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Register a new userCalibration of the Mass-Temperature Relation for Clusters of Galaxies Using Weak Gravitational Lensing
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The main uncertainty in current determinations of the power spectrum normalization, sigma_8, from abundances of X-ray luminous galaxy clusters arises from the calibration of the mass-temperature relation. We use our weak lensing mass determinations of 30 clusters from the hitherto largest sample of clusters with lensing masses, combined with X-ray temperature data from the literature, to calibrate the normalization of this relation at a temperature of 8 keV, M_{500c,8 keV}=(8.7 +/- 1.6) h^{-1} 10^{14} M_sun. This normalization is consistent with previous lensing-based results based on smaller cluster samples, and with some predictions from numerical simulations, but higher than most normalizations based on X-ray derived cluster masses. Assuming the theoretically expected slope alpha=3/2 of the mass-temperature relation, we derive sigma_8 = 0.88 +/-0.09 for a spatially-flat LambdaCDM universe with Omega_m = 0.3. The main systematic errors on the lensing masses result from extrapolating the cluster masses beyond the field-of-view used for the gravitational lensing measurements, and from the separation of cluster/background galaxies, contributing each with a scatter of 20%. Taking this into account, there is still significant intrinsic scatter in the mass-temperature relation indicating that this relation may not be very tight, at least at the high mass end. Furthermore, we find that dynamically relaxed clusters are 75 +/-40% hotter than non-relaxed clusters.
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In light of the tension in cosmological constraints reported by the Planck team between their SZ-selected cluster counts and Cosmic Microwave Background (CMB) temperature anisotropies, we compare the Planck cluster mass estimates with robust, weak-lensing mass measurements from the Weighing the Giants (WtG) project. For the 22 clusters in common between the Planck cosmology sample and WtG, we find an overall mass ratio of $left< M_{Planck}/M_{rm WtG} right> = 0.688 pm 0.072$. Extending the sample to clusters not used in the Planck cosmology analysis yields a consistent value of $left< M_{Planck}/M_{rm WtG} right> = 0.698 pm 0.062$ from 38 clusters in common. Identifying the weak-lensing masses as proxies for the true cluster mass (on average), these ratios are $sim 1.6sigma$ lower than the default mass bias of 0.8 assumed in the Planck cluster analysis. Adopting the WtG weak-lensing-based mass calibration would substantially reduce the tension found between the Planck cluster count cosmology results and those from CMB temperature anisotropies, thereby dispensing of the need for new physics such as uncomfortably large neutrino masses (in the context of the measured Planck temperature anisotropies and other data). We also find modest evidence (at 95 per cent confidence) for a mass dependence of the calibration ratio and discuss its potential origin in light of systematic uncertainties in the temperature calibration of the X-ray measurements used to calibrate the Planck cluster masses. Our results exemplify the critical role that robust absolute mass calibration plays in cluster cosmology, and the invaluable role of accurate weak-lensing mass measurements in this regard.
We describe first results of a project to create weak lensing mass maps for a complete, X-ray luminosity-limited sample of 19 nearby (z < 0.1) southern galaxy clusters scheduled for Sunyaev-Zeldovich observations by the Viper Telescope at the South Pole. We have collected data on 1/3 of the sample and present motivation for the project as well as projected mass maps of two clusters.
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.
We present the K-band luminosity-halo mass relation, $L_{K,500}-M_{500,WL}$, for a subsample of 20 of the 100 brightest clusters in the XXL Survey observed with WIRCam at the Canada-France-Hawaii Telescope (CFHT). For the first time, we have measured this relation via weak-lensing analysis down to $M_{500,WL} =3.5 times 10^{13},M_odot$. This allows us to investigate whether the slope of the $L_K-M$ relation is different for groups and clusters, as seen in other works. The clusters in our sample span a wide range in mass, $M_{500,WL} =0.35-12.10 times 10^{14},M_odot$, at $0<z<0.6$. The K-band luminosity scales as $log_{10}(L_{K,500}/10^{12}L_odot) propto beta log_{10}(M_{500,WL}/10^{14}M_odot)$ with $beta = 0.85^{+0.35}_{-0.27}$ and an intrinsic scatter of $sigma_{lnL_K|M} =0.37^{+0.19}_{-0.17}$. Combining our sample with some clusters in the Local Cluster Substructure Survey (LoCuSS) present in the literature, we obtain a slope of $1.05^{+0.16}_{-0.14}$ and an intrinsic scatter of $0.14^{+0.09}_{-0.07}$. The flattening in the $L_K-M$ seen in previous works is not seen here and might be a result of a bias in the mass measurement due to assumptions on the dynamical state of the systems. We also study the richness-mass relation and find that group-sized halos have more galaxies per unit halo mass than massive clusters. However, the brightest cluster galaxy (BCG) in low-mass systems contributes a greater fraction to the total cluster light than BCGs do in massive clusters; the luminosity gap between the two brightest galaxies is more prominent for group-sized halos. This result is a natural outcome of the hierarchical growth of structures, where massive galaxies form and gain mass within low-mass groups and are ultimately accreted into more massive clusters to become either part of the BCG or one of the brighter galaxies. [Abridged]
Cosmological inference from cluster number counts is systematically limited by the accuracy of the mass calibration, i.e. the empirical determination of the mapping between cluster selection observables and halo mass. In this work we demonstrate a method to quantitatively determine the bias and uncertainties in weak-lensing mass calibration. To this end, we extract a library of projected matter density profiles from hydrodynamical simulations. Accounting for shear bias and noise, photometric redshift uncertainties, mis-centering, cluster member contamination, cluster morphological diversity, and line-of-sight projections, we produce a library of shear profiles. Fitting a one-parameter model to these profiles, we extract the so-called emph{weak lensing mass} $M_text{WL}$. Relating the weak-lensing mass to the halo mass from gravity-only simulations with the same initial conditions as the hydrodynamical simulations allows us to estimate the impact of hydrodynamical effects on cluster number counts experiments. Creating new shear libraries for $sim$1000 different realizations of the systematics, provides a distribution of the parameters of the weak-lensing to halo mass relation, reflecting their systematic uncertainty. This result can be used as a prior for cosmological inference. We also discuss the impact of the inner fitting radius on the accuracy, and determine the outer fitting radius necessary to exclude the signal from neighboring structures. Our method is currently being applied to different Stage~III lensing surveys, and can easily be extended to Stage~IV lensing surveys.
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