Parametric modeling of galaxy cluster density profiles from weak lensing observations leads to a mass bias, whose detailed understanding is critical in deriving accurate mass-observable relations for constraining cosmological models. Drawing from existing methods, we develop a robust framework for calculating this mass bias in one-parameter fits to simulations of dark matter halos. We show that our approach has the advantage of being independent of the absolute noise level, so that only the number of halos in a given simulation and the representativeness of the simulated halos for real clusters limit the accuracy of the bias estimation. While we model the bias as a log-normal distribution and the halos with a Navarro-Frenk-White profile, our method can be generalized to any bias distribution and parametric model of the radial mass distribution. We find that the log-normal assumption is not strictly valid in the presence of miscentring of halos. We investigate the use of cluster centers derived from weak lensing in the context of mass bias, and tentatively find that such centroids can yield sensible mass estimates if the convergence peak has a signal-to-noise ratio approximately greater than four. In this context we also find that the standard approach to estimating the positional uncertainty of weak lensing mass peaks using bootstrapping severely underestimates the true positional uncertainty for peaks with low signal-to-noise ratios. Though we determine the mass and redshift dependence of the bias distribution for a few experimental setups, our focus remains providing a general approach to computing such distributions.

Context. Observations of relaxed, massive, and distant clusters can provide important tests of standard cosmological models, for example by using the gas mass fraction. To perform this test, the dynamical state of the cluster and its gas properties have to be investigated. X-ray analyses provide one of the best opportunities to access this information and to determine important properties such as temperature profiles, gas mass, and the total X-ray hydrostatic mass. For the last of these, weak gravitational lensing analyses are complementary independent probes that are essential in order to test whether X-ray masses could be biased. Aims. We study the very luminous, high redshift (z = 0.902) galaxy cluster Cl J120958.9+495352 using XMM-Newton data. We measure global cluster properties and study the temperature profile and the cooling time to investigate the dynamical status with respect to the presence of a cool core. We use Hubble Space Telescope (HST) weak lensing data to estimate its total mass and determine the gas mass fraction. Methods. We perform a spectral analysis using an XMM-Newton observation of 15 ks cleaned exposure time. As the treatment of the background is crucial, we use two different approaches to account for the background emission to verify our results. We account for point spread function effects and deproject our results to estimate the gas mass fraction of the cluster. We measure weak lensing galaxy shapes from mosaic HST imaging and select background galaxies photometrically in combination with imaging data from the William Herschel Telescope. Results. The X-ray luminosity of Cl J120958.9+495352 in the 0.1–2.4 keV band estimated from our XMM-Newton data is LX = (13.4−1.0+1.2) × 1044 erg/s and thus it is one of the most X-ray luminous clusters known at similarly high redshift. We find clear indications for the presence of a cool core from the temperature profile and the central cooling time, which is very rare at such high redshifts. Based on the weak lensing analysis, we estimate a cluster mass of M500 / 1014 M⊙ = 4.4−2.0+2.2(star.) ± 0.6(sys.) and a gas mass fraction of fgas,2500 = 0.11−0.03+0.06 in good agreement with previous findings for high redshift and local clusters.

We present spectroscopic confirmation of five galaxy clusters at $1.25 1.25$ from three to eight, further demonstrating the efficacy of SZ selection for the highest redshift massive clusters, and enabling detailed study of these systems.

We demonstrate that deep good-seeing VLT/HAWK-I $K_\mathrm{s}$ images complemented with $g$+$z$-band photometry can yield a sensitivity for weak lensing studies of massive galaxy clusters at redshifts \mbox{$0.7\lesssim z \lesssim 1.1$}, which is almost identical to the sensitivity of HST/ACS mosaics of single-orbit depth. Key reasons for this good performance are the excellent image quality frequently achievable for $K_\mathrm{s}$ imaging from the ground, a highly effective photometric selection of background galaxies, and a galaxy ellipticity dispersion that is noticeably lower than for optically observed high-redshift galaxy samples. Incorporating results from the 3D-HST and UltraVISTA surveys we also obtained a more accurate calibration of the source redshift distribution than previously achieved for similar optical weak lensing data sets. Here we studied the extremely massive galaxy cluster RCS2$J$232727.7$-$020437 (\mbox{$z=0.699$}), combining deep VLT/\mbox{HAWK-I} $K_\mathrm{s}$ images (point spread function with a 0\farcs35 full width at half maximum) with LBT/LBC photometry. The resulting weak lensing mass reconstruction suggests that the cluster consists of a single overdensity, which is detected with a peak significance of $10.1\sigma$. We constrained the cluster mass to \mbox{$M_\mathrm{200c}/(10^{15} \mathrm{M}_\odot) =2.06^{+0.28}_{-0.26}(\mathrm{stat.})\pm 0.12 (\mathrm{sys.})$} assuming a spherical Navarro, Frenk \& White model and simulation-based priors on the concentration, making it one of the most massive galaxy clusters known in the \mbox{$z\gtrsim 0.7$} Universe. We also cross-checked the HAWK-I measurements through an analysis of overlapping HST/ACS images, yielding fully consistent estimates of the lensing signal.

We present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak gravitational lensing measurements. These are the first such results obtained from an analysis that simultaneously accounts for selection effects and the underlying mass function, and directly incorporates lensing data to constrain total masses. Our constraints on the scaling relations and their intrinsic scatters are in good agreement with previous studies, and reinforce a picture in which departures from self-similar scaling laws are primarily limited to cluster cores. However, the data are beginning to reveal new features that have implications for cluster astrophysics and provide new tests for hydrodynamical simulations. We find a positive correlation in the intrinsic scatters of luminosity and temperature at fixed mass, which is related to the dynamical state of the clusters. While the evolution of the nominal scaling relations over the redshift range 0.0<z<0.5 is consistent with self similarity, we find tentative evidence that the luminosity and temperature scatters respectively decrease and increase with redshift. Physically, this likely related to the development of cool cores and the rate of major mergers. We also examine the scaling relations of redMaPPer richness and Compton Y from Planck. While the richness–mass relation is in excellent agreement with recent work, the measured Y–mass relation departs strongly from that assumed in the Planck cluster cosmology analysis. The latter result is consistent with earlier comparisons of lensing and Planck scaling-relation-derived masses.

We present new ultraviolet, optical, and X-ray data on the Phoenix galaxy cluster (SPT-CLJ2344-4243). Deep optical imaging reveals previously-undetected filaments of star formation, extending to radii of 50-100 kpc in multiple directions. Combined UV-optical spectroscopy of the central galaxy reveals a massive (2x10^9 Msun)), young ( 4.5 Myr) population of stars, consistent with a time-averaged star formation rate of 610 +/- 50 Msun/yr. We report a strong detection of OVI(1032,1038) which appears to originate primarily in shock-heated gas, but may contain a substantial contribution (>1000 Msun/yr) from the cooling intracluster medium. We confirm the presence of deep X-ray cavities in the inner 10 kpc, which are amongst the most extreme examples of radio-mode feedback detected to date, implying jet powers of 2-7 x10^45 erg/s. We provide evidence that the AGN inflating these cavities may have only recently transitioned from "quasar-mode" to "radio-mode", and may currently be insufficient to completely offset cooling. A model-subtracted residual X-ray image reveals evidence for prior episodes of strong radio-mode feedback at radii of 100 kpc, with extended "ghost" cavities indicating a prior epoch of feedback roughly 100 Myr ago. This residual image also exhibits significant asymmetry in the inner 200 kpc (0.15R500), reminiscent of infalling cool clouds, either due to minor mergers or fragmentation of the cooling ICM. Taken together, these data reveal a rapidly evolving cool core which is rich with structure (both spatially and in temperature), is subject to a variety of highly energetic processes, and yet is cooling rapidly and forming stars along thin, narrow filaments.

The abundance of massive galaxy clusters is a powerful probe of departures from general relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and ``designer,'' derived from a fully self-consistent analysis of current samples of x-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds ${\mathrm{log}}_{10}|{f}_{R0}|l4.79$ and ${\mathrm{log}}_{10}{B}_{0}l3.75$ at the 95.4% confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high-quality cluster growth data for the most massive clusters known out to redshifts $z\ensuremath{\sim}0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data.

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, sigma(8)(Omega(m)/0.3)(0.17) = 0.81 +/- 0.03, with marginalized, one-dimensional constraints of Omega(m) = 0.26 +/- 0.03 and sigma(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 ACDM 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 similar to 6 per cent when the cluster data are combined with other leading probes.

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 `color-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 catalog, 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%. 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 `color-cut` masses for all 51 clusters in the present sample to a total systematic uncertainty of ~7% 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, multi-filter optical and near-IR imaging surveys are coupled with robust photometric redshift methods.

We present improved methods for using stars found in astronomical exposures to calibrate both star and galaxy colors as well as to adjust the instrument flat field. By developing a spectroscopic model for the SDSS stellar locus in color-color space, synthesizing an expected stellar locus, and simultaneously solving for all unknown zeropoints 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 SDSS magnitudes. These techniques yield galaxy magnitudes with reliable color 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 27 cluster fields with at least five bands of photometry, as well as galaxies in the COSMOS field, finding sigma((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 Lambda-CDM cosmology. Photometric redshifts and calibrated colors are used in subsequent papers to measure the masses of 51 galaxy clusters from their weak gravitational shear. We make our Python code for stellar locus matching available at http://big-macs-calibrate.googlecode.com; the code requires only a catalog and filter functions.

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 $\sim 1.6\sigma$ 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.

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 . zCl . 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 catalogs based on the ROSAT All-Sky Survey, and provide a versatile calibration sample for many aspects of cluster cosmology. We have acquired widefield, high-quality imaging using the Subaru and CFHT telescopes 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-color 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 o sets 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 o sets . 100 kpc, weak-lensing mass measurements centered on the Brightest Cluster Galaxies agree well with values determined relative to the X-ray centroids; miscentering 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.