Jori Liesenborgs

The behaviour of dark matter associated with four bright cluster galaxies in the 10 kpc core of Abell 3827

Galaxy cluster Abell 3827 hosts the stellar remnants of four almost equally bright elliptical galaxies within a core of radius 10 kpc. Such corrugation of the stellar distribution is very rare, and suggests recent formation by several simultaneous mergers. We map the distribution of associated dark matter, using new Hubble Space Telescope imaging and Very Large Telescope/Multi-Unit Spectroscopic Explorer integral field spectroscopy of a gravitationally lensed system threaded through the cluster core. We find that each of the central galaxies retains a dark matter halo, but that (at least) one of these is spatially offset from its stars. The best-constrained offset is 1.62(-0.49)(+0.47) kpc, where the 68 per cent confidence limit includes both statistical error and systematic biases in mass modelling. Such offsets are not seen in field galaxies, but are predicted during the long infall to a cluster, if dark matter self-interactions generate an extra drag force. With such a small physical separation, it is difficult to definitively rule out astrophysical effects operating exclusively in dense cluster core environments - but if interpreted solely as evidence for self-interacting dark matter, this offset implies a cross-section sigma(DM)/(m) similar to (1.7 +/- 0.7) x 10(-4) cm(2) g(-1) x (t(infall)/10(9) yr)(-2), where t(infall) is the infall duration.

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 on to 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 minimize the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.

Full lensing analysis of Abell 1703: comparison of independent lens-modelling techniques

The inner mass-prole of the relaxed cluster Abell 1703 is analysed by two very dierent strong-lensing techniques applied to deep ACS and WFC3 imaging. Our parametric method has the accuracy required to reproduce the many sets of multiple images, based on the assumption that mass approximately traces light. We test this assumption with a fully non-parametric, adaptive grid method, with no knowledge of the galaxy distribution. Dierences between the methods are seen on

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 per cent, 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.

Strong-lensing analysis of MS 1358.4+6245: New multiple images and implications for the well-resolved z= 4.92 galaxy

We present a strong-lensing analysis of the galaxy cluster MS 1358.4+6245 (z = 0:33), in deep 6-band ACS/HST imaging. In addition to the well-studied system at z = 4:92, our modelling method uncovers 19 new multiply-lensed images so that a total of 23 images and their redshifts are used to accurately constrain the inner mass distribution. We derive a relatively shallow inner mass prole, d log =d logr’ 0:33 0:05 (r < 200 kpc), with a much higher magnication than estimated previously by models constrained only by the z = 4:92 system. Using these many new images we can apply a non-parametric adaptive-grid method, which also yields a shallow mass prole without prior assumptions, strengthening our conclusions. The total magnication of

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

Mohammed, I (reprint author),Univ Zurich, Inst Theoret Phys, CH-8057 Zurich, Switzerland, irshad@physik.uzh.ch

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 1.60 x 10(14) M(circle dot) within a 0.5 arcmin radius around the cluster centre. 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.

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 Advanced Camera for Surveys images. We find masses of 2.5 x 10 13 and 6.1 × 10 13 M⊙) within a radius of 60 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 +21 -13 arcsec and c vir = 3.91 ± 0.74. The orientation of the elliptical NFW profile closely follows the orientation of the central cluster galaxy and the overall distribution of cluster members.

The Frontier Fields lens modelling comparison project

Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Several research groups have developed techniques independently to achieve this goal. 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 never been directly compared. In this paper, we present for the first time a detailed comparison of methodologies for fidelity, accuracy and precision. For this collaborative exercise, the lens modelling community was provided simulated cluster images that mimic the depth and resolution of the ongoing HST Frontier Fields. The results of the submitted reconstructions with the un-blinded true mass profile of these two clusters are presented here. Parametric, free-form and hybrid techniques have been deployed by the participating groups and we detail the strengths and trade-offs in accuracy and systematics that arise for each methodology. We note in conclusion that several properties of the lensing clusters are recovered equally well by most of the lensing techniques compared in this study. For example, the reconstruction of azimuthally averaged density and mass profiles by both parametric and free-form methods matches the input models at the level of ∼10 per cent. Parametric techniques are generally better at recovering the 2D maps of the convergence and of the magnification. For the best-performing algorithms, the accuracy in the magnification estimate is ∼10 per cent at μ_(true) = 3 and it degrades to ∼30 per cent at μ_(true) ∼ 10.

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 paper 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 scalefactor. 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 of a 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.