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Many applications and algorithms in the field of gravitational lensing make use of meshes with a finite number of nodes to analyse and manipulate data. Specific examples in lensing are astronomical CCD images in general, the reconstruction of density distributions from lensing data, lens-source plane mapping or the characterization and interpolation of a point spread function. We present a numerical framework to interpolate and differentiate in the mesh-free domain, defined by nodes with coordinates that follow no regular pattern. The framework is based on radial basis functions (RBFs) to smoothly represent data around the nodes. We demonstrate the performance of Gaussian RBF-based, mesh-free interpolation and differentiation, which reaches the sub-percent level in both cases. We use our newly developed framework to translate ideas of free-form mass reconstruction from lensing on to the mesh-free domain. By reconstructing a simulated mock lens we find that strong-lensing only reconstructions achieve <10 per cent accuracy in the areas where these constraints are available but provide poorer results when departing from these regions.Weak-lensing only reconstructions give <10 per cent accuracy outside the strong-lensing regime, but cannot resolve the inner core structure of the lens. Once both regimes are combined, accurate reconstructions can be achieved over the full field of view. The reconstruction of a simulated lens, using constraints that mimics real observations, yields accurate results in terms of surface-mass density, Navarro-Frenk-White profile (NFW) parameters, Einstein radius and magnification map recovery, encouraging the application of this method to real data. [ABSTRACT FROM AUTHOR]

According to the current standard model of cosmology, matter in the Universe arranges itself along a network of filamentary structure. These filaments connect the main nodes of this so-called "cosmic web", which are clusters of galaxies. Although its large-scale distribution is clearly characterized by numerical simulations, constraining the dark-matter content of the cosmic web in reality turns out to be difficult. The natural method of choice is gravitational lensing. However, the direct detection and mapping of the elusive filament signal is challenging and in this work we present two methods that are specifically tailored to achieve this task. A linear matched filter aims at detecting the smooth mass-component of filaments and is optimized to perform a shear decomposition that follows the anisotropic component of the lensing signal. Filaments clearly inherit this property due to their morphology. At the same time, the contamination arising from the central massive cluster is controlled in a natural way. The filament 1σ detection is of about κ ∼ 0.01-0.005 according to the filter's template width and length, enabling the detection of structures beyond reach with other approaches. The second, complementary method seeks to detect the clumpy component of filaments. The detection is determined by the number density of subclump identifications in an area enclosing the potential filament, as was found within the observed field with the filter approach. We tested both methods against mocked observations based on realistic N-body simulations of filamentary structure and proved the feasibility of detecting filaments with ground-based data. [ABSTRACT FROM AUTHOR]

Context. Galaxy clusters provide a multitude of observational data across wavelengths, and their structure and morphology are of considerable interest in cosmology as well as astrophysics. Aims. We develop a framework that allows the combination of lensing and non-lensing observations in a free-form and mesh-free approach to infer the projected mass distribution of individual galaxy clusters. This method can be used to test common assumptions on the morphology of clusters in parametric models. Methods. We make use of the lensing reconstruction code SAWLENS2, and expand its capabilities by incorporating an estimate of the projected gravitational potential based on X-ray data that are deprojected using the local Richardson–Lucy method and used to infer the Newtonian potential of the cluster. We discuss how potentially arising numerical artefacts can be treated. Results. We demonstrate the feasibility of our method on a simplified mock Navarro–Frenk–White (NFW) halo and on a cluster from a realistic hydrodynamical simulation. We show how the combination of X-ray and weak lensing data can affect a free-form reconstruction, improving the accuracy in the central region in some cases by a factor of two. [ABSTRACT FROM AUTHOR]

Weak lensing shear estimation typically results in per galaxy statistical errors significantly larger than the sought after gravitational signal of only a few per cent. These statistical errors are mostly a result of shape noise – an estimation error due to the diverse (and a priori unknown) morphology of individual background galaxies. These errors are inversely proportional to the limiting angular resolution at which localized objects, such as galaxy clusters, can be probed with weak lensing shear. In this work, we report on our initial attempt to reduce statistical errors in weak lensing shear estimation using a machine learning approach – training a multilayered convolutional neural network to directly estimate the shear given an observed background galaxy image. We train, calibrate, and evaluate the performance and stability of our estimator using simulated galaxy images designed to mimic the distribution of HST observations of lensed background sources in the CLASH galaxy cluster survey. Using the trained estimator, we produce weak lensing shear maps of the cores of 20 galaxy clusters in the CLASH survey, demonstrating an rms scatter reduced by approximately 26 per cent when compared to maps produced with a commonly used shape estimator. This is equivalent to a survey speed enhancement of approximately 60 per cent. However, given the non-transparent nature of the machine learning approach, this result requires further testing and validation. We provide python code to train and test this estimator on both simulated and real galaxy cluster observations. We also provide updated weak lensing catalogues for the 20 CLASH galaxy clusters studied. [ABSTRACT FROM AUTHOR]

We present integral field spectroscopy of galaxy cluster Abell 3827, using Atacama Large Millimetre Array (ALMA) and Very Large Telescope/Multi-Unit Spectroscopic Explorer. It reveals an unusual configuration of strong gravitational lensing in the cluster core, with at least seven lensed images of a single background spiral galaxy. Lens modelling based on Hubble Space Telescope imaging had suggested that the dark matter associated with one of the cluster's central galaxies may be offset. The new spectroscopic data enable better subtraction of foreground light, and better identification of multiple background images. The inferred distribution of dark matter is consistent with being centred on the galaxies, as expected by Λ cold dark matter. Each galaxy's dark matter also appears to be symmetric. Whilst, we do not find an offset between mass and light (suggestive of self-interacting dark matter) as previously reported, the numerical simulations that have been performed to calibrate Abell 3827 indicate that offsets and asymmetry are still worth looking for in collisions with particular geometries. Meanwhile, ALMA proves exceptionally useful for strong lens image identifications. [ABSTRACT FROM AUTHOR]

We present cosmological parameter constraints from a joint analysis of three cosmological probes: the tomographic cosmic shear signal in ~450 deg² of data from the Kilo Degree Survey (KiDS), the galaxy-matter cross-correlation signal of galaxies from the Galaxies And Mass Assembly (GAMA) survey determined with KiDS weak lensing, and the angular correlation function of the same GAMA galaxies. We use fast power spectrum estimators that are based on simple integrals over the real-space correlation functions, and show that they are practically unbiased over relevant angular frequency ranges. We test our full pipeline on numerical simulations that are tailored to KiDS and retrieve the input cosmology. By fitting different combinations of power spectra, we demonstrate that the three probes are internally consistent. For all probes combined, we obtain S8 ≡ σ8√Ωm/0.3 = 0.800+0.029 -0.027, consistent with Planck and the fiducial KiDS-450 cosmic shear correlation function results. Marginalizing over wide priors on the mean of the tomographic redshift distributions yields consistent results for S8 with an increase of 28 per cent in the error. The combination of probes results in a 26 per cent reduction in uncertainties of S8 over using the cosmic shear power spectra alone. The main gain from these additional probes comes through their constraining power on nuisance parameters, such as the galaxy intrinsic alignment amplitude or potential shifts in the redshift distributions, which are up to a factor of 2 better constrained compared to using cosmic shear alone, demonstrating the value of large-scale structure probe combination. [ABSTRACT FROM AUTHOR]

We study the statistics of peaks in a weak-lensing reconstructed mass map of the first 450 deg2 of the Kilo Degree Survey (KiDS-450). The map is computed with aperture masses directly applied to the shear field with an NFW-like compensated filter. We compare the peak statistics in the observations with that of simulations for various cosmologies to constrain the cosmological parameter S8=σ8Ωm/0.3--√ S8=σ8Ωm/0.3, which probes the (Ωm, σ8) plane perpendicularly to its main degeneracy. We estimate S8 = 0.750 ± 0.059, using peaks in the signal-to-noise range 0 ≤ S/N ≤ 4, and accounting for various systematics, such as multiplicative shear bias, mean redshift bias, baryon feedback, intrinsic alignment, and shear-position coupling. These constraints are ∼ 25 per cent tighter than the constraints from the high significance peaks alone (3 ≤ S/N ≤ 4) which typically trace single-massive haloes. This demonstrates the gain of information from low-S/N peaks. However, we find that including S/N < 0 peaks does not add further information. Our results are in good agreement with the tomographic shear two-point correlation function measurement in KiDS-450. Combining shear peaks with non-tomographic measurements of the shear two-point correlation functions yields a ∼20 per cent improvement in the uncertainty on S8 compared to the shear two-point correlation functions alone, highlighting the great potential of peaks as a cosmological probe. [ABSTRACT FROM AUTHOR]

This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using ∼ 450 deg2 of imaging data from the Kilo Degree Survey (KiDS-450). We measure high signal-to-noise ratio (SNR: ν) weak lensing convergence peaks in the range of 3 < ν < 5, and employ theoretical models to derive expected values. These models are validated using a suite of simulations. We take into account two major systematic effects, the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes. In addition, we investigate the impacts of other potential astrophysical systematics including the projection effects of large-scale structures, intrinsic galaxy alignments, as well as residual measurement uncertainties in the shear and redshift calibration. Assuming a flat Λ cold dark matter model, we find constraints for S8=σ8(Ωm/0.3)0.5=0.746+0.046-0.107 S8=σ8(Ωm/0.3)0.5=0.746-0.107+0.046 according to the degeneracy direction of the cosmic shear analysis and Σ8=σ8(Ωm/0.3)0.38=0.696+0.048-0.050 Σ8=σ8(Ωm/0.3)0.38=0.696-0.050+0.048 based on the derived degeneracy direction of our high-SNR peak statistics. The difference between the power index of S8 and in Σ8 indicates that combining cosmic shear with peak statistics has the potential to break the degeneracy in σ8 and Ωm. Our results are consistent with the cosmic shear tomographic correlation analysis of the same data set and ∼2σ lower than the Planck 2016 results. [ABSTRACT FROM AUTHOR]

We present the tomographic cross-correlation between galaxy lensing measured in the Kilo Degree Survey (KiDS-450) with overlapping lensing measurements of the cosmic microwave background (CMB), as detected by Planck 2015.We compare our joint probe measurement to the theoretical expectation for a flat Λ cold dark matter cosmology, assuming the best-fitting cosmological parameters from the KiDS-450 cosmic shear and Planck CMB analyses. We find that our results are consistent within 1σ with the KiDS-450 cosmology, with an amplitude re-scaling parameter AKiDS = 0.86 ± 0.19. Adopting a Planck cosmology, we find our results are consistent within 2σ, with APlanck = 0.68±0.15.We show that the agreement is improved in both cases when the contamination to the signal by intrinsic galaxy alignments is accounted for, increasing A by ~0.1. This is the first tomographic analysis of the galaxy lensing – CMB lensing cross-correlation signal, and is based on five photometric redshift bins. We use this measurement as an independent validation of the multiplicative shear calibration and of the calibrated source redshift distribution at high redshifts. We find that constraints on these two quantities are strongly correlated when obtained from this technique, which should therefore not be considered as a stand-alone competitive calibration tool. [ABSTRACT FROM AUTHOR]

We determine the concentration-mass relation of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble survey in theories of gravity that directly modify the lensing potential. We model the clusters as Navarro-Frenk-White haloes and fit their lensing signal, in the Cubic Galileon and Nonlocal gravity models, to the lensing convergence profiles of the clusters. We discuss a number of important issues that need to be taken into account, associated with the use of non-parametric and parametric lensing methods, as well as assumptions about the background cosmology. Our results show that the concentration and mass estimates in the modified gravity models are, within the error bars, the same as in Î cold dark matter. This result demonstrates that, for the Nonlocal model, the modifications to gravity are too weak at the cluster redshifts, and for the Galileon model, the screening mechanism is very efficient inside the cluster radius. However, at distances ~(2-20) Mpc h-1 from the cluster centre, we find that the surrounding force profiles are enhanced by ~20-40 per cent in the Cubic Galileon model. This has an impact on dynamical mass estimates, which means that tests of gravity based on comparisons between lensing and dynamical masses can also be applied to the Cubic Galileon model. [ABSTRACT FROM AUTHOR]

We present results from a comprehensive lensing analysis in Hubble Space Telescope (HST) data of the complete Cluster Lensing And Supernova survey with Hubble cluster sample. We identify previously undiscovered multiple images, 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 field of view (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 Navarro-Frenk-White form for the dark matter) to provide a better assessment of the underlying systematics—which is most important for deep, cluster-lensing surveys, especially when studying magnified high-redshift objects. We find that the typical (median), relative systematic differences throughout the central FOV are ∼40% in the (dimensionless) mass density, κ, and ∼20% in the magnification, μ. We show maps of these differences for each cluster, as well as the mass distributions, critical curves, and two-dimensional (2D)-integrated mass profiles. For the Einstein radii (zs = 2) we find that all typically agree within 10% between the two models, and Einstein masses agree, typically, within ∼15%. At larger radii, the total projected, 2D-integrated mass profiles of the two models, within r ∼ 2′, differ by ∼30%. Stacking the surface-density profiles of the sample from the two methods together, we obtain an average slope of dlog (Σ)/dlog (r) ∼ –0.64 ± 0.1, in the radial range [5350] kpc. Last, we also characterize the behavior of the average magnification, surface density, and shear differences between the two models as a function of both the radius from the center and the best-fit values of these quantities. All mass models and magnification maps are made publicly available for the community. [ABSTRACT FROM AUTHOR]

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 crosssection σDM/m ~ (1.7 ± 0.7) × 10-4 cm2 g-1 × (tinfall/109 yr)-2, where tinfall is the infall duration. [ABSTRACT FROM AUTHOR]

We report observations of three gravitationally lensed supernovae (SNe) in the Cluster Lensing And Supernova survey with Hubble (CLASH) Multi-Cycle Treasury program. These objects, SN CLO12Car (z = 1.28), SN CLN12Did (z = 0.85), and SN CLA11Tib (z = 1.14), are located behind three different clusters, MACSJ1720.2+3536 (z = 0.391), RXJ1532.9+3021 (z = 0.345), and A383 (z = 0.187), respectively. Each SN was detected in Hubble Space Telescope optical and infrared images. Based on photometric classification, we find that SNe CLO12Car and CLN12Did are likely to be Type Ia supernovae (SNe Ia), while the classification of SN CLA11Tib is inconclusive. Using multi-color light-curve fits to determine a standardized SN Ia luminosity distance, we infer that SN CLO12Car was ∼1.0 ± 0.2 mag brighter than field SNe Ia at a similar redshift and ascribe this to gravitational lens magnification. Similarly, SN CLN12Did is ∼0.2 ± 0.2 mag brighter than field SNe Ia. We derive independent estimates of the predicted magnification from CLASH strong+weak-lensing maps of the clusters (in magnitude units, 2.5 log10μ): 0.83 ± 0.16 mag for SN CLO12Car, 0.28 ± 0.08 mag for SN CLN12Did, and 0.43 ± 0.11 mag for SN CLA11Tib. The two SNe Ia provide a new test of the cluster lens model predictions: we find that the magnifications based on the SN Ia brightness and those predicted by the lens maps are consistent. Our results herald the promise of future observations of samples of cluster-lensed SNe Ia (from the ground or space) to help illuminate the dark-matter distribution in clusters of galaxies, through the direct determination of absolute magnifications. [ABSTRACT FROM AUTHOR]

The galaxy cluster MACS J0717.5+3745 (z = 0.55) is the largest known cosmic lens, with complex internal structures seen in deep X-ray, Sunyaev-Zel'dovich effect, and dynamical observations. We perform a combined weak- and strong-lensing analysis with wide-field BVRci′z′ Subaru/Suprime-Cam observations and 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble. We find consistent weak distortion and magnification measurements of background galaxies and combine these signals to construct an optimally estimated radial mass profile of the cluster and its surrounding large-scale structure out to 5 Mpc h–1. We find consistency between strong-lensing and weak-lensing in the region where these independent data overlap, <500 kpc h–1. The two-dimensional weak-lensing map reveals a clear filamentary structure traced by distinct mass halos. We model the lensing shear field with nine halos, including the main cluster, corresponding to mass peaks detected above 2.5σκ. The total mass of the cluster as determined by the different methods is Mvir ≈ (2.8 ± 0.4) × 1015M☼. Although this is the most massive cluster known at z > 0.5, in terms of extreme value statistics, we conclude that the mass of MACS J0717.5+3745 by itself is not in serious tension with ΛCDM, representing only a ∼2σ departure above the maximum simulated halo mass at this redshift. [ABSTRACT FROM AUTHOR]

We present a joint shear-and-magnification weak-lensing analysis of a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19 ≲ z ≲ 0.69 selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis uses wide-field multi-color imaging, taken primarily with Suprime-Cam on the Subaru Telescope. From a stacked-shear-only analysis of the X-ray-selected subsample, we detect the ensemble-averaged lensing signal with a total signal-to-noise ratio of ≃ 25 in the radial range of 200-3500 kpc h–1, providing integrated constraints on the halo profile shape and concentration-mass relation. The stacked tangential-shear signal is well described by a family of standard density profiles predicted for dark-matter-dominated halos in gravitational equilibrium, namely, the Navarro-Frenk-White (NFW), truncated variants of NFW, and Einasto models. For the NFW model, we measure a mean concentration of at an effective halo mass of . We show that this is in excellent agreement with Λ cold dark matter (ΛCDM) predictions when the CLASH X-ray selection function and projection effects are taken into account. The best-fit Einasto shape parameter is , which is consistent with the NFW-equivalent Einasto parameter of ∼0.18. We reconstruct projected mass density profiles of all CLASH clusters from a joint likelihood analysis of shear-and-magnification data and measure cluster masses at several characteristic radii assuming an NFW density profile. We also derive an ensemble-averaged total projected mass profile of the X-ray-selected subsample by stacking their individual mass profiles. The stacked total mass profile, constrained by the shear+magnification data, is shown to be consistent with our shear-based halo-model predictions, including the effects of surrounding large-scale structure as a two-halo term, establishing further consistency in the context of the ΛCDM model. [ABSTRACT FROM AUTHOR]

We present profiles of temperature, gas mass, and hydrostatic mass estimated from new and archival X-ray observations of CLASH clusters. We compare measurements derived from XMM and Chandra observations with one another and compare both to gravitational lensing mass profiles derived with CLASH Hubble Space Telescope and Subaru Telescope lensing data. Radial profiles of Chandra and XMM measurements of electron density and enclosed gas mass are nearly identical, indicating that differences in hydrostatic masses inferred from X-ray observations arise from differences in gas-temperature measurements. Encouragingly, gas temperatures measured in clusters by XMM and Chandra are consistent with one another at ∼100-200 kpc radii, but XMM temperatures systematically decline relative to Chandra temperatures at larger radii. The angular dependence of the discrepancy suggests that additional investigation on systematics such as the XMM point-spread function correction, vignetting, and off-axis responses is yet required. We present the CLASH-X mass-profile comparisons in the form of cosmology-independent and redshift-independent circular-velocity profiles. We argue that comparisons of circular-velocity profiles are the most robust way to assess mass bias. Ratios of Chandra hydrostatic equilibrium (HSE) mass profiles to CLASH lensing profiles show no obvious radial dependence in the 0.3-0.8 Mpc range. However, the mean mass biases inferred from the weak-lensing (WL) and SaWLens data are different. As an example, the weighted-mean value at 0.5 Mpc is 〈 b〉 = 0.12 for the WL comparison and 〈 b〉 = –0.11 for the SaWLens comparison. The ratios of XMM HSE mass profiles to CLASH lensing profiles show a pronounced radial dependence in the 0.3-1.0 Mpc range, with a weighted mean mass bias value rising to 〈 b〉 ≳ 0.3 at ∼1 Mpc for the WL comparison and 〈 b〉 ≈ 0.25 for the SaWLens comparison. The enclosed gas mass profiles from both Chandra and XMM rise to a value ≈1/8 times the total-mass profiles inferred from lensing at ≈0.5 Mpc and remain constant outside of that radius, suggesting that Mgas × 8 profiles may be an excellent proxy for total-mass profiles at ≳ 0.5 Mpc in massive galaxy clusters. [ABSTRACT FROM AUTHOR]

We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z = 0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BVRcIcz′ imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble program. We find good agreement in the regions of overlap between several weak- and strong-lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large-scale structure with the major axis running approximately northwest-southeast (NW-SE), aligned with the cluster and its brightest galaxy shapes, showing elongation with a ∼2: 1 axis ratio in the plane of the sky. Our full-lensing mass profile exhibits a shallow profile slope dln Σ/dln R ∼ –1 at cluster outskirts (R ≳ 1 Mpc h–1), whereas the mass distribution excluding the NW-SE excess regions steepens farther out, well described by the Navarro-Frenk-White form. Assuming a spherical halo, we obtain a virial mass Mvir = (1.1 ± 0.2 ± 0.1) × 1015M☼h–1 and a halo concentration cvir = 6.9 ± 1.0 ± 1.2 (cvir ∼ 5.7 when the central 50 kpc h–1 is excluded), which falls in the range 4 ≲ 〈 c〉 ≲ 7 of average c(M, z) predictions for relaxed clusters from recent Λ cold dark matter simulations. Our full-lensing results are found to be in agreement with X-ray mass measurements where the data overlap, and when combined with Chandra gas mass measurements, they yield a cumulative gas mass fraction of 13.7+4.5– 3.0% at 0.7 Mpc h–1(≈ 1.7 r2500), a typical value observed for high-mass clusters. [ABSTRACT FROM AUTHOR]