ALBERT

Description: We employ robust weak gravitational lensing measurements to improve cosmological constraints from measurements of the galaxy cluster mass function and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky Survey. Our lensing analysis constrains the absolute mass scale of such clusters at the 8 per cent level, including both statistical and systematic uncertainties. Combining it with the survey data and X-ray follow-up observations, we find a tight constraint on a combination of the mean matter density and late-time normalization of the matter power spectrum, 8 ( m /0.3) 0.17  = 0.81 ± 0.03, with marginalized, one-dimensional constraints of m  = 0.26 ± 0.03 and 8  = 0.83 ± 0.04. For these two parameters, this represents a factor of 2 improvement in precision with respect to previous work, primarily due to the reduced systematic uncertainty in the absolute mass calibration provided by the lensing analysis. Our new results are in good agreement with constraints from cosmic microwave background (CMB) data, both Wilkinson Microwave Anisotropy Probe ( WMAP ) and Planck (plus WMAP polarization), under the assumption of a flat CDM cosmology with minimal neutrino mass. Consequently, we find no evidence for non-minimal neutrino mass from the combination of cluster data with CMB, supernova and baryon acoustic oscillation measurements, regardless of which all-sky CMB data set is used (and independent of the recent claimed detection of B modes on degree scales). We also present improved constraints on models of dark energy (both constant and evolving), modifications of gravity, and primordial non-Gaussianity. Assuming flatness, the constraints for a constant dark energy equation of state from the cluster data alone are at the 15 per cent level, improving to ~6 per cent when the cluster data are combined with other leading probes.

Description: In light of the tension in cosmological constraints reported by the Planck team between their Sunyaev–Zel'dovich-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 〈 M Planck / M WtG 〉 = 0.688 ± 0.072. Extending the sample to clusters not used in the Planck cosmology analysis yields a consistent value of 〈 M Planck / M WtG 〉 = 0.698 ± 0.062 from 38 clusters in common. Identifying the weak-lensing masses as proxies for the true cluster mass (on average), these ratios are ~1.6 lower than the default bias factor 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.

Description: We present improved methods for using stars found in astronomical exposures to calibrate both star and galaxy colours as well as to adjust the instrument flat-field. By developing a spectroscopic model for the Sloan Digital Sky Survey (SDSS) stellar locus in colour–colour space, synthesizing an expected stellar locus, and simultaneously solving for all unknown zero-points when fitting to the instrumental locus, we increase the calibration accuracy of stellar locus matching. We also use a new combined technique to estimate improved flat-field models for the Subaru SuprimeCam camera, forming ‘star flats’ based on the magnitudes of stars observed in multiple positions or through comparison with available measurements in the SDSS catalogue. These techniques yield galaxy magnitudes with reliable colour calibration (0.01–0.02 mag accuracy) that enable us to estimate photometric redshift probability distributions without spectroscopic training samples. We test the accuracy of our photometric redshifts using spectroscopic redshifts z s for ~5000 galaxies in 27cluster fields with at least five bands of photometry, as well as galaxies in the Cosmic Evolution Survey (COSMOS) field, finding (( z p  –  z s )/(1 +  z s )) 0.03 for the most probable redshift z p . We show that the full posterior probability distributions for the redshifts of galaxies with five-band photometry exhibit good agreement with redshifts estimated from thirty-band photometry in the COSMOS field. The growth of shear with increasing distance behind each galaxy cluster shows the expected redshift–distance relation for a flat cold dark matter (-CDM) cosmology. Photometric redshifts and calibrated colours are used in subsequent papers to measure the masses of 51 galaxy clusters from their weak gravitational shear and determine improved cosmological constraints. We make our python code for stellar locus matching publicly available at http://big-macs-calibrate.googlecode.com ; the code requires only input catalogues and filter transmission functions.

Description: We report weak-lensing masses for 51 of the most X-ray luminous galaxy clusters known. This cluster sample, introduced earlier in this series of papers, spans redshifts 0.15   z cl   0.7, and is well suited to calibrate mass proxies for current cluster cosmology experiments. Cluster masses are measured with a standard ‘colour-cut’ lensing method from three-filter photometry of each field. Additionally, for 27 cluster fields with at least five-filter photometry, we measure high-accuracy masses using a new method that exploits all information available in the photometric redshift posterior probability distributions of individual galaxies. Using simulations based on the COSMOS-30 catalogue, we demonstrate control of systematic biases in the mean mass of the sample with this method, from photometric redshift biases and associated uncertainties, to better than 3 per cent. In contrast, we show that the use of single-point estimators in place of the full photometric redshift posterior distributions can lead to significant redshift-dependent biases on cluster masses. The performance of our new photometric redshift-based method allows us to calibrate ‘colour-cut’ masses for all 51 clusters in the present sample to a total systematic uncertainty of 7 per cent on the mean mass, a level sufficient to significantly improve current cosmology constraints from galaxy clusters. Our results bode well for future cosmological studies of clusters, potentially reducing the need for exhaustive spectroscopic calibration surveys as compared to other techniques, when deep, multifilter optical and near-IR imaging surveys are coupled with robust photometric redshift methods.

Description: This is the first in a series of papers in which we measure accurate weak-lensing masses for 51 of the most X-ray luminous galaxy clusters known at redshifts 0.15   z Cl   0.7, in order to calibrate X-ray and other mass proxies for cosmological cluster experiments. The primary aim is to improve the absolute mass calibration of cluster observables, currently the dominant systematic uncertainty for cluster count experiments. Key elements of this work are the rigorous quantification of systematic uncertainties, high-quality data reduction and photometric calibration, and the ‘blind’ nature of the analysis to avoid confirmation bias. Our target clusters are drawn from X-ray catalogues based on the ROSAT All-Sky Survey, and provide a versatile calibration sample for many aspects of cluster cosmology. We have acquired wide-field, high-quality imaging using the Subaru Telescope and Canada–France–Hawaii Telescope for all 51 clusters, in at least three bands per cluster. For a subset of 27 clusters, we have data in at least five bands, allowing accurate photometric redshift estimates of lensed galaxies. In this paper, we describe the cluster sample and observations, and detail the processing of the SuprimeCam data to yield high-quality images suitable for robust weak-lensing shape measurements and precision photometry. For each cluster, we present wide-field three-colour optical images and maps of the weak-lensing mass distribution, the optical light distribution and the X-ray emission. These provide insights into the large-scale structure in which the clusters are embedded. We measure the offsets between X-ray flux centroids and the brightest cluster galaxies in the clusters, finding these to be small in general, with a median of 20 kpc. For offsets 100 kpc, weak-lensing mass measurements centred on the brightest cluster galaxies agree well with values determined relative to the X-ray centroids; miscentring is therefore not a significant source of systematic uncertainty for our weak-lensing mass measurements. In accompanying papers, we discuss the key aspects of our photometric calibration and photometric redshift measurements (Kelly et al.), and measure cluster masses using two methods, including a novel Bayesian weak-lensing approach that makes full use of the photometric redshift probability distributions for individual background galaxies (Applegate et al.). In subsequent papers, we will incorporate these weak-lensing mass measurements into a self-consistent framework to simultaneously determine cluster scaling relations and cosmological parameters.