The projected gravitational potential of the galaxy cluster MACS J1206 derived from galaxy kinematics

¹ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany
e-mail: dennis.stock@stud.uni-heidelberg.de
² INAF–Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34131 Trieste, Italy
³ Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Denmark
⁴ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
⁵ INAF–Osservatorio Astronomico di Capodimonte, via Moiariello 16, 80131 Napoli, Italy
⁶ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, via Saragat 1, 44122 Ferrara, Italy

Received: 22 July 2015
Accepted: 7 October 2015

Abstract

We reconstruct the radial profile of the projected gravitational potential of the galaxy cluster MACS J1206 from 592 spectroscopic measurements of velocities of cluster members. To accomplish this, we use a method we have developed recently based on the Richardson-Lucy deprojection algorithm and an inversion of the spherically-symmetric Jeans equation. We find that, within the uncertainties, our reconstruction agrees very well with a potential reconstruction from weak and strong gravitational lensing as well as with a potential obtained from X-ray measurements. In addition, our reconstruction is in good agreement with several common analytic profiles of the lensing potential. Varying the anisotropy parameter in the Jeans equation, we find that isotropy parameters, which are either small, β ≲ 0.2, or decrease with radius, yield potential profiles that strongly disagree with that obtained from gravitational lensing. We achieve the best agreement between our potential profile and the profile from gravitational lensing if the anisotropy parameter rises steeply to β ≈ 0.6 within ≈ 0.5 Mpc and stays constant further out.