dual quasars.

A persistent excess of galaxy-galaxy strong lensing observed in galaxy clusters

Context. Previous studies have revealed that the estimated probability of galaxy-galaxy strong lensing in observed galaxy clusters exceeds the expectations from the Λ cold dark matter cosmological model by one order of magnitude. Aims. We aim to understand the origin of this excess by analyzing a larger set of simulated galaxy clusters, and investigating how the theoretical expectations vary under different adopted prescriptions and numerical implementations of star formation and feedback in simulations. Methods. We performed a ray-tracing analysis of 324 galaxy clusters from the THREE HUNDRED project, comparing the GADGET-X and GIZMO-SIMBA runs. These simulations, which start from the same initial conditions, were performed with different implementations of hydrodynamics and galaxy formation models tailored to match different observational properties of the intracluster medium and cluster galaxies. Results. We find that galaxies in the GIZMO-SIMBA simulations develop denser stellar cores than their GADGET-X counterparts. Consequently, their probability for galaxy-galaxy strong lensing is higher by a factor of ∼3. This increment is still insufficient to fill the gap with observations as a discrepancy by a factor ∼4 still persists. In addition, we find that several simulated galaxies have Einstein radii that are too large compared to observations. Conclusions. We conclude that a persistent excess of galaxy-galaxy strong lensing exists in observed galaxy clusters. The origin of this discrepancy with theoretical predictions is still unexplained in the framework of the cosmological hydrodynamical simulations. This might signal a hitherto unknown issue with either the simulation methods or our assumptions regarding the standard cosmological model.

Streamlined lensed quasar identification in multiband images via ensemble networks

Quasars experiencing strong lensing offer unique viewpoints on subjects related to the cosmic expansion rate, the dark matter profile within the foreground deflectors, and the quasar host galaxies. Unfortunately, identifying them in astronomical images is challenging since they are overwhelmed by the abundance of non-lenses. To address this, we have developed a novel approach by ensembling cutting-edge convolutional networks (CNNs) - for instance, ResNet, Inception, NASNet, MobileNet, EfficientNet, and RegNet – along with vision transformers (ViTs) trained on realistic galaxy-quasar lens simulations based on the Hyper Suprime-Cam (HSC) multiband images. While the individual model exhibits remarkable performance when evaluated against the test dataset, achieving an area under the receiver operating characteristic curve of >97.3% and a median false positive rate of 3.6%, it struggles to generalize in real data, indicated by numerous spurious sources picked by each classifier. A significant improvement is achieved by averaging these CNNs and ViTs, resulting in the impurities being downsized by factors up to 50. Subsequently, combining the HSC images with the UKIRT, VISTA, and unWISE data, we retrieve approximately 60 million sources as parent samples and reduce this to 892 609 after employing a photometry preselection to discover z > 1.5 lensed quasars with Einstein radii of θE < 5″. Afterward, the ensemble classifier indicates 3080 sources with a high probability of being lenses, for which we visually inspect, yielding 210 prevailing candidates awaiting spectroscopic confirmation. These outcomes suggest that automated deep learning pipelines hold great potential in effectively detecting strong lenses in vast datasets with minimal manual visual inspection involved.

Much ado about no offset – characterizing the anomalous multiple-image configuration and the model-driven displacement between light and mass in the multiplane strong lens Abell 3827

ABSTRACT Abell 3827 is a unique galaxy cluster with a dry merger in its core causing a highly resolved multiple-image configuration of a blue spiral galaxy at zs = 1.24. The surface brightness profiles of four merging galaxies around zd = 0.099 complicate a clear identification of the number of images and finding corresponding small-scale features across them. The entailed controversies about offsets between luminous and dark matter have never been settled and dark matter characteristics in tension with bounds from complementary probes and simulations seemed necessary to explain this multiple-image configuration. We resolve these issues with a systematic study of possible feature matchings across all images and their impact on the reconstructed mass density distribution. From the local lens properties directly constrained by these feature matchings without imposing any global lens model, we conclude that none of them are consistent with expected local characteristics from standard single-lens-plane lensing, nor can they be motivated by the light distribution in the cluster. Inspecting complementary spectroscopic data, we show that all these results originate from an insufficient constraining power of the data and seem to hint at a thick lens and not at exotic forms of dark matter or modified gravity. If the thick-lens hypothesis can be corroborated with follow-up multiplane lens modelling, A3827 suffers from a full three-dimensional degeneracy in the distribution of dark matter because combinations of shearings and scalings in a single lens plane can also be represented by an effective shearing and a rotation caused by multiple lens planes.

An Initial Analysis of a Strongly Lensed QSO Candidate Identified by LAMOST

From 2011 to 2021, LAMOST has released a total of 76,167 quasar data. We try to search for gravitationally lensed QSOs by limiting coordinate differences and redshift differences of these QSOs. The name, brightness, spectrum, photometry and other information of each QSO will be visually checked carefully. Special attention should be paid to check whether there are groups of galaxies, gravitationally lensed arcs, Einstein crosses, or Einstein rings near the QSOs. Through careful selection, we select LAMOST J160603.01+290050.8 (A) and LAMOST J160602.81+290048.7 (B) as a candidate and perform an initial analysis. Components A and B are 3.″36 apart and they display blue during photometric observations. The redshift values of components A and B are 0.2% different, their Gaia_g values are 1.3% different, and their ugriz values are 1.0% or less different. For the spectra covering from 3690 to 9100 Å, the emission lines of C ii, Mg, H γ, O iii, and H β are present for both components A and B and the ratio of flux(B) to flux(A) from LAMOST is basically a constant, around 2.2. However, no galaxies have been found between components A and B. Inada et al. identified them as binary quasars. But we accidentally find a galaxy group near components A and B. If the center of dark matter in the galaxy group is at the center between components A and B, components A and B are probably gravitationally lensed QSOs. We estimate that the Einstein mass is 1.46 × 1011 M ⊙ and the total mass of the lens is 1.34 × 1013 M ⊙. The deflection angle is 1.″97 at positions A and B and the velocity dispersion is 261 km s−1. Theoretically, this candidate could be a pair of fold images of a strong lensing system by a galaxy group, and we will investigate the possibility when the redshifts of nearby galaxies are available.

Strong lensing selection effects

Contact. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, αsps, defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards higher stellar masses, smaller half-mass radii, and higher dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of 0.5″, the strong lensing bias in αsps is 10%, while that in the central dark matter mass is 5%. The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. Time-delay measurements of H0 from lensed quasars can take advantage of prior information obtained from galaxy-galaxy lenses with similar Einstein radii.

The effect of the perturber population on subhalo measurements in strong gravitational lenses

ABSTRACT Analyses of extended arcs in strong gravitational lensing images to date have constrained the properties of dark matter by measuring the parameters of one or two individual subhaloes. However, since such analyses are reliant on likelihood-based methods like Markov-chain Monte Carlo or nested sampling, they require various compromises to the realism of lensing models for the sake of computational tractability, such as ignoring the numerous other subhaloes and line-of-sight haloes in the system, assuming a particular form for the source model and requiring the noise to have a known likelihood function. Here, we show that a simulation-based inference method called truncated marginal neural ratio estimation (TMNRE) makes it possible to relax these requirements by training neural networks to directly compute marginal posteriors for subhalo parameters from lensing images. By performing a set of inference tasks on mock data, we verify the accuracy of TMNRE and show it can compute posteriors for subhalo parameters marginalized over populations of hundreds of substructures, as well as lens and source uncertainties. We also find that the multilayer perceptron (MLP) mixer network works far better for such tasks than the convolutional architectures explored in other lensing analyses. Furthermore, we show that since TMNRE learns a posterior function it enables direct statistical checks that would be extremely expensive with likelihood-based methods. Our results show that TMNRE is well-suited for analysing complex lensing data, and that the full subhalo and line-of-sight halo population must be included when measuring the properties of individual dark matter substructures with this technique.

A MUSE view of the massive merging galaxy cluster ACT-CL J0102−4915 (El Gordo) at z = 0.87

We present a detailed strong lensing analysis of the massive and distant (z = 0.870) galaxy cluster ACT-CL J0102−4915 (ACT0102, also known as El Gordo), taking advantage of new spectroscopic data from the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope and archival imaging from the Hubble Space Telescope. Thanks to the MUSE data, we were able to measure secure redshifts for 374 single objects, including 23 multiply lensed galaxies, and 167 cluster members of ACT0102. We used the observed positions of 56 multiple images, along with their new spectroscopic redshift measurements, as constraints for our strong lensing model. Remarkably, some multiple images are detected out to a large projected distance of ≈1 Mpc from the brightest cluster galaxy, allowing us to estimate a projected total mass value of 1.84−0.04+0.03 × 1015 M⊙ within that radius. We find that we need two extended cluster mass components, the mass contributions from the cluster members and the additional lensing effect of a foreground (z = 0.633) group of galaxies, to predict the positions of all multiple images with a root mean square offset of 0″​​.75. The main cluster-scale mass component is centred very close to the brightest cluster galaxy, and the other extended mass component is located in the north-west region of the cluster. These two mass components have very similar values of mass projected within 300 kpc of their centres, namely 2.29−0.10+0.09 × 1014 M⊙ and 2.10−0.09+0.08 × 1014 M⊙, in agreement with the major merging scenario of ACT0102. We make publicly available the lens model, including the magnification maps and posterior distributions of the model parameter values, as well as the full spectroscopic catalogue containing all redshift measurements obtained with MUSE.

Follow-up analyses to the O3 LIGO–Virgo–KAGRA lensing searches

ABSTRACT Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects leading to distortion in the signals. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some follow-up analyses that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system by applying these analyses to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. These analyses cover the strong lensing, millilensing, and microlensing regimes. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations.

The return of GOLUM: improving distributed joint parameter estimation for strongly lensed gravitational waves

ABSTRACT Owing to the forecasted improved sensitivity of ground-based gravitational-wave detectors, new research avenues will become accessible. This is the case for gravitational-wave strong lensing, predicted with a non-negligible observation rate in the coming years. However, because one needs to investigate all the event pairs in the data, searches for strongly lensed gravitational waves are often computationally heavy, and one faces high false-alarm rates. In this paper, we present upgrades made to the golum software, making it more reliable while increasing its speed by re-casting the look-up table, imposing a sample control, and implementing symmetric runs on the two lensed images. We show how the recovered posteriors have improved coverage of the parameter space and how we increase the pipeline’s stability. Finally, we show the results obtained by performing a joint analysis of all the events reported until the GWTC-3 catalogue, finding similar conclusions to the ones presented in the literature.

Detectability of microlensed gravitational waves

ABSTRACT Gravitational lensing describes the bending of the trajectories of light and gravitational waves due to the gravitational potential of a massive object. Strong lensing by galaxies can create multiple images with different overall amplifications, arrival times, and image types. If, furthermore, the gravitational wave encounters a star along its trajectory, microlensing will take place. Previously, it has been shown that the effects of microlenses on strongly-lensed type-I images could be negligible in practice, at least in the low magnification regime. In this work, we study the same effect on type-II strongly-lensed images by computing the microlensing amplification factor. As opposed to being magnified, type-II images are typically demagnified. Moreover, microlensing on top of type-II images induces larger mismatches with un-microlensed waveforms than type-I images. These results are broadly consistent with recent literature and serve to confirm the findings. In addition, we investigate the possibility of detecting and analysing microlensed signals through Bayesian parameter estimation with an isolated point mass lens template, which has been adopted in recent parameter estimation literature. In particular, we simulate gravitational waves microlensed by a microlens embedded in a galaxy potential near moderately magnified type-I and II macroimages, with variable lens masses, source parameters and macromagnifcations. Generally, an isolated point mass model could be used as an effective template to detect a type-II microlensed image but not for type-I images, demonstrating the necessity for more realistic microlensing search templates.

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

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

Detecting strong gravitational lensing of gravitational waves with TianQin

Detecting strong gravitational lensing of gravitational waves with TianQin