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We present the first weak-lensing-based scaling relation between galaxy cluster mass, M_wl, and integrated Compton parameter Y_sph. Observations of 18 galaxy clusters at z~0.2 were obtained with the Subaru 8.2-m telescope and the Sunyaev-Zeldovich Array. The M_wl-Y_sph scaling relations, measured at Delta=500, 1000, and 2500 rho_c, are consistent in slope and normalization with previous results derived under the assumption of hydrostatic equilibrium (HSE). We find an intrinsic scatter in M_wl at fixed Y_sph of 20%, larger than both previous measurements of M_HSE-Y_sph scatter as well as the scatter in true mass at fixed Y_sph found in simulations. Moreover, the scatter in our lensing-based scaling relations is morphology dependent, with 30-40% larger M_wl for undisturbed compared to disturbed clusters at the same Y_sph at r_500. Further examination suggests that the segregation may be explained by the inability of our spherical lens models to faithfully describe the three-dimensional structure of the clusters, in particular, the structure along the line-of-sight. We find that the ellipticity of the brightest cluster galaxy, a proxy for halo orientation, correlates well with the offset in mass from the mean scaling relation, which supports this picture. This provides empirical evidence that line-of-sight projection effects are an important systematic uncertainty in lensing-based scaling relations.
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We present the first scaling relation between weak-lensing galaxy cluster mass, $M_{WL}$, and near-infrared luminosity, $L_K$. Our results are based on 17 clusters observed with wide-field instruments on Subaru, the United Kingdom Infrared Telescope, the Mayall Telescope, and the MMT. We concentrate on the relation between projected 2D weak-lensing mass and spectroscopically confirmed luminosity within 1Mpc, modelled as $M_{WL} propto L_{K}^b$, obtaining a power law slope of $b=0.83^{+0.27}_{-0.24}$ and an intrinsic scatter of $sigma_{lnM_{WL}|L_{K}}=10^{+8}_{-5}%$. Intrinsic scatter of ~10% is a consistent feature of our results regardless of how we modify our approach to measuring the relationship between mass and light. For example, deprojecting the mass and measuring both quantities within $r_{500}$, that is itself obtained from the lensing analysis, yields $sigma_{lnM_{WL}|L_{K}}=10^{+7}_{-5}%$ and $b=0.97^{+0.17}_{-0.17}$. We also find that selecting members based on their (J-K) colours instead of spectroscopic redshifts neither increases the scatter nor modifies the slope. Overall our results indicate that near-infrared luminosity measured on scales comparable with $r_{500}$ (typically 1Mpc for our sample) is a low scatter and relatively inexpensive proxy for weak-lensing mass. Near-infrared luminosity may therefore be a useful mass proxy for cluster cosmology experiments.
We present the first measurement of the relationship between the Sunyaev-Zeldovich effect signal and the mass of galaxy clusters that uses gravitational lensing to measure cluster mass, based on 14 X-ray luminous clusters at z~0.2 from the Local Cluster Substructure Survey. We measure the integrated Compton y-parameter, Y, and total projected mass of the clusters (M_GL) within a projected clustercentric radius of 350 kpc, corresponding to mean overdensities of 4000-8000 relative to the critical density. We find self-similar scaling between M_GL and Y, with a scatter in mass at fixed Y of 32%. This scatter exceeds that predicted from numerical cluster simulations, however, it is smaller than comparable measurements of the scatter in mass at fixed T_X. We also find no evidence of segregation in Y between disturbed and undisturbed clusters, as had been seen with T_X on the same physical scales. We compare our scaling relation to the Bonamente et al. relation based on mass measurements that assume hydrostatic equilibrium, finding no evidence for a hydrostatic mass bias in cluster cores (M_GL = 0.98+/-0.13 M_HSE), consistent with both predictions from numerical simulations and lensing/X-ray-based measurements of mass-observable scaling relations at larger radii. Overall our results suggest that the Sunyaev-Zeldovich effect may be less sensitive than X-ray observations to the details of cluster physics in cluster cores.
The use of galaxy clusters as precision cosmological probes relies on an accurate determination of their masses. However, inferring the relationship between cluster mass and observables from direct observations is difficult and prone to sample selection biases. In this work, we use weak lensing as the best possible proxy for cluster mass to calibrate the Sunyaev-Zeldovich (SZ) effect measurements from the APEX-SZ experiment. For a well-defined (ROSAT) X-ray complete cluster sample, we calibrate the integrated Comptonization parameter, $Y_{rm SZ}$, to the weak-lensing derived total cluster mass, $M_{500}$. We employ a novel Bayesian approach to account for the selection effects by jointly fitting both the SZ Comptonization, $Y_{rm SZ}text{--}M_{500}$, and the X-ray luminosity, $L_{rm x}text{--}M_{500}$, scaling relations. We also account for a possible correlation between the intrinsic (log-normal) scatter of $L_{rm x}$ and $Y_{rm SZ}$ at fixed mass. We find the corresponding correlation coefficient to be $r= 0.47_{-0.35}^{+0.24}$, and at the current precision level our constraints on the scaling relations are consistent with previous works. For our APEX-SZ sample, we find that ignoring the covariance between the SZ and X-ray observables biases the normalization of the $Y_{rm SZ}text{--}M_{500}$ scaling high by $1text{--}2sigma$ and the slope low by $sim 1sigma$, even when the SZ effect plays no role in the sample selection. We conclude that for higher-precision data and larger cluster samples, as anticipated from on-going and near-future cluster cosmology experiments, similar biases (due to intrinsic covariances of cluster observables) in the scaling relations will dominate the cosmological error budget if not accounted for correctly.
Uncertainty in the mass-observable scaling relations is currently the limiting factor for galaxy cluster based cosmology. Weak gravitational lensing can provide a direct mass calibration and reduce the mass uncertainty. We present new ground-based weak lensing observations of 19 South Pole Telescope (SPT) selected clusters at redshifts $0.29 leq z leq 0.61$ and combine them with previously reported space-based observations of 13 galaxy clusters at redshifts $0.576 leq z leq 1.132$ to constrain the cluster mass scaling relations with the Sunyaev-Zeldovich effect (SZE), the cluster gas mass mgas, and yx, the product of mgas and X-ray temperature. We extend a previously used framework for the analysis of scaling relations and cosmological constraints obtained from SPT-selected clusters to make use of weak lensing information. We introduce a new approach to estimate the effective average redshift distribution of background galaxies and quantify a number of systematic errors affecting the weak lensing modelling. These errors include a calibration of the bias incurred by fitting a Navarro-Frenk-White profile to the reduced shear using $N$-body simulations. We blind the analysis to avoid confirmation bias. We are able to limit the systematic uncertainties to 5.6% in cluster mass (68% confidence). Our constraints on the mass--X-ray observable scaling relations parameters are consistent with those obtained by earlier studies, and our constraints for the mass--SZE scaling relation are consistent with the simulation-based prior used in the most recent SPT-SZ cosmology analysis. We can now replace the external mass calibration priors used in previous SPT-SZ cosmology studies with a direct, internal calibration obtained on the same clusters.
We present novel statistical tools to cross-correlate frequency cleaned thermal Sunyaev-Zeldovich (tSZ) maps and tomographic weak lensing (wl) convergence maps. Moving beyond the lowest order cross-correlation, we introduce a hierarchy of mixed higher-order statistics, the cumulants and cumulant correlators, to analyze non-Gaussianity in real space, as well as corresponding polyspectra in the harmonic domain. Using these moments, we derive analytical expressions for the joint two-point probability distribution function (2PDF) for smoothed tSZ (y_s) and convergence (kappa_s) maps. The presence of tomographic information allows us to study the evolution of higher order {em mixed} tSZ-weak lensing statistics with redshift. We express the joint PDFs p_{kappa y}(kappa_s,y_s) in terms of individual one-point PDFs (p_{kappa}(kappa_s), p_y(y_s)) and the relevant bias functions (b_{kappa}(kappa_s), b_y(y_s)). Analytical results for two different regimes are presented that correspond to the small and large angular smoothing scales. Results are also obtained for corresponding {em hot spots} in the tSZ and convergence maps. In addition to results based on hierarchical techniques and perturbative methods, we present results of calculations based on the lognormal approximation. The analytical expressions derived here are generic and applicable to cross-correlation studies of arbitrary tracers of large scale structure including e.g. that of tSZ and soft X-ray background.
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