The presence of an invisible substructure has previously been detected in the gravitational lens galaxy SDSSJ0946+1006 through its perturbation of the lensed images. Using flexible models for the main halo and the subhalo perturbation to fit the lensed images, we demonstrate that the subhalo has an extraordinarily high central density and steep density slope. The inferred concentration for the subhalo is well above the expected scatter in concentrations for $Λ$CDM halos of similar mass. We robustly infer the subhalo's projected mass within 1 kpc to be $\sim 2$-$3.7\times 10^9$M$_\odot$ at $>$95% CL for all our lens models, while the average slope of the subhalo's projected density profile over the radial range 0.75-1.25 kpc is constrained to be steeper than isothermal ($γ_{2D} \lesssim -1$). By modeling the subhalo light directly, we infer a conservative upper bound on its luminosity $L_V < 1.2\times 10^8L_\odot$ at 95% CL, which shows that the perturber is dark matter dominated. To compare to $Λ$CDM expectations, we analyze subhalos within analogues of lensing galaxies in the Illustris TNG100-1 simulation over many lines of sight, and find hundreds of subhalos that achieve a projected mass within 1 kpc of $\gtrsim 2\times10^9M_\odot$. However, less than 1% of the mock observations yield a log-slope steep enough to be consistent with our lensing models, and they $all$ have stellar masses in excess of that allowed by observations by about an order of magnitude or more. We conclude that the presence of such a dark, highly concentrated subhalo is unexpected in a $Λ$CDM universe. Finally, we show that this tension with CDM is not significantly reduced if the perturber is assumed to be a line-of-sight structure, rather than a subhalo.
We investigate how strong lensing of dusty, star-forming galaxies by foreground galaxies can be used as a probe of dark matter halo substructure. We find that spatially resolved spectroscopy of lensed sources allows dramatic improvements to measurements of lens parameters. In particular we find that modeling of the full, three-dimensional (angular position and radial velocity) data can significantly facilitate substructure detection, increasing the sensitivity of observables to lower mass subhalos. We carry out simulations of lensed dusty sources observed by early ALMA (Cycle 1) and use a Fish…
The cold dark matter scenario of hierarchical large-scale structure formation predicts the existence of abundant subhalos around large galaxies. However, the number of observed dwarf galaxies is far from this theoretical prediction, suggesting that most of the subhalos could be dark or quite faint. Gravitational lensing is a powerful tool to probe the mass distribution directly irrespective of whether it is visible or dark. Time delay anomalies in strongly lensed quasar systems are complementary to flux ratio anomalies in probing dark matter substructure in galaxies. Here we propose that lense…
We investigate how Einstein rings and magnified arcs are affected by small-mass dark-matter haloes placed along the line-of-sight to gravitational lens systems. By comparing the gravitational signature of line-of-sight haloes with that of substructures within the lensing galaxy, we derive a mass-redshift relation that allows us to rescale the detection threshold (i.e. lowest detectable mass) for substructures to a detection threshold for line-of-sight haloes at any redshift. We then quantify the line-of-sight contribution to the total number density of low-mass objects that can be detected thr…
We study the application of machine learning techniques for the detection of the astrometric signature of dark matter substructure. In this proof of principle a population of dark matter subhalos in the Milky Way will act as lenses for sources of extragalactic origin such as quasars. We train {\it ResNet-18}, a state-of-the-art convolutional neural network to classify angular velocity maps of a population of quasars into lensed and no lensed classes. We show that an SKA -like survey with extended operational baseline can be used to probe the substructure content of the Milky Way, and demonstra…
Gravitational lens flux-ratio anomalies provide a powerful technique for measuring dark matter substructure in distant galaxies. However, before using these flux-ratio anomalies to test galaxy formation models, it is imperative to ascertain that the given anomalies are indeed due to the presence of dark matter substructure and not due to some other component of the lensing galaxy halo or to propagation effects. Here we present the case of CLASS~B1555+375, which has a strong radio-wavelength flux-ratio anomaly. Our high-resolution near-infrared Keck~II adaptive optics imaging and archival Hubbl…
Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant $H_0$. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer $H_0$. We base the mock lenses on six quadruply-imaged q…
A promising route for revealing the existence of dark matter structures on mass scales smaller than the faintest galaxies is through their effect on strong gravitational lenses. We examine the role of local, lens-proximate clustering in boosting the lensing probability relative to contributions from substructure and unclustered line-of-sight (LOS) halos. Using two cosmological simulations that can resolve halo masses of $M_{\rm halo} \simeq 10^{9}\ M_{\odot}$ (in a simulation box of length $L_{\rm box}{\sim}100\,{\rm Mpc}$) and $10^{7}\ M_{\odot}$ ($L_{\rm box}\sim20\,{\rm Mpc}$), we demonstra…
Discrepancies between the observed and model-predicted radio flux ratios are seen in a number of quadruply-lensed quasars. The most favored interpretation of these anomalies is that CDM substructures present in lensing galaxies perturb the lens potentials and alter image magnifications and thus flux ratios. So far no consensus has emerged regarding whether or not the predicted CDM substructure abundance fully accounts for the lensing flux anomaly observations. Accurate modeling relies on a realistic lens sample in terms of both the lens environment and internal structures and substructures. In…
Lensing flux-ratio anomalies have been frequently observed and taken as evidence for the presence of abundant dark matter substructures in lensing galaxies, as predicted by the cold dark matter (CDM) model of cosmogony. In previous work, we examined the cusp-caustic relations of the multiple images of background quasars lensed by galaxy-scale dark matter haloes, using a suite of high-resolution N-body simulations (the Aquarius simulations). In this work, we extend our previous calculations to incorporate both the baryonic and diffuse dark components in lensing haloes. We include in each lensin…
We consider three extensions of the Navarro, Frenk and White (NFW) profile and investigate the intrinsic degeneracies among the density profile parameters on the gravitational lensing effect of satellite galaxies on highly magnified Einstein rings. In particular, we find that the gravitational imaging technique can be used to exclude specific regions of the considered parameter space, and therefore, models that predict a large number of satellites in those regions. By comparing the lensing degeneracy with the intrinsic density profile degeneracies, we show that theoretical predictions based on…
Strong gravitational lenses can be used to detect low mass subhalos, based on deviations in image fluxes and positions from what can be achieved with a smooth mass distribution. So far, this method has been limited by the small number of (radio-loud, microlensing free) systems which can be analysed for the presence of substructure. Using the gravitational lens B1422+231, we demonstrate that adaptive optics integral field spectroscopy can also be used to detect dark substructures. We analyse data obtained with OSIRIS on the Keck I Telescope, using a Bayesian method that accounts for uncertainti…
Strong gravitational lensing observations can test structure formation models by constraining the masses and concentrations of subhaloes in massive galaxy clusters. Recent work has concluded that cluster subhaloes are more abundant and/or concentrated than predicted by $Λ$CDM simulations; this finding has been interpreted as arising from unidentified issues with simulations or an incorrect understanding of the nature of dark matter. We test these hypotheses by comparing observed subhalo masses and maximum circular velocities $v_\mathrm{max}$ to predictions from the high resolution Hydrangea ga…
Strong gravitational lensing can be used to directly measure the mass function of their satellites, thus testing one of the fundamental predictions of cold dark matter cosmological models. Given the importance of this test it is essential to ensure that galaxies acting as strong lenses have dark and luminous satellites which are representative of the overall galaxy population. We address this issue by measuring the number and spatial distribution of luminous satellites in ACS imaging around lens galaxies from the Sloan Lens Advanced Camera for Surveys (SLACS) lenses, and comparing them with th…
We use high-resolution Aquarius simulations of Milky Way-sized haloes in the LCDM cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with ~ 10^8 particles (at a mass resolution ~ 10^3-4 M_sun/h) within its virial radius. Subhaloes with masses larger than 10^5 M_sun/h are well resolved, an improvement of at least two orders of magnitude over previous lensing studies. We incorporate a baryonic component modelled as a Hernquist profile and account for the response of the dark matter via adiabatic contraction. We focus on the "anomalous" flu…
Flux ratio anomalies in quasar lenses can be attributed to dark matter substructure surrounding the lensing galaxy and, thus, used to constrain the substructure mass fraction. Previous applications of this approach infer a substructure abundance that potentially in tension with the predictions of a $Λ$CDM cosmology. However, the assumption that all flux ratio anomalies are due to substructure is a strong one, and alternative explanations have not been fully investigated. Here, we use new high-resolution near-IR Keck~II adaptive optics imaging for the lens system CLASS B0712+472 to perform pixe…
We map the lensing-inferred substructure in the first three clusters observed by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z = 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the derived subhalo mass functions (SHMFs) to theoretical predictions from analytical models and with numerical simulations in a Lambda Cold Dark Matter (LCDM) cosmology. Mimicking our observational cluster member selection criteria in the HSTFF, we report excellent agreement in both amplitud…
We introduce a machine learning method for estimating the sensitivity of strong lens observations to dark matter subhaloes in the lens. Our training data include elliptical power-law lenses, Hubble Deep Field sources, external shear, and noise and PSF for the Euclid VIS instrument. We set the concentration of the subhaloes using a $v_\mathrm{max}$-$r_\mathrm{max}$ relation. We then estimate the dark matter subhalo sensitivity in $16{,}000$ simulated strong lens observations with depth and resolution resembling Euclid VIS images. We find that, with a $3σ$ detection threshold, $2.35$ per cent of…
Low-mass structures of dark matter (DM) are expected to be entirely devoid of light-emitting regions and baryons. Precisely because of this lack of baryonic feedback, small-scale substructures of the Milky Way are a relatively pristine testing ground for discovering aspects of DM microphysics and primordial fluctuations on subgalactic scales. In this work, we report results from the first search for Galactic DM subhalos with time-domain astrometric weak gravitational lensing. The analysis is based on a matched-filter template of local lensing corrections to the proper motion of stars in the Ma…
Cold dark matter (CDM) constitutes most of the matter in the Universe. The interplay between dark and luminous matter in dense cosmic environments like galaxy clusters is studied theoretically using cosmological simulations. Observed gravitational lensing is used to test and characterize the properties of substructures - the small-scale distribution of dark matter - in clusters. An apt metric, the probability of strong lensing events produced by dark matter substructure, is devised and computed for 11 galaxy clusters. We report that observed cluster substructures are more efficient lenses than…
A fundamental prediction of the cold dark matter cosmology is the existence of a large number of dark subhalos around galaxies, most of which should be entirely devoid of stars. Confirming the existence of dark substructures stands among the most important empirical challenges in modern cosmology: if they are found and quantified with the mass spectrum expected, then this would close the door on a vast array of competing theories. But in order for observational programs of this kind to reach fruition, we need robust predictions. Here we explore substructure predictions for lensing using galaxy…
The arrival times, positions, and fluxes of multiple images in strong lens systems can be used to infer the presence of dark subhalos in the deflector, and thus test predictions of cold dark matter models. However, gravitational lensing does not distinguish between perturbations to a smooth gravitational potential arising from baryonic and non-baryonic mass. In this work, we quantify the extent to which the stellar mass distribution of a deflector can reproduce flux ratio and astrometric anomalies typically associated with the presence of a dark matter subhalo. Using Hubble Space Telescope ima…
Probing Dark Matter Substructure with Image Number Anomaly in Strong Lensing Systems
School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
We present an analysis of seven strongly gravitationally lensed quasars and the corresponding constraints on the properties of dark matter. Our results are derived by modelling the lensed image positions and flux-ratios using a combination of smooth macro models and a population of low-mass haloes within the mass range 10^6 to 10^9 Msun. Our lens models explicitly include higher-order complexity in the form of stellar discs and luminous satellites, as well as low-mass haloes located along the observed lines of sight for the first time. Assuming a Cold Dark Matter (CDM) cosmology, we infer an a…
We introduce a Bayesian solution to the problem of inferring the density profile of strong gravitational lenses when the lens galaxy may contain multiple dark or faint substructures. The source and lens models are based on a superposition of an unknown number of non-negative basis functions (or "blobs") whose form was chosen with speed as a primary criterion. The prior distribution for the blobs' properties is specified hierarchically, so the mass function of substructures is a natural output of the method. We use reversible jump Markov Chain Monte Carlo (MCMC) within Diffusive Nested Sampling…
Strong gravitational lensing provides a powerful test of Cold Dark Matter (CDM) as it enables the detection and mass measurement of low mass haloes even if they do not contain baryons. Compact lensed sources such as Active Galactic Nuclei (AGN) are particularly sensitive to perturbing subhalos, but their use as a test of CDM has been limited by the small number of systems which have significant radio emission which is extended enough avoid significant lensing by stars in the plane of the lens galaxy, and red enough to be minimally affected by differential dust extinction. Narrow-line emission …
We propose a novel method to select satellite galaxies in outer regions of galaxy groups or clusters using weak gravitational lensing. The method is based on the theoretical expectation that the tangential shear pattern around satellite galaxies would appear with negative values at an offset distance from the center of the main halo. We can thus locate the satellite galaxies statistically with an offset distance of several lensing smoothing scales by using the standard reconstruction of surface mass density maps from weak lensing observation. We test the idea using high-resolution cosmological…
Multiple image gravitational lens systems, and especially quads are invaluable in determining the amount and distribution of mass in galaxies. This is usually done by mass modeling using parametric or free-form methods. An alternative way of extracting information about lens mass distribution is to use lensing degeneracies and invariants. Where applicable, they allow one to make conclusions about whole classes of lenses without model fitting. Here, we use approximate, but observationally useful invariants formed by the three relative polar angles of quad images around the lens center to show t…
We present a morphological study of the 17 lensed Lyman-$α$ emitter (LAE) galaxies of the Baryon Oscillation Spectroscopic Survey Emission-Line Lens Survey (BELLS) for the GALaxy-Ly$α$ EmitteR sYstems (BELLS GALLERY) sample. This analysis combines the magnification effect of strong galaxy-galaxy lensing with the high resolution of the Hubble Space Telescope ($HST$) to achieve a physical resolution of $\sim$80 pc for this $2<z<3$ LAE sample, allowing a detailed characterization of the LAE rest-frame ultraviolet continuum surface brightness profiles and substructure. We use lens-model reconstruc…
The analysis of optical images of galaxy-galaxy strong gravitational lensing systems can provide important information about the distribution of dark matter at small scales. However, the modeling and statistical analysis of these images is extraordinarily complex, bringing together source image and main lens reconstruction, hyper-parameter optimization, and the marginalization over small-scale structure realizations. We present here a new analysis pipeline that tackles these diverse challenges by bringing together many recent machine learning developments in one coherent approach, including va…
We present the results of a search for galaxy substructures in a sample of 11 gravitational lens galaxies from the Sloan Lens ACS Survey. We find no significant detection of mass clumps, except for a luminous satellite in the system SDSS J0956+5110. We use these non-detections, in combination with a previous detection in the system SDSS J0946+1006, to derive constraints on the substructure mass function in massive early-type host galaxies with an average redshift z ~ 0.2 and an average velocity dispersion of 270 km/s. We perform a Bayesian inference on the substructure mass function, within a …
Recently, Meneghetti et al. reported an excess of small-scale gravitational lenses in galaxy clusters. We study its implications for self-interacting dark matter (SIDM), compared with standard cold dark matter (CDM). We design controlled N-body simulations that incorporate observational constraints. The presence of early-type galaxies in cluster substructures can deepen gravitational potential and reduce tidal mass loss. Both scenarios require a relatively high baryon concentration in the substructure to accommodate the lensing measurements, and their tangential caustics are similar. The SIDM …
Dents in the Mirror: A Novel Probe of Dark Matter Substructure in Galaxy Clusters from the Astrometric Asymmetry of Lensed Arcs
School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天体物理学系）；Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文系）；Department of Physics, University of California at Santa Barbara（加州大学圣塔芭芭拉分校物理系）
In the standard structure formation scenario based on the cold dark matter paradigm, galactic halos are predicted to contain a large population of dark matter subhalos. While the most massive members of the subhalo population can appear as luminous satellites and be detected in optical surveys, establishing the existence of the low mass and mostly dark subhalos has proven to be a daunting task. Galaxy-scale strong gravitational lenses have been successfully used to study mass substructures lying close to lensed images of bright background sources. However, in typical galaxy-scale lenses, the s…
Observations of structure at sub-galactic scales are crucial for probing the properties of dark matter, which is the dominant source of gravity in the universe. It will become increasingly important for future surveys to distinguish between line-of-sight halos and subhalos to avoid wrong inferences on the nature of dark matter. We reanalyze a sub-galactic structure (in lens JVAS B1938+666) that has been previously found using the gravitational imaging technique in galaxy-galaxy lensing systems. This structure has been assumed to be a satellite in the halo of the main lens galaxy. We fit the re…
We present a detailed mass reconstruction and a novel study on the substructure properties in the core of the CLASH and Frontier Fields galaxy cluster MACS J0416.1-2403. We show and employ our extensive spectroscopic data set taken with the VIMOS instrument as part of our CLASH-VLT program, to confirm spectroscopically 10 strong lensing systems and to select a sample of 175 plausible cluster members to a limiting stellar mass of log(M_*/M_Sun) ~ 8.6. We reproduce the measured positions of 30 multiple images with a remarkable median offset of only 0.3" by means of a comprehensive strong lensing…
The positions of multiple images in galaxy lenses are related to the galaxy mass distribution. Smooth elliptical mass profiles were previously shown to be inadequate in reproducing the quad population. In this paper, we explore the deviations from such smooth elliptical mass distributions. Unlike most other work, we use a model-free approach based on the relative polar image angles of quads, and their position in 3D space with respect to the Fundamental Surface of Quads. The FSQ is defined by quads produced by elliptical lenses. We have generated thousands of quads from synthetic populations o…
We present the analysis of a sample of twenty-four SLACS-like galaxy-galaxy strong gravitational lens systems with a background source and deflectors from the Illustris-1 simulation. We study the degeneracy between the complex mass distribution of the lenses, substructures, the surface brightness distribution of the sources, and the time delays. Using a novel inference framework based on Approximate Bayesian Computation, we find that for all the considered lens systems, an elliptical and cored power-law mass density distribution provides a good fit to the data. However, the presence of cores i…
We introduce the Baryon Oscillation Spectroscopic Survey (BOSS) Emission-Line Lens Survey (BELLS) for GALaxy-Ly$α$ EmitteR sYstems (BELLS GALLERY) Survey, which is a Hubble Space Telescope program to image a sample of galaxy-scale strong gravitational lens candidate systems with high-redshift Ly$α$ emitters (LAEs) as the background sources. The goal of the BELLS GALLERY Survey is to illuminate dark substructures in galaxy-scale halos by exploiting the small-scale clumpiness of rest-frame far-UV emission in lensed LAEs, and to thereby constrain the slope and normalization of the substructure-ma…
A shot in the dark: searching for dark substructures in the RX J0437+00 galaxy cluster
University of Hertfordshire（赫特福德大学）；Durham University（杜伦大学）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；STAR Institute, Quartier Agora - Allée du six Août, 19c B-4000 Liège, Belgium（列日STAR研究所）；Univ. Grenoble Alpes, CNRS, Grenoble INP*, LPSC-IN2P3, 38000 Grenoble, France（格勒诺布尔阿尔卑斯大学）
Probing Dark Matter Substructures with Free-Form Modelling: A Case Study of the `Jackpot' Strong Lens
Zhengzhou University（郑州大学）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Beijing Normal University（北京师范大学）；Newcastle University（纽卡斯尔大学）；Durham University（杜伦大学）
We study the highly magnified arc SGAS J122651.3+215220 caused by a star-forming galaxy at $z_s=2.93$ crossing the lensing caustic cast by the galaxy cluster SDSS J1226+2152 ($z_l=0.43$), using Hubble Space Telescope observations. We report in the arc several asymmetric surface brightness features whose angular separations are a fraction of an arcsecond from the lensing critical curve and appear to be highly but unequally magnified image pairs of underlying compact sources, with one brightest pair having clear asymmetry consistently across four filters. One explanation of unequal magnification…
Dark matter substructure has the potential to discriminate between broad classes of dark matter models. With this in mind, we construct novel solutions to the equations of motion governing condensate dark matter candidates, namely axion Bose-Einstein condensates and superfluids. These solutions are highly compressed along one axis and thus have a disk-like geometry. We discuss linear stability of these solutions, consider the astrophysical implications as a large-scale dark disk or as small scale substructure, and find a characteristic signal in strong gravitational lensing. This adds to the g…
