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

TL;DR

This paper reconstructs the gravitational potential profile of galaxy cluster MACS J1206 using galaxy kinematics and compares it with lensing and X-ray data, finding good agreement with specific anisotropy parameters.

Contribution

It introduces a novel method combining Richardson-Lucy deprojection and Jeans equation inversion to derive the gravitational potential from galaxy velocities.

Findings

Reconstructed potential agrees with lensing and X-ray measurements within uncertainties.

Best agreement occurs with anisotropy parameter rising steeply to about 0.6 within 0.5 Mpc.

Potential profiles with small or decreasing anisotropy parameters disagree with lensing results.

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. For doing so, 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, $\beta\lesssim0.2$, or decrease with radius yield potential profiles which 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 quite steeply to $\beta\approx0. 6$ within $\approx0.5\,\mathrm{Mpc}$ and stays constant further out.