Cross-correlation Weak Lensing of SDSS galaxy Clusters II: Cluster Density Profiles and the Mass--Richness Relation

Abstract

We interpret and model the statistical weak lensing measurements around 130,000 groups and clusters of galaxies in the Sloan Digital Sky Survey presented by Sheldon et al. (2007). We present non-parametric inversions of the 2D shear profiles to the mean 3D cluster density and mass profiles in bins of both optical richness and cluster i-band luminosity. Since the mean cluster density profile is proportional to the cluster-mass correlation function, the mean profile is spherically symmetric by the assumptions of large-scale homogeneity and isotropy. We correct the inferred 3D profiles for systematic effects, including non-linear shear and the fact that cluster halos are not all precisely centered on their brightest galaxies. We also model the measured cluster shear profile as a sum of contributions from the brightest central galaxy, the cluster dark matter halo, and neighboring halos. We infer the relations between mean cluster virial mass and optical richness and luminosity over two orders of magnitude in cluster mass; the virial mass at fixed richness or luminosity is determined with a precision of ∼ 13% including both statistical and systematic errors. We also constrain the halo concentration parameter and halo bias as a function of cluster mass; both are in good agreement with predictions from N-body simulations of LCDM models. The methods employed here will be applicable to deeper, wide-area optical surveys that aim to constrain the nature of the dark energy, such as the Dark Energy Survey, the Large Synoptic Survey Telescope and space-based surveys.

Observational probes of cosmic acceleration

“…Cosmological analyses from optical samples have typically been less constraining because of uncertain mass calibration (see, e.g., Bahcall et al, 2003;Gladders et al, 2007;Wen et al, 2010). However, recent work that uses stacked weak lensing analysis for mass calibration (Johnston et al, 2007;Mandelbaum et al, 2008;Sheldon et al, 2009) has allowed optical samples to achieve the same level of precision as X-ray samples , with comparable levels of systematic error. Constraints from SZ selected samples are emerging (Vanderlinde et al, 2010;Sehgal et al, 2011;Reichardt et al, 2013), and while they are currently weak because of the relatively large uncertainty in the SZ-mass scaling relation, the extensive follow-up campaigns that are currently underway will reduce this scaling uncertainty and bring these constraints to a level comparable to those from optical and X-ray cluster catalogs (e.g.…”

“…In other words, the stacked weak lensing signal is the cluster-shear correlation function, which can be inverted to yield the mean 3-d mass profile of clusters in the bin (Johnston et al, 2007). Because this measurement allows one to stack many clusters, one can easily obtain high signalto-noise measurements even for low mass clusters and large angular distances (Mandelbaum et al, 2008;Sheldon et al, 2009).…”

“…The miscentering problem is most difficult in the optical, where the center is typically chosen to be a specific galaxy but the choice of galaxy is not necessarily obvious; X-ray studies of SDSS maxBCG clusters suggest that the mis-centered fraction is about 30% (Andreon and Moretti, 2011). Mis-centering is currently one of the dominant systematics in stacked cluster lensing, introducing uncertainties at the ≈ 5% − 10% level (Johnston et al, 2007). There are ongoing efforts aimed at improving cluster centering (George et al, 2012, Rykoff et al in preparation).…”

Dark energy two decades after: observables, probes, consistency tests

“…[308,309]), γ t is the tangentially-projected shear, and Σ crit is the critical surface density, a known function of the distances to the source and the lens. Current measurements constrain the density profiles and bias of dark matter halos [301,[310][311][312] as well as the relation between their masses and luminosities [313,314]. In the future, galaxyshear correlations have the potential to constrain dark energy models [315] and modified gravity models for the accelerating universe [316].…”

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

“…Nearby, lower-mass haloes bias the recovered mass high by a few percent: 2.5 ± 0.3% and 6.3 ± 1.1% for T M L and QU M L respectively. This bias can be mitigated by explicitly fitting for the 2-halo term [38,39]. This, however, will slightly worsen the constraints on the recovered lensing mass because of the additional nuisance parameters involved in the fitting process.…”