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 quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences of $H_0$. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value of $H_0$ that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from $0.7 - 2.4\%$. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and sets a precision limit on inferences from single lenses.
Strong lensing time delays can measure the Hubble constant H$_0$ independent of any other probe. Assuming commonly used forms for the radial mass density profile of the lenses, a 2\% precision has been achieved with 7 Time-Delay Cosmography (TDCOSMO) lenses, in tension with the H$_0$ from the cosmic microwave background. However, without assumptions on the radial mass density profile -- and relying exclusively on stellar kinematics to break the mass-sheet degeneracy -- the precision drops to 8\% with the current data of the 7 TDCOSMO lenses, insufficient to resolve the H$_0$ tension. With the …
In the context of gravitational lensing, the density profile of lensing galaxies is often considered to be perfectly elliptical. Potential angular structures are generally ignored, except to explain flux ratios anomalies. Surprisingly, the impact of azimuthal structures on extended images of the source has not been characterized, nor its impact on the H0 inference. We address this task by creating mock images of a point source embedded in an extended source, lensed by an elliptical galaxy on which multipolar components are added to emulate boxy/discy isodensity contours. Modeling such images w…
Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, $H_{0}$, independent of traditional distance ladder methodology. A current potential limitation of time delay distance measurements is the "mass-sheet transformation" (MST) which leaves the lensed imaging unchanged but changes the distance measurements and the derived value of $H_0$. In this work we show that the standard method of addressing the MST in time delay cosmography, through a combination of high-resolution imaging and th…
The H0LiCOW collaboration inferred via gravitational lensing time delays a Hubble constant $H_0=73.3^{+1.7}_{-1.8}$ km s$^{-1}{\rm Mpc}^{-1}$, describing deflector mass density profiles by either a power-law or stars plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in $H_0$. We quantify any potential effect of the MST with flexible mass models that are maximally degenerate with H0. Our calculation is based on a new hierarchical approach in which the MST is only constrained by …
We have measured the redshifts and single-aperture velocity dispersions of eight lens galaxies using the data collected by the Echellette Spectrograph and Imager (ESI) and Low Resolution Imaging Spectrometer (LRIS) at W.M. Keck observatory on different observing nights spread over three years (2018-2020). These results, combined with other ancillary data, such as high-resolution images of the lens systems, and time delays, are necessary to increase the sample size of the quasar-galaxy lens systems for which the Hubble constant can be measured, using the time-delay strong lensing method, hence …
TDCOSMO 2026: A 3% measurement of the Hubble constant from strong lensing and stellar kinematics
Stony Brook University（石溪大学）；University of Oxford（牛津大学）；Universitat de Barcelona（巴塞罗那大学）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究院）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究研究所）；University of California, Davis（加州大学戴维斯分校）；Université de Montpellier（蒙彼利埃大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；University of Geneva（日内瓦大学）
TDCOSMO 2026: new insights on the Hubble tension from strong lensing time delays
Stony Brook University（石溪大学）；University of Oxford（牛津大学）；Universitat de Barcelona（巴塞罗那大学）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；University of California, Davis（加州大学戴维斯分校）；Université de Montpellier（蒙彼利埃大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；University of Geneva（日内瓦大学）
TDCOSMO XXV: Measuring H0 to 6.5% precision with quasar strong lensing and maximally flexible mass-sheet dynamics
University of California, Los Angeles（加州大学洛杉矶分校）；ETH Zurich（苏黎世联邦理工学院）；Université de Genève（日内瓦大学）；European Southern Observatory（欧洲南方天文台）；Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Stony Brook University（石溪大学）；Université de Montpellier（蒙彼利埃大学）
基于四重成像类星体SDSSJ1433+6007，结合哈勃空间望远镜成像、时间延迟监测和空间分辨恒星运动学，通过联合透镜和动力学模型并考虑质量片变换的最大灵活性，在平坦ΛCDM宇宙学下以6.5%精度测得哈勃常数$H_0 = 73.2^{+4.8}_{-4.7}$ km s$^{-1}$ Mpc$^{-1}$，并发现内部质量片参数$λ_{\rm int}=1.12^{+0.05}_{-0.06}$与1有2σ偏离。
The Sensitivity of Substructure Lensing to SIDM Core-collapse Model Variation
The Ohio State University（俄亥俄州立大学）；University of Minnesota（明尼苏达大学）；Texas A&M University（德克萨斯农工大学）；University of New Mexico（新墨西哥大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Institute for Advanced Study（高等研究院）；Carnegie Science（卡内基科学）
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…
The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of $H_0$. A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated on a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as…
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…
TDCOSMO XXVI: Uniform lens modeling of eight doubly imaged quasars
Stony Brook University（石溪大学）；University of Chicago（芝加哥大学）；Independent University, Bangladesh（孟加拉独立大学）；Stockholm University（斯德哥尔摩大学）；ETH Zurich（苏黎世联邦理工学院）；Université de Genève（日内瓦大学）；Universidad de Valparaíso（瓦尔帕莱索大学）；University of Liège（列日大学）；Universitat de Barcelona（巴塞罗那大学）；Institut Català de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚高级研究所）；Institut dEstudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究研究所）
TDCOSMO XXXI: New techniques in line-of-sight studies of time delay lenses
CNRS & Université de Montpellier（法国国家科学研究中心与蒙彼利埃大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of California, Davis（加州大学戴维斯分校）；Argonne National Laboratory（阿贡国家实验室）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Université de Genève（日内瓦大学）
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…
We present a reconstructions of galaxy-cluster-scale mass distributions from simulated gravitational lensing data sets including strong lensing, weak lensing shear, and measurements of quadratic image distortions -- flexion. The lensing data is constructed to make a direct comparison between mass reconstructions with and without flexion. We show that in the absence of flexion measurements, significant galaxy-group scale substructure can remain undetected in the reconstructed mass profiles, and that the resulting profiles underestimate the aperture mass in the substructure regions by $\sim25-40…
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…
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…
While our current cosmological model places galaxy clusters at the nodes of a filament network (the cosmic web), we still struggle to detect these filaments at high redshifts. We perform a weak lensing study for a sample of 16 massive, medium-high redshift (0.4<z<0.9) galaxy clusters from the DAFT/FADA survey, that are imaged in at least three optical bands with Subaru/Suprime-Cam or CFHT/MegaCam. We estimate the cluster masses using an NFW fit to the shear profile measured in a KSB-like method, adding our contribution to the calibration of the observable-mass relation required for cluster abu…
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 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…
TDCOSMO XIV: Practical Techniques for Estimating External Convergence of Strong Gravitational Lens Systems and Applications to the SDSS J0924+0219 System
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…
Mass clumps in gravitational lens galaxies can perturb lensed images in characteristic ways. Strong lens flux ratios have been used to constrain the amount of dark matter substructure in lens galaxies, and various other observables have been considered as additional probes of substructure. We study the general theory of lensing with stochastic substructure in order to understand how lensing observables depend on the mass function and spatial distribution of clumps. We find that magnification perturbations are mainly sensitive to the total mass in substructure projected near the lensed images; …
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…
We investigate the spectro-photometric variability of quasars due to lensing of small mass substructure (from several tens to several hundreds solar masses). The aim of this paper is to explore the milli/microlensing influence on the flux anomaly observed between images of a lensed quasar in different spectral bands and possible influence of small mass structure lensing of non-macrolensed quasars.We find that spectro-photometric variability may be also caused by lensing of small mass diffuse structure and can produce the flux anomaly which is sometimes seen in different images of a lensed quas…
We report a mass reconstruction of A1689 using Particle Based Lensing (PBL), a new technique for Strong+Weak lensing that allows a variable resolution depending on the data density and the signal-to-noise. Using PBL we also calculate the covariance matrix for the resulting mass map. The reconstruction of A1689 shows a secondary mass peak in the north-east direction confirming previous optical observations. This indicates that the central region of the cluster is still undergoing a weak merger. We have used this mass map to measure power ratios of the dark matter distribution and compared it to…
TDCOSMO: XX. WFI2033--4723, the First Quadruply-Imaged Quasar Modeled with JWST Imaging
Department of Physics and Astronomy, UCLA（加州大学洛杉矶分校物理与天文系）；Department of Physics and Astronomy, Stony Brook University（纽约州立大学石溪分校物理与天文系）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Center for Astronomy, Space Science and Astrophysics, Independent University, Bangladesh（孟加拉国独立大学天文学、空间科学与天体物理中心）；Research Center for the Early Universe, Graduate School of Science, The University of Tokyo（东京大学理学研究科早期宇宙研究中心）；IPAC, California Institute of Technology（加州理工学院红外处理分析中心）；Space Telescope Science Institute（太空望远镜科学研究所）
In this paper, we undertake a study to determine what insight can be reliably gleaned from the comparison of the X-ray and the weak lensing mass maps of galaxy clusters. We do this by investigating the 2D substructure within three high-resolution cosmological simulations of galaxy clusters. Our main results focus on non-radiative gas dynamics, but we also consider the effects of radiative cooling at high redshift. For our analysis, we use a novel approach, based on unsharp-masking, to identify substructures in 2D surface mass density and X-ray surface brightness maps. At full resolution (~ 15 …
High resolution dark matter only simulations provide a realistic and fully general means to study the theoretical predictions of cosmological structure formation models for gravitational lensing. Due to the finite number of particles, the density field only becomes smooth on scales beyond a few times the local mean interparticle separation. This introduces noise on the gravitational lensing properties such as the surface mass density, the deflection angles and the magnification. At some small-scale mass limit, the noise due to the discreteness of the N-body simulation becomes comparable to the…
With galaxy groups constructed from the Sloan Digital Sky Survey (SDSS), we analyze the expected galaxy-galaxy lensing signals around satellite galaxies residing in different host haloes and located at different halo-centric distances. We use Markov Chain Monte Carlo (MCMC) method to explore the potential constraints on the mass and density profile of subhaloes associated with satellite galaxies from SDSS-like surveys and surveys similar to the Large Synoptic Survey Telescope (LSST). Our results show that for SDSS-like surveys, we can only set a loose constraint on the mean mass of subhaloes. …
We explore the halo-to-halo variation of dark matter substructure in galaxy-sized dark matter halos, focusing on its implications for strongly gravitational lensed systems. We find that the median value for projected substructure mass fractions within projected radii of 3% of the host halo virial radius is approximately fsub ~ 0.25%, but that the variance is large with a 95-percentile range of 0 <= fsub <= 1%. We quantify possible effects of substructure on quadruply-imaged lens systems using the cusp relation and the simple statistic, Rcusp. We estimate that the probability of obtaining the l…
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…
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…
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…
In recent years, it has become possible to detect individual dark matter subhalos near images of strongly lensed extended background galaxies. Typically, only the most massive subhalos in the strong lensing region may be detected this way. In this work, we show that strong lenses may also be used to constrain the much more numerous population of lower mass subhalos that are too small to be detected individually. In particular, we show that the power spectrum of projected density fluctuations in galaxy halos can be measured using strong gravitational lensing. We develop the mathematical framewo…
We obtain the projected mass distributions for two Subaru/Suprime-Cam fields in the southwest region (r\simlt 60') of the Coma cluster (z=0.0236) by weak lensing analysis and detect eight subclump candidates. We quantify the contribution of background large-scale structure (LSS) on the projected mass distributions using SDSS multi-bands and photometric data, under the assumption of mass-to-light ratio for field galaxies. We find that one of eight subclump candidates, which is not associated with any member galaxies, is significantly affected by LSS lensing. The mean projected mass for seven su…
TDCOSMO XXVIII. The Hubble constant from the quadruply lensed quasar J1537$-$3010 with precise time delays
University of Geneva（日内瓦大学）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Laboratoire Univers et Particules de Montpellier (LUPM), CNRS & Université Montpellier（蒙彼利埃宇宙与粒子实验室（LUPM），法国国家科学研究中心与蒙彼利埃大学）；STAR Institute, University of Liège（列日大学STAR研究所）；Armagh Observatory and Planetarium（阿马天文台和天文馆）；Fermi National Accelerator Laboratory（费米国家加速器实验室）
Galaxy clusters are considered as excellent probes for cosmology. For that purpose, their mass needs to be measured and their structural properties needs to be understood. We propose a method for galaxy cluster mass reconstruction which combines information from strong lensing, weak lensing shear and flexion. We extend the weak lensing analysis to the inner parts of the cluster and, in particular, improve the resolution of substructure. We use simulations to show that the method recovers the mass density profiles of the cluster. We find that the weak lensing flexion is sensitive to substructur…
Lensing flux-ratio anomalies are most likely caused by gravitational lensing by small-scale dark matter structures. These anomalies offer the prospect of testing a fundamental prediction of the cold dark matter (CDM) cosmological model: the existence of numerous substructures that are too small to host visible galaxies. In two previous studies we found that the number of subhalos in the six high-resolution simulations of CDM galactic halos of the Aquarius project is not sufficient to account for the observed frequency of flux ratio anomalies seen in selected quasars from the CLASS survey. Thes…
It is of great interest to measure the properties of substructures in dark matter halos at galactic and cluster scales. Here we suggest a method to constrain substructure properties using the variance of weak gravitational flexion in a galaxy-galaxy lensing context. We show the effectiveness of flexion variance in measuring substructures in N-body simulations of dark matter halos, and present the expected galaxy-galaxy lensing signals. We show the insensitivity of the method to the overall galaxy halo mass, and predict the method's signal-to-noise for a space-based all-sky survey, showing that…
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…
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…
In this work we study the relevance of the cosmic web and substructures on the matter and lensing power spectra measured from halo mock catalogues extracted from the N-body simulations. Since N-body simulations are computationally expensive, it is common to use faster methods that approximate the dark matter field as a set of halos. In this approximation, we replace mass concentrations in N-body simulations by a spherically symmetric Navarro-Frenk-White halo density profile. We also consider the full mass field as the sum of two distinct fields: dark matter halos ($M>9\times 10^{12}~M_{\odot}$…
Gravitational lensing time delays are well known to depend on cosmological parameters, but they also depend on the details of the mass distribution of the lens. It is usual to model the mass distribution and use time-delay observations to infer cosmological parameters, but it is naturally also possible to take the cosmological parameters as given and use time delays as constraints on the mass distribution. This paper develops a method to isolate what exactly those constraints are, using a principal-components analysis of ensembles of free-form mass models. We find that time delays provide tigh…
Strong gravitational lensing is a promising probe of the substructure of dark matter halos. Deep learning methods have the potential to accurately identify images containing substructure, and differentiate WIMP dark matter from other well motivated models, including vortex substructure of dark matter condensates and superfluids. This is crucial in future efforts to identify the true nature of dark matter. We implement, for the first time, a classification approach to identifying dark matter substructure based on simulated strong lensing images with different substructure. Utilizing convolution…
