CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z = 0.44 galaxy cluster MACS J1206.2-0847^⋆,⋆⋆

¹ INAF−Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34131 Trieste, Italy
e-mail: biviano@oats.inaf.it
² ESO (European Southern Observatory), 85748 Garching bei München, Germany
³ INAF−Osservatorio Astronomico di Capodimonte, via Moiariello, 16 80131 Napoli, Italy
⁴ Dipartimento di Fisica, Univ. degli Studi di Trieste, via Tiepolo 11, 34143 Trieste, Italy
⁵ Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
⁶ INAF−IASF-Milano, via Bassini 15, 20133 Milano, Italy
⁷ Department of Physics and Astronomy, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
⁸ Observatories of the Carnegie Institution of Washington, Pasadena, CA 91 101, USA
⁹ Institute of Astronomy and Astrophysics, Academia Sinica, PO Box 23-141, 10617 Taipei, Taiwan
¹⁰ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
¹¹ Institut für Theoretische Astrophysik, Zentrum für Astronomie, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
¹² University of Vienna, Department of Astrophysics, Türkenschanzstr. 17, 1180 Wien, Austria
¹³ INAF−Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
¹⁴ INFN, Sezione di Bologna, via Ranzani 1, 40127 Bologna, Italy
¹⁵ Dipartimento di Fisica, Universitá degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
¹⁶ Department of Physics and Astronomy, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
¹⁷ GEPI, Paris Observatory, 77 avenue Denfert Rochereau, 75014 Paris, France
¹⁸ University Denis Diderot, 4 rue Thomas Mann, 75205 Paris, France
¹⁹ CEA Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France
²⁰ INAF−Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
²¹ Instituto de Astrofísica de Andalucía (CSIC), C/Camino Bajo de Huétor 24, 18008 Granada, Spain
²² Department of Theoretical Physics, University of the Basque Country, PO Box 644, 48080 Bilbao, Spain
²³ Department of Astronomy, Universidad de Concepcion, Casilla 160-C, Concepcion, Chile
²⁴ Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
²⁵ Laboratoire AIM-Paris-Saclay, CEA/DSM-CNRS, Université Paris Diderot, Irfu/Service d’Astrophysique, CEA Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France
²⁶ Department of Astronomy, University of California, Berkeley, CA, USA
²⁷ Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA
²⁸ Department of Physics, The Ohio State University, Columbus, OH, USA
²⁹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr, Pasadena, CA 91109, USA
³⁰ European Laboratory for Particle Physics (CERN), 1211 Geneva 23, Switzerland
³¹ University Observatory Munich, Scheinerstrasse 1, 81679 München, Germany
³² Max-Planck-Institut für extraterrestrische Physik, Postfach 1312, Giessenbachstr., 85741 Garching, Germany

Received: 24 May 2013
Accepted: 29 July 2013

Abstract

Aims. We constrain the mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z = 0.44 CLASH cluster MACS J1206.2-0847, using the projected phase-space distribution of cluster galaxies in combination with gravitational lensing.

Methods. We use an unprecedented data-set of ≃600 redshifts for cluster members, obtained as part of a VLT/VIMOS large program, to constrain the cluster mass profile over the radial range ~0–5 Mpc (0–2.5 virial radii) using the MAMPOSSt and Caustic methods. We then add external constraints from our previous gravitational lensing analysis. We invert the Jeans equation to obtain the velocity-anisotropy profiles of cluster members. With the mass-density and velocity-anisotropy profiles we then obtain the first determination of a cluster pseudo-phase-space density profile.

Results. The kinematics and lensing determinations of the cluster mass profile are in excellent agreement. This is very well fitted by a NFW model with mass M₂₀₀ = (1.4 ± 0.2) × 10¹⁵ M_⊙ and concentration c₂₀₀ = 6 ± 1, only slightly higher than theoretical expectations. Other mass profile models also provide acceptable fits to our data, of (slightly) lower (Burkert, Hernquist, and Softened Isothermal Sphere) or comparable (Einasto) quality than NFW. The velocity anisotropy profiles of the passive and star-forming cluster members are similar, close to isotropic near the center and increasingly radial outside. Passive cluster members follow extremely well the theoretical expectations for the pseudo-phase-space density profile and the relation between the slope of the mass-density profile and the velocity anisotropy. Star-forming cluster members show marginal deviations from theoretical expectations.

Conclusions. This is the most accurate determination of a cluster mass profile out to a radius of 5 Mpc, and the only determination of the velocity-anisotropy and pseudo-phase-space density profiles of both passive and star-forming galaxies for an individual cluster. These profiles provide constraints on the dynamical history of the cluster and its galaxies. Prospects for extending this analysis to a larger cluster sample are discussed.