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Register a new userWeak Lensing Galaxy Cluster Field Reconstruction
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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.
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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.
Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering $sigma_8$ and matter density parameter $Omega_m$. The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted $sigma_{ln Mc}$. We show that combining the cluster weak lensing observable $Delta Sigma$ with the projected cluster-galaxy cross-correlation function $w_{p,cg}$ and galaxy auto-correlation function $w_{p,gg}$ can break the degeneracy between $sigma_8$ and $sigma_{ln Mc}$ to achieve tight, percent-level constraints on $sigma_8$. Using a grid of cosmological N-body simulations, we compute derivatives of $Delta Sigma$, $w_{p,cg}$, and $w_{p,gg}$ with respect to $sigma_8$, $Omega_m$, $sigma_{ln Mc}$ and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Suvery (DES) cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining $Delta Sigma$, $w_{p,cg}$, and $w_{p,gg}$ measured over $0.3-30.0 ; h^{-1} ; mathrm{Mpc}$, for clusters at $z=0.35-0.55$ above a mass threshold $M_capprox 2times 10^{14} ; h^{-1} ; mathrm{M_{odot}}$, we forecast a $1.4%$ constraint on $sigma_8$ while marginalizing over $sigma_{ln Mc}$ and all HOD parameters. Reducing the mass threshold to $1times 10^{14} ; h^{-1} ; mathrm{M_{odot}}$ and adding a $z=0.15-0.35$ redshift bin sharpens this constraint to $0.8%$. The small scale $(r_p < 3.0 ; h^{-1} ; mathrm{Mpc})$ ``mass function and large scale $(r_p > 3.0 ; h^{-1} ; mathrm{Mpc})$ ``halo-mass cross-correlation regimes of $Delta Sigma$ have comparable constraining power, allowing internal consistency tests from such an analysis.
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.
Intrinsic variations of the projected density profiles of clusters of galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We present a semi-analytical model to account for this effect, based on a combination of variations in halo concentration, ellipticity and orientation, and the presence of correlated haloes. We calibrate the parameters of our model at the 10 per cent level to match the empirical cosmic variance of cluster profiles at M_200m=10^14...10^15 h^-1 M_sol, z=0.25...0.5 in a cosmological simulation. We show that weak lensing measurements of clusters significantly underestimate mass uncertainties if intrinsic profile variations are ignored, and that our model can be used to provide correct mass likelihoods. Effects on the achievable accuracy of weak lensing cluster mass measurements are particularly strong for the most massive clusters and deep observations (with ~20 per cent uncertainty from cosmic variance alone at M_200m=10^15 h^-1 M_sol and z=0.25), but significant also under typical ground-based conditions. We show that neglecting intrinsic profile variations leads to biases in the mass-observable relation constrained with weak lensing, both for intrinsic scatter and overall scale (the latter at the 15 per cent level). These biases are in excess of the statistical errors of upcoming surveys and can be avoided if the cosmic variance of cluster profiles is accounted for.
Weak gravitational lensing of background galaxies is a unique, direct probe of the distribution of matter in clusters of galaxies. We review several important aspects of cluster weak gravitational lensing together with recent advances in weak lensing techniques for measuring cluster lensing profiles and constraining cluster structure parameters.
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