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Register a new userCosmology with Stacked Cluster Weak Lensing and Cluster-Galaxy Cross-Correlations
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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.
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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.
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.
We use dense redshift surveys of nine galaxy clusters at $zsim0.2$ to compare the galaxy distribution in each system with the projected matter distribution from weak lensing. By combining 2087 new MMT/Hectospec redshifts and the data in the literature, we construct spectroscopic samples within the region of weak-lensing maps of high (70--89%) and uniform completeness. With these dense redshift surveys, we construct galaxy number density maps using several galaxy subsamples. The shape of the main cluster concentration in the weak-lensing maps is similar to the global morphology of the number density maps based on cluster members alone, mainly dominated by red members. We cross correlate the galaxy number density maps with the weak-lensing maps. The cross correlation signal when we include foreground and background galaxies at 0.5$z_{rm cl}<z<2z_{rm cl}$ is $10-23$% larger than for cluster members alone at the cluster virial radius. The excess can be as high as 30% depending on the cluster. Cross correlating the galaxy number density and weak-lensing maps suggests that superimposed structures close to the cluster in redshift space contribute more significantly to the excess cross correlation signal than unrelated large-scale structure along the line of sight. Interestingly, the weak-lensing mass profiles are not well constrained for the clusters with the largest cross correlation signal excesses ($>$20% for A383, A689 and A750). The fractional excess in the cross correlation signal including foreground and background structures could be a useful proxy for assessing the reliability of weak-lensing cluster mass estimates.
We study the impact of lensing corrections on modeling cross correlations between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in different redshift bins. Estimating the importance of these corrections becomes necessary in the light of anticipated high-accuracy measurements of these observables. While higher order lensing corrections (sometimes also referred to as post Born corrections) have been shown to be negligibly small for lensing auto correlations, they have not been studied for cross correlations. We evaluate the contributing four-point functions without making use of the Limber approximation and compute line-of-sight integrals with the numerically stable and fast FFTlog formalism. We find that the relative size of lensing corrections depends on the respective redshift distributions of the lensing sources and galaxies, but that they are generally small for high signal-to-noise correlations. We point out that a full assessment and judgement of the importance of these corrections requires the inclusion of lensing Jacobian terms on the galaxy side. We identify these additional correction terms, but do not evaluate them due to their large number. We argue that they could be potentially important and suggest that their size should be measured in the future with ray-traced simulations. We make our code publicly available.
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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