Model-independent and model-based local lensing properties of CL0024+1654 from multiply-imaged galaxies

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 multiple images on the local lens properties determined at the positions of the five multiple images of the source at $z_\mathrm{s}=1.675$. All approaches show high agreement on the local values of $\mathcal{J}$, $f$, and $g$. We find that Lenstool obtains the tightest confidence bounds even for convergences around one using constraints from six multiple image systems, while the best Grale model is generated only using constraints from all multiple images with resolved brightness features and adding limited small-scale mass corrections. Yet, confidence bounds as large as the values themselves can occur for convergences close to one in all approaches. Our results are in agreement with previous findings, supporting the light-traces-mass assumption and the merger hypothesis for CL0024. Comparing the three different approaches allows to detect modelling biases. Given that the lens properties remain approximately constant over the extension of the image areas covered by the resolvable brightness features, the model-independent approach determines the local lens properties to a comparable precision but within less than a second. (shortened)Comment: 22 pages, published in A&A 612 A17, comments welcom

Non-parametric strong lens inversion of SDSS J1004+4112

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 image at that location. An inversion which includes the central image provides tighter constraints on the shape of the central part of the mass map. The resulting model also predicts a central image of a second galaxy where indeed an object is visible in the available ACS images. We find masses of 2.5x10^13 M_O and 6.1x10^13 M_O within a radius of 60 kpc and 110 kpc respectively, confirming the results from other authors. The resulting mass map is compatible with an elliptical generalization of a projected NFW profile, with r_s = 58_{-13}^{+21} arcsec and c_vir = 3.91 +/- 0.74. The orientation of the elliptical NFW profile follows closely the orientation of the central cluster galaxy and the overall distribution of cluster members.Comment: 11 pages, accepted for publication in MNRA

Lensing degeneracies and mass substructure

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 scale factor. Apart from illustrating that the mass sheet degeneracy is not broken by the presence of multiple sources at different redshifts, it will become apparent that the newly constructed mass distribution necessarily alters the existing mass density precisely at the locations of the images in the lens system, and that this change in mass density is linked to the factors with which the sources were rescaled. Combined with the fact that the monopole degeneracy introduces a large amount of uncertainty about the density in between the images, this means that both degeneracies are in fact closely related to substructure in the mass distribution. An example simulated lensing situation based on an elliptical version of a Navarro-Frenk-White profile explicitly shows that such degeneracies are not easily broken by observational constraints, even when multiple sources are present. Instead, the fact that each lens inversion method makes certain assumptions, implicit or explicit, about the smoothness of the mass distribution means that in practice the degeneracies are broken in an artificial manner rather than by observed properties of the lens system.Comment: 10 pages, accepted for publication by MNRA

Non-parametric strong lens inversion of Cl~0024+1654: illustrating the monopole degeneracy

The cluster lens Cl 0024+1654 is undoubtedly one of the most beautiful examples of strong gravitational lensing, providing five large images of a single source with well-resolved substructure. Using the information contained in the positions and the shapes of the images, combined with the null space information, a non-parametric technique is used to infer the strong lensing mass map of the central region of this cluster. This yields a strong lensing mass of 1.60x10^14 M_O within a 0.5' radius around the cluster center. This mass distribution is then used as a case study of the monopole degeneracy, which may be one of the most important degeneracies in gravitational lensing studies and which is extremely hard to break. We illustrate the monopole degeneracy by adding circularly symmetric density distributions with zero total mass to the original mass map of Cl 0024+1654. These redistribute mass in certain areas of the mass map without affecting the observed images in any way. We show that the monopole degeneracy and the mass-sheet degeneracy together lie at the heart of the discrepancies between different gravitational lens reconstructions that can be found in the literature for a given object, and that many images/sources, with an overall high image density in the lens plane, are required to construct an accurate, high-resolution mass map based on strong-lensing data.Comment: 9 pages, accepted for publication by MNRA

A genetic algorithm for the non-parametric inversion of strong lensing systems

We present a non-parametric technique to infer the projected-mass distribution of a gravitational lens system with multiple strong-lensed images. The technique involves a dynamic grid in the lens plane on which the mass distribution of the lens is approximated by a sum of basis functions, one per grid cell. We used the projected mass densities of Plummer spheres as basis functions. A genetic algorithm then determines the mass distribution of the lens by forcing images of a single source, projected back onto the source plane, to coincide as well as possible. Averaging several tens of solutions removes the random fluctuations that are introduced by the reproduction process of genomes in the genetic algorithm and highlights those features common to all solutions. Given the positions of the images and the redshifts of the sources and the lens, we show that the mass of a gravitational lens can be retrieved with an accuracy of a few percent and that, if the sources sufficiently cover the caustics, the mass distribution of the gravitational lens can also be reliably retrieved. A major advantage of the algorithm is that it makes full use of the information contained in the radial images, unlike methods that minimise the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.Comment: 11 pages, accepted for publication by MNRA

A Systematic Review of Strong Gravitational Lens Modeling Software

Despite expanding research activity in gravitational lens modeling, there is no particular software which is considered a standard. Much of the gravitational lens modeling software is written by individual investigators for their own use. Some gravitational lens modeling software is freely available for download but is widely variable with regard to ease of use and quality of documentation. This review of 13 software packages was undertaken to provide a single source of information. Gravitational lens models are classified as parametric models or non-parametric models, and can be further divided into research and educational software. Software used in research includes the GRAVLENS package (with both gravlens and lensmodel), Lenstool, LensPerfect, glafic, PixeLens, SimpLens, Lensview, and GRALE. In this review, GravLensHD, G-Lens, Gravitational Lensing, lens and MOWGLI are categorized as educational programs that are useful for demonstrating various aspects of lensing. Each of the 13 software packages is reviewed with regard to software features (installation, documentation, files provided, etc.) and lensing features (type of model, input data, output data, etc.) as well as a brief review of studies where they have been used. Recent studies have demonstrated the utility of strong gravitational lensing data for mass mapping, and suggest increased use of these techniques in the future. Coupled with the advent of greatly improved imaging, new approaches to modeling of strong gravitational lens systems are needed. This is the first systematic review of strong gravitational lens modeling software, providing investigators with a starting point for future software development to further advance gravitational lens modeling research

Mass-Galaxy offsets in Abell 3827, 2218 and 1689: intrinsic properties or line-of-sight substructures?

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 chance line-of-sight coincidences in $\Lambda CDM$ simulations --- for Abell 3827 and Abell 2218 the offsets appear to be intrinsic. In the case of Abell 1689, we see no significant offsets in the central region, but we do detect a possible line of sight structure: it appears only when sources at z\ga 3 are used for reconstructing the mass. We discuss possible origins of the mass-galaxy offsets in Abell 3827 and Abell 2218: these include pure gravitational effects like dynamical friction, but also non-standard mechanisms like self-interacting dark-matter.Comment: 14 pages, 9 figures; Accepted for publication in MNRA

Quantifying substructures in {\it Hubble Frontier Field} clusters: comparison with ΛCDM\Lambda CDM simulations

The Hubble Frontier Fields (HFF) are six clusters of galaxies, all showing indications of recent mergers, which have recently been observed for lensed images. As such they are the natural laboratories to study the merging history of galaxy clusters. In this work, we explore the 2D power spectrum of the mass distribution $P_{\rm M}(k)$ as a measure of substructure. We compare $P_{\rm M}(k)$ of these clusters (obtained using strong gravitational lensing) to that of $\Lambda$CDM simulated clusters of similar mass. To compute lensing $P_{\rm M}(k)$, we produced free-form lensing mass reconstructions of HFF clusters, without any light traces mass (LTM) assumption. The inferred power at small scales tends to be larger if (i)~the cluster is at lower redshift, and/or (ii)~there are deeper observations and hence more lensed images. In contrast, lens reconstructions assuming LTM show higher power at small scales even with fewer lensed images; it appears the small scale power in the LTM reconstructions is dominated by light information, rather than the lensing data. The average lensing derived $P_{\rm M}(k)$ shows lower power at small scales as compared to that of simulated clusters at redshift zero, both dark-matter only and hydrodynamical. The possible reasons are: (i)~the available strong lensing data are limited in their effective spatial resolution on the mass distribution, (ii)~HFF clusters have yet to build the small scale power they would have at $z\sim 0$, or (iii)~simulations are somehow overestimating the small scale power.Comment: 13 pages, 10 figures, 1 table; Accepted for publication in MNRA

Non-parametric inversion of gravitational lensing systems with few images using a multi-objective genetic algorithm

Galaxies acting as gravitational lenses are surrounded by, at most, a handful of images. This apparent paucity of information forces one to make the best possible use of what information is available to invert the lens system. In this paper, we explore the use of a genetic algorithm to invert in a non-parametric way strong lensing systems containing only a small number of images. Perhaps the most important conclusion of this paper is that it is possible to infer the mass distribution of such gravitational lens systems using a non-parametric technique. We show that including information about the null space (i.e. the region where no images are found) is prerequisite to avoid the prediction of a large number of spurious images, and to reliably reconstruct the lens mass density. While the total mass of the lens is usually constrained within a few percent, the fidelity of the reconstruction of the lens mass distribution depends on the number and position of the images. The technique employed to include null space information can be extended in a straightforward way to add additional constraints, such as weak lensing data or time delay information.Comment: 9 pages, accepted for publication by MNRA