Cosmology and astrophysics from relaxed galaxy clusters - IV. Robustly calibrating hydrostatic masses with weak lensing

D. E. Applegate, A. Mantz, S. W. Allen, A. von der Linden, R. Glenn Morris, S. Hilbert, Patrick L. Kelly, D. L. Burke, H. Ebeling, D. A. Rapetti, R. W. Schmidt

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This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses measures the combined bias of X-ray hydrostatic masses from both astrophysical and instrumental sources. While we cannot disentangle the two sources of bias, only the combined bias is relevant for calibrating cosmological measurements using relaxed clusters. Assuming a fixed cosmology, and within a characteristic radius (r2500) determined from the X-ray data, we measure a lensing to X-ray mass ratio of 0.96 ± 9 per cent (stat) ± 9 per cent (sys). We find no significant trends of this ratio with mass, redshift or the morphological indicators used to select the sample. Our results imply that any departures from hydrostatic equilibrium at these radii are offset by calibration errors of comparable magnitude, with large departures of tensof- percent unlikely. In addition, we find a mean concentration of the sample measured from lensing data of c200 = 3.0-1.8.+4.4 Anticipated short-term improvements in lensing systematics, and a modest expansion of the relaxed lensing sample, can easily increase the measurement precision by 30-50 per cent, leading to similar improvements in cosmological constraints that employ X-ray hydrostatic mass estimates, such as on Ωm from the cluster gas mass fraction.

Original languageEnglish (US)
Pages (from-to)1522-1534
Number of pages13
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
StatePublished - Apr 1 2016
Externally publishedYes

Bibliographical note

Funding Information:
We thank our other collaborators in the WtG series, including Pat Burchat, Mark Allen, and David Donovan. DEA would like to thank Lorenzo Lovisari and Tim Schrabback for helpful discussions. SH thanks MPA and RZG for hospitality and for providing access to their computing facilities and the MXXL simulation data. DEA recognizes the support of the German Federal Ministry of Economics and Technology (BMWi) under project 50 OR 1210. This work is supported in part by the US Department of Energy under contract number DE-AC02-76SF00515. This work was also supported by the National Science Foundation under Grant no. AST-0807458. AM acknowledges the support of NSF grant AST-1140019. The authors acknowledge support from programmesHSTAR-12654.01-A, HST-GO-12009.02-A, and HST-GO-11100.02-A provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. This work is also supported by the National Aeronautics and Space Administration through Chandra Award Numbers TM1-12010X, GO0-11149X, GO9-0141X, and GO8-9119X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. The Dark Cosmology Centre (DARK) is funded by the Danish National Research Foundation. Based in part on data collected at Subaru Telescope (University of Tokyo) and obtained from the SMOKA, which is operated by the Astronomy Data Center, National Astronomical Observatory of Japan. Based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada?France? Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de l?Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science. The SDSS-III web site is This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, Caltech, under contract with NASA. This research has made use of data obtained from the Chandra Data Archive and the Chandra Source Catalog, and software provided by the ChandraX-ray Center (CXC) in the application packages CIAO, ChIPS, and Sherpa. This research was powered by the Python scientific software stack, including Numpy, Scipy, Matplotlib, and PyMC.


  • Cosmology: observations
  • Gravitational lensing: weak
  • X-rays: galaxies: clusters
  • galaxies: clusters: general

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