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Arya FarahiDepartment of Physics and Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USAV. GuglielmoDepartment of Physics and Astronomy, University of Padova, Vicolo Osservatorio 3, 35122 Padova, ItalyA. E. EvrardDepartment of Physics and Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USABianca M. PoggiantiINAF–Osservatorio astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, ItalyChristophe AdamiAix-Marseille UniversitéS. EttoriINAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, ItalyF. GastaldelloIstituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milan, ItalyPaul GilesSchool of PhysicsB. J. MaughanSchool of PhysicsDavid RapettiLaboratory for Atmospheric and Space PhysicsM. SerenoINAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, ItalyB. AltieriHerschel Science Centre, European Space Astronomy Centre, ESA, 28691 Villanueva de la Cañada, SpainI. K. BaldryAstrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UKM. BirkinshawSchool of PhysicsM. BolzonellaINAF–Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, ItalyA. BongiornoINAF–Osservatorio Astronomico di Roma, via Frascati 33, 00078 Monte Porzio Catone (Rome), ItalyM. J. I. BrownSchool of Physics, Monash University, Clayton, Victoria 3800, AustraliaL. ChiappettiIstituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milan, ItalySimon P. DriverInternational Centre for Radio Astronomy ResearchA. ElyivDipartimento di Fisica e Astronomia, Università di Bologna, viale Berti Pichat 6/2, 40127 Bologna, ItalyB. GarilliIstituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milan, ItalyL. GuennouAstrophysics and Cosmology Research Unit, University of KwaZulu-Natal, 4041 Durban, South AfricaAndrew HopkinsAustralian Astronomical Observatory, Box 915, North Ryde 1670, AustraliaA. IovinoINAF, Osservatorio Astronomico di Brera, via Brera 28, 20159 Milano, ItalyE. KoulouridisSorbonne Paris CitéJ. LiskeUniversität Hamburg, Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, GermanySophie MaurogordatoObservatoire de la Côte d’AzurM. S. OwersMacquarie UniversityF. PacaudArgelander Institut für Astronomie, Universität Bonn, Auf dem Huegel 71, 53121 Bonn, GermanyM. PierreCommissariat à l'Énergie Atomique et aux Énergies AlternativesM. PlionisInstituto Nacional de Astrofísica Óptica y Electrónica, AP 51 y 216, 72000 Puebla, MexicoT. J. PonmanSchool of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UKA. S. G. RobothamSchool of PhysicsT. SadibekovaCEA Paris-SaclayM. ScodeggioIstituto di Astrofisica Spaziale e Fisica Cosmica Milano, via Bassini 15, 20133 Milan, ItalyRichard TuffsMax-Planck Institut füer Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, GermanyI. ValtchanovHerschel Science Centre, European Space Astronomy Centre, ESA, 28691 Villanueva de la Cañada, Spain
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Annotatsiya

An X-ray survey with the XMM-Newton telescope, XMM-XXL, has identified hundreds of galaxy groups and clusters in two 25 deg$^2$ 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. Our goals are: i) to determine parameters of the scaling between galaxy velocity dispersion and X-ray temperature, $T_{\rm 300kpc}$, for the halos hosting XXL-selected clusters, and; ii) to infer the log-mean scaling of total halo mass with temperature, $\langle \ln M_{200} \, | \, T, z \rangle$. We apply an ensemble velocity likelihood to a sample of $> 1500$ spectroscopic redshifts within $132$ spectroscopically confirmed clusters with redshifts $z < 0.6$ to model, $\langle \ln σ_{\rm gal}\,|\,T,z\rangle$, where $σ_{\rm gal}$ is the velocity dispersion of XXL cluster member galaxies and $T$ is a 300 kpc aperture temperature. To infer total halo mass we use a precise virial relation for massive halos calibrated by N-body simulations along with a single degree of freedom summarizing galaxy velocity bias with respect to dark matter. For the XXL-N cluster sample, we find $σ_{\rm gal} \propto T^{0.63\pm0.05}$, 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, $\langle\ln (E(z) M_{200}/10^{14}\,{\rm M}_{\odot})|T,z\rangle=π+α\ln(T/T_p )+β\ln (E(z)/E(z_p) )$ using pivot values ${\rm k}T_{p}=2.2\,{\rm keV}$ and $z_p=0.25$, with normalization $π=0.45\pm0.24$ and slope $α=1.89\pm0.15$. We obtain only weak constraints on redshift evolution, $β=-1.29\pm1.14$.

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