The XXL Survey

XXIII. The mass scale of XXL clusters from ensemble spectroscopy^★

¹ Department of Physics and Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USA
e-mail: aryaf@umich.edu
² INAF–Osservatorio astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy
³ Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France
⁴ Department of Physics and Astronomy, University of Padova, Vicolo Osservatorio 3, 35122 Padova, Italy
⁵ Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
⁶ INAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
⁷ Istituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milan, Italy
⁸ School of Physics, HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK
⁹ Center for Astrophysics and Space Astronomy, Department of Astrophysical and Planetary Science, University of Colorado, Boulder, CO 80309, USA
¹⁰ NASA Ames Research Center, Moffett Field, CA 94035, USA
¹¹ Dipartimento di Fisica e Astronomia, Università di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
¹² Herschel Science Centre, European Space Astronomy Centre, ESA, 28691 Villanueva de la Cañada, Spain
¹³ Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
¹⁴ INAF–Osservatorio Astronomico di Roma, via Frascati 33, 00078 Monte Porzio Catone (Rome), Italy
¹⁵ School of Physics, Monash University, Clayton, Victoria 3800, Australia
¹⁶ International Centre for Radio Astronomy Research (ICRAR), The University of Western Australia, M468, 35 Stirling Highway, Crawley, WA 6009, Australia
¹⁷ SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
¹⁸ Main Astronomical Observatory, Academy of Sciences of Ukraine, 27 Akademika Zabolotnoho St., 03680 Kyiv, Ukraine
¹⁹ Astrophysics and Cosmology Research Unit, University of KwaZulu-Natal, 4041 Durban, South Africa
²⁰ Australian Astronomical Observatory, Box 915, North Ryde 1670, Australia
²¹ INAF, Osservatorio Astronomico di Brera, via Brera 28, 20159 Milano, Italy
²² AIM, CEA, CNRS, Univ. Paris-Saclay, Univ. Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France
²³ Universität Hamburg, Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
²⁴ Laboratoire Lagrange, UMR 7293, Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d'Azur, 06304 Nice, France
²⁵ Department of Physics and Astronomy, Macquarie University, NSW 2109, Australia and Australian Astronomical Observatory PO Box 915, North Ryde NSW 1670, Australia
²⁶ Argelander Institut für Astronomie, Universität Bonn, Auf dem Huegel 71, 53121 Bonn, Germany
²⁷ Aristotle University of Thessaloniki, Physics Department, 54124 Thessaloniki, Greece
²⁸ Instituto Nacional de Astrofísica Óptica y Electrónica, AP 51 y 216, 72000 Puebla, Mexico
²⁹ IAASARS, National Observatory of Athens, 15236 Penteli, Greece
³⁰ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
³¹ Ulugh Beg Astronomical Institute of Uzbekistan Academy of Science, 33 Astronomicheskaya str., Tashkent, 100052 Uzbekistan
³² Max-Planck Institut füer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

Received: 6 June 2017
Accepted: 14 November 2017

Abstract

Context. An X-ray survey with the XMM-Newton telescope, XMM-XXL, has identified hundreds of galaxy groups and clusters in two 25 deg² fields. Combining spectroscopic and X-ray observations in one field, we determine how the kinetic energy of galaxies scales with hot gas temperature and also, by imposing prior constraints on the relative energies of galaxies and dark matter, infer a power-law scaling of total mass with temperature.

Aims. Our goals are: i) to determine parameters of the scaling between galaxy velocity dispersion and X-ray temperature, T_{300 kpc}, for the halos hosting XXL-selected clusters, and; ii) to infer the log-mean scaling of total halo mass with temperature, ⟨lnM₂₀₀ | T_{300 kpc}, z⟩.

Methods. We applied an ensemble velocity likelihood to a sample of >1500 spectroscopic redshifts within 132 spectroscopically confirmed clusters with redshifts z < 0.6 to model, ⟨lnσ_gal | T_{300 kpc}, z⟩, where σ_gal is the velocity dispersion of XXL cluster member galaxies and T_{300 kpc} is a 300 kpc aperture temperature. To infer total halo mass we used a precise virial relation for massive halos calibrated by N-body simulations along with a single degree of freedom summarising galaxy velocity bias with respect to dark matter.

Results. For the XXL-N cluster sample, we find σ_gal ∝ T_{300 kpc}^0.63±0.05, a slope significantly steeper than the self-similar expectation of 0.5. Assuming scale-independent galaxy velocity bias, we infer a mean logarithmic mass at a given X-ray temperature and redshift, 〈ln(E(z)M₂₀₀/10¹⁴ M_⊙)|T₃₀₀ kpc, z〉 = π_T + α_T ln (T₃₀₀ kpc/T_p) + β_T ln (E(z)/E(z_p)) using pivot values kT_p = 2.2 keV and z_p = 0.25, with normalization π_T = 0.45 ± 0.24 and slope α_T = 1.89 ± 0.15. We obtain only weak constraints on redshift evolution, β_T = −1.29 ± 1.14.

Conclusions. The ratio of specific energies in hot gas and galaxies is scale dependent. Ensemble spectroscopic analysis is a viable method to infer mean scaling relations, particularly for the numerous low mass systems with small numbers of spectroscopic members per system. Galaxy velocity bias is the dominant systematic uncertainty in dynamical mass estimates.