No Arabic abstract
Weak lensing applied to deep optical images of clusters of galaxies provides a powerful tool to reconstruct the distribution of the gravitating mass associated to these structures. We use the shear signal extracted by an analysis of deep exposures of a region centered around the galaxy cluster Abell 209, at redshift z=0.2, to derive both a map of the projected mass distribution and an estimate of the total mass within a characteristic radius. We use a series of deep archival R-band images from CFHT-12k, covering an area of 0.3 deg^2. We determine the shear of background galaxy images using a new implementation of the modified Kaiser-Squires-Broadhurst pipeline for shear determination, which we has been tested against the ``Shear TEsting Program 1 and 2 simulations. We use mass aperture statistics to produce maps of the 2 dimensional density distribution, and parametric fits using both Navarro-Frenk-White (NFW) and singular-isothermal-sphere profiles to constrain the total mass. The projected mass distribution shows a pronounced asymmetry, with an elongated structure extending from the SE to the NW. This is in general agreement with the optical distribution previously found by other authors. A similar elongation was previously detected in the X-ray emission map, and in the distribution of galaxy colours. The circular NFW mass profile fit gives a total mass of M_{200} = 7.7^{+4.3}_{-2.7} 10^{14} solar masses inside the virial radius r_{200} = 1.8pm 0.3 Mpc. The weak lensing profile reinforces the evidence for an elongated structure of Abell 209, as previously suggested by studies of the galaxy distribution and velocities.
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 singular value decomposition. In the other case, the model parameters are estimated using a Bayesian MCMC optimization implemented in the lensing software Lenstool. Methods are compared on simulated data with varying galaxy density fields. We pay particular attention to the errors estimated with resampling. We find the multi-scale grid model optimized with MCMC to provide the best results, but at high computational cost, especially when considering resampling. The SVD method is much faster but yields noisy maps, although this can be mitigated with resampling. The FLens method is a good compromise with fast computation, high signal to noise reconstruction, but lower resolution maps. All three methods are applied to the MACS J0717+3745 galaxy cluster field, and reveal the filamentary structure discovered in Jauzac et al. 2012. We conclude that sensitive priors can help to get high signal to noise, and unbiased reconstructions.
Merging clusters of galaxies are unique in their power to directly probe and place limits on the self-interaction cross-section of dark matter. Detailed observations of several merging clusters have shown the intracluster gas to be displaced from the centroids of dark matter and galaxy density by ram pressure, while the latter components are spatially coincident, consistent with collisionless dark matter. This has been used to place upper limits on the dark matter particle self-inteaction cross-section of order 1 cm^2/g. The cluster Abell 520 has been seen as a possible exception. We revisit A520 presenting new HST ACS mosaic images and a Magellan image set. We perform a detailed weak lensing analysis and show that the weak lensing mass measurements and morphologies of the core galaxy-filled structures are mostly in good agreement with previous works. There is however one significant difference -- we do not detect the previously claimed dark core that contains excess mass with no significant galaxy overdensity at the location of the X-ray plasma. This peak has been suggested to be indicative of a large self-interaction cross-section for dark matter (at least ~5 sigma larger than the upper limit of 0.7 cm^2/g determined by observations of the Bullet Cluster). We find no such indication and instead find that the mass distribution of A520, after subtraction of the X-ray plasma mass, is in good agreement with the luminosity distribution of the cluster galaxies. We conclude that A520 shows no evidence to contradict the collisionless dark matter scenario.
Weak gravitational lensing of background galaxies provides a direct probe of the projected matter distribution in and around galaxy clusters. Here we present a self-contained pedagogical review of cluster--galaxy weak lensing, covering a range of topics relevant to its cosmological and astrophysical applications. We begin by reviewing the theoretical foundations of gravitational lensing from first principles, with special attention to the basics and advanced techniques of weak gravitational lensing. We summarize and discuss key findings from recent cluster--galaxy weak-lensing studies on both observational and theoretical grounds, with a focus on cluster mass profiles, the concentration--mass relation, the splashback radius, and implications from extensive mass calibration efforts for cluster cosmology.
Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, the mass-sheet degeneracy transformation has limited its success. We present a novel method for a cluster mass reconstruction which combines weak and strong lensing information on common scales and can, as a consequence, break the mass-sheet degeneracy. We extend the weak lensing formalism to the inner parts of the cluster and combine it with the constraints from multiple image systems. We demonstrate the feasibility of the method with simulations, finding an excellent agreement between the input and reconstructed mass also on scales within and beyond the Einstein radius. Using a single multiple image system and photometric redshift information of the background sources used for weak and strong lensing analysis, we find that we are effectively able to break the mass-sheet degeneracy, therefore removing one of the main limitations on cluster mass estimates. We conclude that with high resolution (e.g. HST) imaging data the method can more accurately reconstruct cluster masses and their profiles than currently existing lensing techniques.
We report the first weak-lensing detection of a large-scale filament funneling matter onto the core of the massive galaxy cluster MACSJ0717.5+3745. Our analysis is based on a mosaic of 18 multi-passband images obtained with ACS aboard the HST, covering an area of sim 10x20 arcmin^2. We use a weak-lensing pipeline developed for the COSMOS survey, modified for the analysis of galaxy clusters, to produce a weak-lensing catalogue. A mass map is then computed by applying a weak-gravitational-lensing multi-scale reconstruction technique designed to describe irregular mass distributions such as the one investigated here. We test the resulting mass map by comparing the mass distribution inferred for the cluster core with the one derived from strong-lensing constraints and find excellent agreement. The filament is detected within the 3 sigma detection contour of the lensing mass reconstruction, and underlines the importance of filaments for theoretical and numerical models of the mass distribution in the Cosmic Web. We measure the filaments projected length as sim 4.5 h_{74}^{-1} Mpc, and its mean density as (2.92 pm 0.66)10^8 h_{74} M_{odot} kpc^{-2}. Combined with the redshift distribution of galaxies obtained after an extensive spectroscopic follow-up in the area, we can rule out any projection effect resulting from the chance alignment on the sky of unrelated galaxy group-scale structures. Assuming plausible constraints concerning the structures geometry based on its galaxy velocity field, we construct a 3D model of the large-scale filament. Within this framework, we derive the three-dimensional length of the filament to be 18 h_{74}^{-1} Mpc, and a deprojected density in terms of the critical density of the Universe of (206 pm 46) rho_{crit}, a value that lies at the very high end of the range predicted by numerical simulations.