Due to the finite amount of observational data, the best-fit parameters corresponding to the reconstructed cluster mass have uncertainties. In turn, these uncertainties affect the inferences made from these mass models. Following our earlier work, we have studied the effect of such uncertainties on the singularity maps in simulated and actual galaxy clusters. The mass models for both simulated and real clusters have been constructed using grale. The final best-fit mass models created using grale give the simplest singularity maps and a lower limit on the number of point singularities that a lens has to offer. The simple nature of these singularity maps also puts a lower limit on the number of three image (tangential and radial) arcs that a cluster lens has. Hence, we estimate the number of galaxy sources giving rise to the three image arcs, which can be observed with the James Webb Space Telescope (JWST). We find that we expect to observe at least 20-30 tangential and 5-10 radial three-image arcs in the Hubble Frontier Fields cluster lenses with the JWST.
We study the image formation near point singularities (swallowtail and umbilics) in the simulated strongly lensed images of Hubble Ultra Deep Field (HUDF) by the Hubble Frontier Fields (HFF) clusters. In this work, we only consider nearly half of the brightest (a total of 5271) sources in the HUDF region. For every HFF cluster, we constructed 11 realizations of strongly lensed HUDF with an arbitrary translation of the cluster centre within the central region of HUDF and an arbitrary rotation. In each of these realizations, we visually identify the characteristic/exotic image formation correspo…
Accurate reconstruction of the spatial distributions of the Point Spread Function (PSF) is crucial for high precision cosmic shear measurements. Nevertheless, current methods are not good at recovering the PSF fluctuations of high spatial frequencies. In general, the residual PSF fluctuations are spatially correlated, therefore can significantly contaminate the correlation functions of the weak lensing signals. We propose a method to correct for this contamination statistically, without any assumptions on the PSF and galaxy morphologies or their spatial distribution. We demonstrate our idea wi…
Upcoming and ongoing large area weak lensing surveys will also discover large samples of galaxy clusters. Accurate and precise masses of galaxy clusters are of major importance for cosmology, for example, in establishing well calibrated observational halo mass functions for comparison with cosmological predictions. We investigate the level of statistical uncertainties and sources of systematic errors expected for weak lensing mass estimates. Future surveys that will cover large areas on the sky, such as Euclid or LSST and to lesser extent DES, will provide the largest weak lensing cluster samp…
We develop a new method of combining cluster observables (number counts and cluster-cluster correlation functions) and stacked weak lensing signals of background galaxy shapes, both of which are available in a wide-field optical imaging survey. Assuming that the clusters have secure redshift estimates, we show that the joint experiment enables a self-calibration of important systematic errors including the source redshift uncertainty and the cluster mass-observable relation, by adopting a single population of background source galaxies for the lensing analysis. It allows us to use the relative…
Abell 2744, a massive Hubble Frontier Fields merging galaxy cluster with many multiple images in the core has been the subject of many lens inversions using different methods. While most existing studies compare various inversion methods, we focus on a comparison of reconstructions that use different input lensing data. Since the quantity and quality of lensing data is constantly improving, it makes sense to ask if the estimated uncertainties are robust against changes in the data. We address this question using free-form Grale, which takes only image information as input, and nothing pertaini…
Predisposition of galaxy clusters to producing exotic hyperbolic umbilic lensing configurations
Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574（里昂大学）；University of Hertfordshire（赫特福德大学）；Durham University（杜伦大学）；Indian Institute of Science（印度科学学院）；University of Hawaii（夏威夷大学）
We present cosmological parameter constraints based on a joint modeling of galaxy-lensing cross correlations and galaxy clustering measurements in the SDSS, marginalizing over small-scale modeling uncertainties using mock galaxy catalogs, without explicit modeling of galaxy bias. We show that our modeling method is robust to the impact of different choices for how galaxies occupy dark matter halos and to the impact of baryonic physics (at the $\sim2\%$ level in cosmological parameters) and test for the impact of covariance on the likelihood analysis and of the survey window function on the the…
Gravitational lens models with negative convergence(surface mass density projected onto the lens plane) inspired by modified gravity theories, exotic matter and energy have been recently discussed in such a way that a static and spherically-symmetric modified spacetime metric depends on the inverse distance to the power of positive $n$(n=1 for Schwarzschild metric, n=2 for Ellis wormhole) in the weak-field approximation [Kitamura, Nakajima and Asada, PRD 87, 027501 (2013)], and it has been shown that demagnification of images could occur for $n>1$ lens models associated with exotic matter (and…
We present a method that accurately propagates residual uncertainties in photometric redshift distributions into the cosmological inference from weak lensing measurements. The redshift distributions of tomographic redshift bins are parameterised using a flexible modified Gaussian mixture model. We fit this model to pre-calibrated redshift distributions and implement an analytic marginalisation over the potentially several hundred redshift nuisance parameters in the weak lensing likelihood, which is demonstrated to accurately recover the cosmological posterior. By iteratively fitting cosmologic…
Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularisation, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the l…
In a recent paper we have discussed the higher order singularities in gravitational lensing. We have shown that a singularity map, comprising of $A_3$-lines and unstable (point) singularities ($A_4$ and $D_4$), is a compact representation of high magnification regions corresponding to a given lens model for all possible source redshifts. It marks all the optimal locations for deep surveys in the lens plane. Here we present singularity maps for ten different cluster lenses selected from the \textit{Hubble Frontier fields} (HFF) and the \textit{Reionization Lensing Cluster Survey} (RELICS) surve…
We test the effects of varying the cosmological parameter values used in the strong lens modeling process for the six Hubble Frontier Fields (HFF) galaxy clusters. The standard procedure for generating high fidelity strong lens models includes careful consideration of uncertainties in the output models that result from varying model parameters within the bounds of available data constraints. It is not, however, common practice to account for the effects of cosmological parameter value uncertainties. The convention is to instead use a single fiducial "concordance cosmology" and generate lens mo…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties …
Optical weak lensing surveys have become a powerful tool for precision cosmology, but remain subject to systematic effects that can severely bias cosmological parameter estimates if not carefully removed. We discuss the possibility of performing complementary weak lensing surveys at radio/microwave frequencies, using detections of CO-emitting galaxies with resolved continuum images from ngVLA. This method has completely different systematic uncertainties to optical weak lensing shear measurements (e.g. in terms of blending, PSF, and redshift uncertainties), and can provide additional informati…
We propose a new model-independent strategy to calibrate the distance relation in Type Ia supernova (SN) observations and to probe the intrinsic properties of SNe Ia, especially the absolute magnitude $M_B$, basing on strong lensing observations in the upcoming Large Synoptic Survey Telescope (LSST) era. The strongly lensed quasars can provide the Time Delay Distances (TDD) and the Angular Diameter Distances (ADD) to the lens galaxies. These absolute distance measurements can model-independently anchor the SNe Ia at cosmological distances. We simulated 55 high-quality lensing systems with $5\%…
We present new methods for lensing reconstruction from CMB temperature fluctuations which have smaller mean-field and reconstruction noise bias corrections than current lensing estimators, with minimal loss of signal-to-noise. These biases are usually corrected using Monte Carlo simulations, and to the extent that these simulations do not perfectly mimic the underlying sky there are uncertainties in the bias corrections. The bias-hardened estimators which we present can have reduced sensitivity to such uncertainties, and provide a desirable cross-check on standard results. To test our approach…
Exotic objects such as the Ellis wormhole are expected to act as gravitational lenses. Much like their nonexotic counterparts, information about these lenses can be found by considering the strong and weak lensing fields they induce. In this work, we consider how weak gravitational lensing flexion can provide information beyond that of shear. We find that directional flexion can distinguish between the case of a positive or negative convergence where directional shear cannot, and therefore can provide a unique lensing signature for objects with an Ellis wormhole-type metric. We also consider c…
Modeling Redshift Uncertainties in Roman Weak Lensing Cosmology
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Duke University（杜克大学）；University of Arizona（亚利桑那大学）；Stony Brook University（石溪大学）；University of Chicago（芝加哥大学）；University of Pittsburgh（匹兹堡大学）
With the Hubble Frontier Fields program, gravitational lensing has provided a powerful way to extend the study of the ultraviolet luminosity function (LF) of galaxies at $z \sim 6$ down to unprecedented magnitude limits. At the same time, significant discrepancies between different studies were found at the very faint end of the LF. In an attempt to understand such disagreements, we present a comprehensive assessment of the uncertainties associated with the lensing models and the size distribution of galaxies. We use end-to-end simulations from the source plane to the final LF that account for…
We identify new strong lensing clusters of galaxies from the Sloan Digital Sky Survey III (SDSS DR8) by visually inspecting color images of a large sample of clusters of galaxies. We find 68 new clusters showing giant arcs in addition to 30 known lensing systems. Among 68 cases, 13 clusters are "almost certain" lensing systems with tangential giant arcs, 22 clusters are "probable" and 31 clusters are "possible" lensing systems. We also find two exotic systems with blue rings. The giant arcs have angular separations of 2.0"-25.7" from the bright central galaxies. We note that the rich clusters …
The discovery of gravitational waves from binary black hole mergers has renewed interest in primordial black holes forming a part of the dark matter density of our Universe. Various tests have been proposed to test this hypothesis. One of the cleanest tests is the lensing of fast radio bursts. In this situation, the presence of a compact object near the line of sight produces two images of the radio burst. If the images are sufficiently separated in time, this technique can constrain the presence of primordial black holes. One can also try to detect the lensed image of the mini-bursts within t…
We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological…
Cosmological inference from cluster number counts is systematically limited by the accuracy of the mass calibration, i.e. the empirical determination of the mapping between cluster selection observables and halo mass. In this work we demonstrate a method to quantitatively determine the bias and uncertainties in weak-lensing mass calibration. To this end, we extract a library of projected matter density profiles from hydrodynamical simulations. Accounting for shear bias and noise, photometric redshift uncertainties, mis-centering, cluster member contamination, cluster morphological diversity, a…
We present results from a comprehensive lensing analysis in HST data, of the complete CLASH cluster sample. We identify new multiple-images previously undiscovered allowing improved or first constraints on the cluster inner mass distributions and profiles. We combine these strong-lensing constraints with weak-lensing shape measurements within the HST FOV to jointly constrain the mass distributions. The analysis is performed in two different common parameterizations (one adopts light-traces-mass for both galaxies and dark matter while the other adopts an analytical, elliptical NFW form for the …
We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential sys…
We investigate the caustic topologies for binary gravitational lenses made up of two objects whose gravitational potential declines as $1/r^n$. With $n<1$ this corresponds to power-law dust distributions like the singular isothermal sphere. The $n>1$ regime can be obtained with some violations of the energy conditions, one famous example being the Ellis wormhole. Gravitational lensing provides a natural arena to distinguish and identify such exotic objects in our Universe. We find that there are still three topologies for caustics as in the standard Schwarzschild binary lens, with the main nov…
We perform weak lensing tomographic peak studies using the first-year shear data from Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) survey. The effective area used in our analyses after field selection, mask and boundary exclusions is $\sim 58 °^2$. The source galaxies are divided into low- and high-redshift bins with $0.2\le z_p\le0.85$ and $0.85\le z_p\le1.5$, respectively. We utilize our halo-based theoretical peak model including the projection effect of large-scale structures to derive cosmological constraints from the observed tomographic high peak abundances with the signal-to-no…
Based on a mass-selected sample of galaxy-scale strong gravitational lenses from the SLACS, BELLS, LSD and SL2S surveys and using a well-motivated fiducial set of lens-galaxy parameters we tested the weak-field metric on kiloparsec scales and found a constraint on the post-Newtonian parameter $γ= 0.995^{+0.037}_{-0.047}$ under the assumption of a flat $Λ$CDM universe with parameters taken from \textit{Planck} observations. General relativity (GR) predicts exactly $γ=1$. Uncertainties concerning the total mass density profile, anisotropy of the velocity dispersion and the shape of the light-pro…
Strong gravitational lensing of time variable sources such as quasars and supernovae creates observable time delays between the multiple images. Time delays can provide a powerful cosmographic probe through the "time delay distance" involving the ratio of lens, source, and lens-source distances. However, lightcurves of lensed images have measurement gaps, noise, systematics such as microlensing from substructure along an image line of sight, and no a priori functional model, making robust time delay estimation challenging. Using Gaussian process techniques, we demonstrate success in accurate b…
Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic - the peak count as a function of signal to noise ratio (SNR). We adopt the sparse hierarchical Bayesian m…
We discuss the effects of inhomogeneous sky-coverage on CMB lens reconstruction, focusing on application to the recently launched Planck satellite. We discuss the mean-field which is induced by noise inhomogeneities, as well as three approaches to lens reconstruction in this context: an optimal maximum-likelihood approach which is computationally expensive to evaluate, and two suboptimal approaches which are less intensive. The first of these is only sub-optimal at the five per-cent level for Planck, and the second prevents biasing due to uncertainties in the noise model.
Extensive surveys of galaxy clusters motivate us to assess the likelihood of cluster-cluster lensing (CCL), namely, gravitational-lensing of a background cluster by a foreground cluster. We briefly describe the characteristics of CCLs in optical, X-ray and SZ measurements, and calculate their predicted numbers for $Λ$CDM parameters and a viable range of cluster mass functions and their uncertainties. The predicted number of CCLs in the strong-lensing regime varies from several ($<10$) to as high as a few dozen, depending mainly on whether lensing triaxiality bias is accounted for, through the …
FAIR Universe Weak Lensing ML Uncertainty Challenge: Handling Uncertainties and Distribution Shifts for Precision Cosmology
Lawrence Berkeley National Laboratory（伯克利劳伦斯国家实验室）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学，CNRS/IN2P3，IJCLab）；ChaLearn；University of Washington（华盛顿大学）；University of California, Berkeley（加州大学伯克利分校）；University of Toronto（多伦多大学）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of California, San Diego（圣地亚哥大学）
Astrophysical uncertainties challenge 21-cm forecasts: A primordial black hole case study
Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（瓦伦西亚大学与西班牙国家研究委员会联合物理研究所）；C.N. Yang Institute for Theoretical Physics, Stony Brook University（纽约州立大学石溪分校杨振宁理论物理研究所）；INFN Sezione di Pisa（意大利国家核物理研究所比萨分部）；INFN Sezione di Roma（意大利国家核物理研究所罗马分部）
We study the effects of strong lensing on the observed number counts of mm sources using a ray tracing simulation and two number count models of unlensed sources. We employ a quantitative treatment of maximum attainable magnification factor depending on the physical size of the sources, also accounting for effects of lens halo ellipticity. We calculate predicted number counts and redshift distributions of mm galaxies including the effects of strong lensing and compare with the recent source count measurements of the South Pole Telescope (SPT). The predictions have large uncertainties, especial…
Galaxy shapes are subject to distortions due to the tidal field of the Universe. The cross-correlation of galaxy lensing with the lensing of the Cosmic Microwave Background (CMB) cannot easily be separated from the cross-correlation of galaxy intrinsic shapes with CMB lensing. Previous work suggested that the intrinsic alignment contamination can be $15\%$ of this cross-spectrum for the CFHT Stripe 82 (CS82) and Atacama Cosmology Telescope surveys. Here we re-examine these estimates using up-to-date observational constraints of intrinsic alignments at a redshift more similar to that of CS82 ga…
The gravitational lensing effects in the weak gravitational field by exotic lenses have been investigated intensively to find nonluminous exotic objects. Gravitational lensing based on 1/r^n fall-off metric, as a one-parameter model that can treat by hand both the Schwarzschild lens (n=1) and the Ellis wormhole (n=2) in the weak field, has been recently studied. Only for n=1 case, however, it has been explicitly shown that effects of relativistic lens images by the strong field on the light curve can be neglected. We discuss whether relativistic images by the strong field can be neglected for …
We perform a measurement of the mass--richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey. We have carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-$z$ biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centering, halo triaxiality, and projection effects. We also compare measurements of the lensing signal from two independently-produced shear and photometric redshift catalogues to chara…
It is generally thought that galaxies are embedded in dark matter halos extending well beyond their luminous matter. The existence of these galactic halos is mainly derived from the larger than expected velocities of stars and gas in the outskirts of spiral galaxies. Much less is known about dark matter around early-type (elliptical or lenticular) galaxies. We use gravitational lensing to derive the masses of early-type galaxies deflecting light of background quasars. This provides a robust measurement of the total mass within the Einstein ring, a circle whose diameter is comparable to the sep…
CMB lensing tomography, or the cross-correlation between CMB lensing maps and large-scale structure tracers over a well-defined redshift range, has the potential to map the amplitude and growth of structure over cosmic time, provide some of the most stringent tests of gravity, and break important degeneracies between cosmological parameters. In this work, we use the unWISE galaxy catalog to provide three samples at median redshifts $z \sim 0.6, 1.1$ and 1.5, fully spanning the Dark Energy dominated era, together with the most recent Planck CMB lensing maps. We obtain a combined cross-correlati…
CMB Stage-4 experiments will reduce the uncertainties on the gravitational lensing potential by an order of magnitude compared to current measurements, and will also produce a Sunyaev-Zel'dovich (SZ) cluster catalog containing $\sim10^{5}$ objects, two orders of magnitudes higher than what is currently available. In this paper we propose to combine these two observables and show that it is possible to calibrate the masses of the full Stage-4 cluster catalog internally owing to the high signal to noise measurement of the CMB lensing convergence field. We find that a CMB Stage-4 experiment will …
When combining cosmological and oscillations results to constrain the neutrino sector, the question of the propagation of systematic uncertainties is often raised. We address this issue in the context of the derivation of an upper bound on the sum of the neutrino masses ($Σm_ν$) with recent cosmological data. This work is performed within the ${\mathrm{Λ{CDM}}}$ model extended to $Σm_ν$, for which we advocate the use of three mass-degenerate neutrinos. We focus on the study of systematic uncertainties linked to the foregrounds modelling in CMB data analysis, and on the impact of the present kn…
We investigate how observations of strong lensing can be used to infer cosmological parameters, in particular the equation of state of dark energy. We focus on the growth of the critical lines of lensing clusters with the source redshift as this behaviour depends on the distance-redshift relation and is therefore cosmologically sensitive. Purely analytical approaches are generally insufficient because they rely on axisymmetric mass distributions and thus cannot take irregular critical curves into account. We devise a numerical method based on the Metropolis-Hastings algorithm: an elliptical ge…
In this paper we probe five cosmological models for which the dark energy equation of state parameter, $w(z)$, is parameterized as a function of redshift using strong lensing data in the galaxy cluster Abell 1689. We constrain the parameters of the $w(z)$ functions by reconstructing the lens model under each one of these cosmologies with strong lensing measurements from two galaxy clusters: Abell 1689 and a mock cluster, Ares, from the Hubble Frontier Fields Comparison Challenge, to validate our methodology. To quantify how the cosmological constraints are biased due to systematic effects in t…
To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and $\textit{Euclid}$) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct $\textit{maximum a posteriori}$ spherical weak lensing dark-matter mass-maps, with pri…
Weak gravitational lensing allows one to reconstruct the spatial distribution of the projected mass density across the sky. These "mass maps" provide a powerful tool for studying cosmology as they probe both luminous and dark matter. In this paper, we present a weak lensing mass map reconstructed from shear measurements in a 139 sq. deg area from the Dark Energy Survey (DES) Science Verification (SV) data. We compare the distribution of mass with that of the foreground distribution of galaxies and clusters. The overdensities in the reconstructed map correlate well with the distribution of opti…
We present the first strong-gravitational-lensing analysis of the galaxy cluster RXJ0437.1+0043 (RXJ0437; z = 0.285). Newly obtained, deep MUSE observations, Keck/MOSFIRE near-infrared spectroscopy, and Hubble Space Telescope SNAPshot imaging reveal 13 multiply imaged background galaxies, three of them (at z=1.98, 2.97, and 6.02, respectively) in hyperbolic umbilic (H-U) lensing configurations. The H-U images are located only 20 -- 50 kpc from the cluster centre, i.e., at distances well inside the Einstein radius where images from other lens configurations are demagnified and often unobservabl…
We present a detailed strong lensing analysis of an HST/ACS legacy dataset for the first gravitational lens, Q0957+561. With deep imaging we identify 24 new strongly lensed features, which we use to constrain mass models. We model the stellar component of the lens galaxy using the observed luminosity distribution, and the dark matter halo using several different density profiles. We draw on the weak lensing analysis by Nakajima et al. (2009) to constrain the mass sheet and environmental terms in the lens potential. Adopting the well-measured time delay, we find H_0 = 85 (+14/-13) km/s/Mpc (68%…
