Cluster Mass Profiles From a Bayesian Analysis of Weak-Lensing Distortion and Magnification Measurements: Applications to Subaru Data

Abstract

We directly construct model-independent mass profiles of galaxy clusters from combined weak-lensing distortion and magnification measurements within a Bayesian statistical framework, which allows for a full parameter-space extraction of the underlying signal. This method applies to the full range of radius outside the Einstein radius, and recovers the absolute mass normalization. We apply our method to deep Subaru imaging of five high-mass (> 10 15 M ⊙ ) clusters, A1689, A1703, A370, Cl0024+17, and RXJ1347-11, to obtain accurate profiles to beyond the virial radius (r vir ). For each cluster the lens distortion and magnification data are shown to be consistent with each other, and the total signalto-noise ratio of the combined measurements ranges from 13 to 24 per cluster. We form a modelindependent mass profile from stacking the clusters, which is detected at 37σ out to R ≈ 1.7r vir . The projected logarithmic slope γ 2D (R) ≡ d ln Σ/d ln R steepens from γ 2D = −1.01 ± 0.09 at R ≈ 0.1r vir to γ 2D = −1.92 ± 0.51 at R ≈ 0.9r vir . We also derive for each cluster inner strong-lensing based mass profiles from deep Advanced Camera for Surveys observations with the Hubble Space Telescope, which we show overlap well with the outer Subaru-based profiles and together are well described by a generalized form of the Navarro-Frenk-White profile, except for the ongoing merger RXJ1347-11, with modest variations in the central cusp slope (−d ln ρ/d ln r < ∼ 0.9). The improvement here from adding the magnification measurements is significant, ∼ 30% in terms of cluster mass profile measurements, compared with the lensing distortion signal.

A Precise Cluster Mass Profile Averaged From the Highest-Quality Lensing Data

“…This extends our recent weak-lensing work by Umetsu et al (2011), where a Bayesian method was developed for a direct reconstruction of the projected cluster mass profile from complementary weak-lensing distortion and magnification effects , the combination of which can be used to unambiguously determine the absolute mass normalization. For a massive cluster acting as a super-critical lens, the strong-and weak-lensing regimes contribute equal logarithmic coverage of the radial profile , so that here we concentrate on those clusters for which we have high-quality data in both these regimes.…”

“…Careful lensing work on individual clusters has shown that full mass profiles constructed from combined strong-and weaklensing measurements show a continuous steepening radial trend consistent with the predicted form for the family of collisionless CDM halos (Gavazzi et al 2003;Broadhurst et al 2005aUmetsu et al 2010Umetsu et al , 2011. Intriguingly these initial results from combined strong-and weak-lensing measurements reveal a relatively high degree of halo concentration in lensing clusters (e.g., Gavazzi et al 2003;Kneib et al 2003;Zitrin et al 2011d), lying well above the mass-concentration relation for cluster-sized halos predicted by the ΛCDM model, despite careful attempts to correct for potential projection and selection biases inherent to lensing (Hennawi et al 2007;Meneghetti et al 2010b).…”

“…Gravitational lensing of background galaxies offers a robust way of directly obtaining the mass distribution of galaxy clusters (see Bartelmann & Schneider 2001;Umetsu 2010, and references therein) without requiring any assumptions on the dynamical and physical state of the system (Clowe et al 2006;Okabe & Umetsu 2008). A detailed examination of this fundamental prediction has been the focus of our preceding work (Broadhurst et al 2005aMedezinski et al 2007;Umetsu et al 2009Umetsu et al , 2010Umetsu et al , 2011Lemze et al 2009). …”

“…Deep multicolor images of massive cluster cores from Advanced Camera for Surveys (ACS) observations with the Hubble Space Telescope (HST) allow us to identify many sets of multiple images spanning a wide range of redshifts for detailed stronglens modeling (e.g., Broadhurst et al 2005b;Zitrin et al 2009Zitrin et al , 2010Zitrin et al , 2011aZitrin et al , 2011cZitrin et al , 2011d. The wide-field prime-focus cameras of Subaru and Canada-France-Hawaii Telescope (CFHT) have been routinely producing data of sufficient quality to obtain accurate measurements of the weak-lensing signal, providing model-independent cluster mass profiles out to beyond the virial radius (e.g., Broadhurst et al 2005aLimousin et al 2007;Umetsu et al 2009Umetsu et al , 2010Umetsu et al , 2011Coe et al 2010). Our earlier work has demonstrated that without adequate color information, the weak-lensing signal can be heavily diluted particularly toward the cluster center by the presence of unlensed cluster members, leading to biased cluster mass profile measurements with underestimated concentrations and internal inconsistency, with the weak-lensing-based profile underpredicting the observed Einstein radius (Broadhurst et al 2005a;Medezinski et al 2010).…”

Improving lensing cluster mass estimate with flexion

“…In practical observations, the nonvanishing and unresolved small scale angular correlation can increase the variance of counts in cells thus washing out the lensing signal (van Waerbeke 2000). This local clustering noise can be overcome by performing an azimuthal average around the cluster so that the observed quantity is now nµ(θ) = dNµ(θ, z, < m)/dΩ (Umetsu et al 2011;Umetsu 2013). We can therefore define a likelihood function as…”