In the near future, ultra deep observations of galaxy clusters with HST or JWST will uncover $300-1000$ lensed multiple images, increasing the current count per cluster by up to an order of magnitude. This will further refine our view of clusters, leading to a more accurate and precise mapping of the total and dark matter distribution in clusters, and enabling a better understanding of background galaxy population and their luminosity functions. However, to effectively use that many images as input to lens inversion will require a re-evaluation of, and possibly upgrades to the existing methods. In this paper we scrutinize the performance of the free-form lens inversion method Grale in the regime of $150-1000$ input images, using synthetic massive galaxy clusters. Our results show that with an increasing number of input images, Grale produces improved reconstructed mass distributions, with the fraction of the lens plane recovered at better than $10\%$ accuracy increasing from $40-50\%$ for $\sim\!\!150$ images to $65\%$ for $\sim\!1000$ images. The reconstructed time delays imply a more precise measurement of $H_0$, with $\lesssim 1\%$ bias. While the fidelity of the reconstruction improves with the increasing number of multiple images used as model constraints, $\sim 150$ to $\sim 1000$, the lens plane rms deteriorates from $\sim 0.11''$ to $\sim 0.28''$. Since lens plane rms is not necessarily the best indicator of the quality of the mass reconstructions, looking for an alternative indicator is warranted.
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…
The information about the mass density of galaxy clusters provided by the gravitational lens effect has inspired many inversion techniques. In this article, updates to the previously introduced method in Grale are described, and explored in a number of examples. The first looks into a different way of incorporating time delay information, not requiring the unknown source position. It is found that this avoids a possible bias that leads to "over-focusing" the images, i.e. providing source position estimates that lie in a considerably smaller region than the true positions. The second is inspire…
We use the Beyond Ultra-deep Frontier Fields and Legacy Observations (BUFFALO) strong lensing image catalog of the merging galaxy cluster Abell 370 to obtain a mass model using the free-form lens inversion algorithm GRALE. The improvement of the strong lensing data quality results in a lens plane rms of only 0.45 arcsec, about a factor of two lower than that of our existing HFF v4 reconstruction. We attribute the improvement to spectroscopic data and use of the full reprocessed HST mosaics. In our reconstructed mass model, we found indications of three distinct mass features in Abell 370: (i) …
We reconstruct the projected mass distribution of a massive merging Hubble Frontier Fields cluster MACSJ0416 using the genetic algorithm based free-form technique called Grale. The reconstructions are constrained by 149 lensed images identified by Jauzac et al. using HFF data. No information about cluster galaxies or light is used, which makes our reconstruction unique in this regard. Using visual inspection of the maps, as well as galaxy-mass correlation functions we conclude that overall light does follow mass. Furthermore, the fact that brighter galaxies are more strongly clustered with mas…
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 le…
We investigate to which precision local magnification ratios, $\mathcal{J}$, ratios of convergences, $f$, and reduced shears, $g = (g_{1}, g_{2})$, can be determined model-independently for the five resolved multiple images of the source at $z_\mathrm{s}=1.675$ in CL0024. We also determine if a comparison to the respective results obtained by the parametric modelling program Lenstool and by the non-parametric modelling program Grale can detect biases in the lens models. For these model-based approaches we additionally analyse the influence of the number and location of the constraints from mul…
MACS J0717 is the most massive and extended of the Hubble Frontier Field clusters. It is one of the more difficult clusters to model, and we argue that this is in part due to the line of sight structure (LoS) at redshifts beyond 2. We show that the Grale mass reconstruction based on sources at 3<z_s<4.1 has at least 10^{13}M_sun more mass than that based on nearby sources, z_s<2.6, and attribute the excess mass to a putative LoS, which is at least 75" from the cluster center. Furthermore, the lens-model fitted z_s's of the recent Kawamata et al. reconstruction are biased systematically low com…
Multiple image gravitational lensing systems with measured time delays provide a promising one-step method for determining $H_0$. MACS J1149, which lenses SN Refsdal into a quad S1-S4, and two other widely separated images, SX and SY, is a perfect candidate. If time delays are pinned down, the remaining uncertainty arises from the mass distribution in the lens. In MACS J1149, the mass in the relevant lens plane region can be constrained by (i) many multiple images, (ii) the mass of the galaxy splitting S1-S4 (which, we show, is correlated with $H_0$), (iii) magnification of SX (also correlated…
In this article we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints, is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an …
We have made mass maps of three strong-lensing clusters, Abell 3827, Abell 2218 and Abell 1689, in order to test for mass-light offsets. The technique used is GRALE, which enables lens reconstruction with minimal assumptions, and specifically with no information about the cluster light being given. In the first two of these clusters, we find local mass peaks in the central regions that are displaced from the nearby galaxies by a few to several kpc. These offsets {\em could\/} be due to line of sight structure unrelated to the clusters, but that is very unlikely, given the typical levels of cha…
Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate how sparse optimisation can address the problem. As a first step towards a full free-form lens modelling technique, we consider linear inversion of the lensed source under sparse regularisation and joint deblending from the lens light profile. The method is based on morphological component analysis, assuming a known mass model. We show with numerical experime…
This paper continues a series in which we intend to show how all observables of galaxy clusters can be combined to recover the two-dimensional, projected gravitational potential of individual clusters. Our goal is to develop a non-parametric algorithm for joint cluster reconstruction taking all cluster observables into account. In this paper, we begin with the relation between the Compton-y parameter and the Newtonian gravitational potential, assuming hydrostatic equilibrium and a polytropic stratification of the intracluster gas. We show how Richardson-Lucy deconvolution can be used to conver…
Cosmic Microwave Background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise polarization data from next-generation experiments. In this paper we explain why the quadratic estimator will also be suboptimal for measuring lensing on very small scales, even for measurements in temperature where this estimator typically performs well. Though maximum likelihood methods could be implemented to improve performance, we explore a much simpler solu…
We develop a novel statistical strong lensing approach to probe the cosmological parameters by exploiting multiple redshift image systems behind galaxies or galaxy clusters. The method relies on free-form mass inversion of strong lenses and does not need any additional information other than gravitational lensing. Since in free-form lensing the solution space is a high-dimensional convex polytope, we consider Bayesian model comparison analysis to infer the cosmological parameters. The volume of the solution space is taken as a tracer of the probability of the underlying cosmological assumption…
With upcoming (continuum) surveys of high-resolution radio telescopes, detection rates of fast radio bursts (FRBs) might approach $10^5$ per sky per day by future extremely large observatories, such as the possible extension of the Square Kilometer Array (SKA) to a phase 2 array. Depending on the redshift distribution of FRBs and using the repeating FRB121102 as a model, we calculate a detection rate of multiply-imaged FRBs with their multiply-imaged hosts caused by the distribution of galaxy-cluster scale gravitational lenses of the order of $10^{-4}$ per square degree per year for a minimum …
Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Models
Université de Montréal（蒙特利尔大学）；Mila；Ciela Institute（Ciela研究所）；CCA, Flatiron Institute（CCA与Flatiron研究所）；Perimeter Institute for Theoretical Physics（理论物理研究所）；Trottier Space Institute（Trottier空间研究所）
The inversion of gravitational lens systems is hindered by the fact that multiple mass distributions are often equally compatible with the observed properties of the images. Besides using clear examples to illustrate the effect of the so-called monopole and mass sheet degeneracies, this article introduces the most general form of said mass sheet degeneracy. While the well known version of this degeneracy rescales a single source plane, this generalization allows any number of sources to be rescaled. Furthermore, it shows how it is possible to rescale each of those sources with a different scal…
Strong gravitational lensing provides a wealth of astrophysical information on the baryonic and dark matter content of galaxies. It also serves as a valuable cosmological probe by allowing us to measure the Hubble constant independently of other methods. These applications all require the difficult task of inverting the lens equation and simultaneously reconstructing the mass profile of the lens along with the original light profile of the unlensed source. As there is no reason for either the lens or the source to be simple, we need methods that both invert the lens equation with a large numbe…
We report new observations of the 110-111 (6 cm) and 211-212 (2 cm) transitions of ortho-formaldehyde (o-H2CO) in absorption at z=0.68466 toward the gravitational lens system B0218+357. Radiative transfer modeling indicates that both transitions are anti-inverted relative to the 4.6 K cosmic microwave background (CMB), regardless of the source covering factor, with excitation temperatures of ~1 K and 1.5-2 K for the 110-111 and 211-212 lines, respectively. Using these observations and a large velocity gradient radiative transfer model that assumes a gradient of 1 km s^-1 pc^-1, we obtain a mol…
Lensing in the Blue IV: The First Weak Gravitational Lensing Maps from the Stratosphere
Northeastern University（东北大学）；New York University（纽约大学）；University of Cambridge（剑桥大学）；University of Toronto（多伦多大学）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；California Institute of Technology（加州理工学院）；Stanford University（斯坦福大学）
In this paper, we compare three methods to reconstruct galaxy cluster density fields with weak lensing data. The first method called FLens integrates an inpainting concept to invert the shear field with possible gaps, and a multi-scale entropy denoising procedure to remove the noise contained in the final reconstruction, that arises mostly from the random intrinsic shape of the galaxies. The second and third methods are based on a model of the density field made of a multi-scale grid of radial basis functions. In one case, the model parameters are computed with a linear inversion involving a s…
Using the power of gravitational lensing magnification by massive galaxy clusters, the Hubble Frontier Fields provide deep views of six patches of the high redshift Universe. The combination of deep Hubble imaging and exceptional lensing strength has revealed the greatest numbers of multiply-imaged galaxies available to constrain models of cluster mass distributions. However, even with $\mathcal{O}(100)$ images per cluster, the uncertainties associated with the reconstructions are not negligible. The goal of this paper is to show the diversity of model magnification predictions. We examine 7 a…
Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Deriving a lens magnification map for a galaxy cluster is a classic inversion problem and many methods have been developed over the past two decades to solve it. Several research groups have developed techniques independently to map the predominantly dark matter distribution in cluster lenses. While these methods have all provided remarkably high precision mass maps, particularly with exquisite imaging data from the Hubble Space Telescope (HST), the reconstructions themselves have ne…
We reconstruct the radial profile of the projected gravitational potential of the galaxy cluster MACS-J1206 from 592 spectroscopic measurements of velocities of cluster members. For doing so, we use a method we have developed recently based on the Richardson-Lucy deprojection algorithm and an inversion of the spherically-symmetric Jeans equation. We find that, within the uncertainties, our reconstruction agrees very well with a potential reconstruction from weak and strong gravitational lensing as well as with a potential obtained from X-ray measurements. In addition, our reconstruction is in …
