Reconstructing the projected gravitational potential of galaxy clusters from galaxy kinematics

TL;DR

This paper presents a novel method to reconstruct the projected gravitational potential of galaxy clusters using galaxy kinematic data, achieving high accuracy within 1.2 Mpc/h of the cluster center.

Contribution

It introduces a new approach combining deprojection of velocity dispersions with a polytropic relation to recover the cluster's gravitational potential from galaxy kinematics.

Findings

Reconstruction deviation is less than 10% within 1.2 Mpc/h.

Method successfully applied to simulated galaxy clusters.

Provides a promising tool for cluster potential analysis.

Abstract

We develop a method for reconstructing the two-dimensional, projected gravitational potential of galaxy clusters from observed line-of-sight velocity dispersions of cluster galaxies. It is the third of an intended series of papers aiming at a unique reconstruction method for cluster potentials combining lensing, X-ray, Sunyaev-Zel'dovich and kinematic data. The observed galaxy velocity dispersions are deprojected using the Richardson-Lucy algorithm. The obtained radial velocity dispersions are then related to the gravitational potential by using the tested assumption of a polytropic relation between the effective galaxy pressure and the density. Once the gravitational potential is obtained in three dimensions, projection along the line-of-sight yields the two-dimensional potential. For simplicity we adopt spherical symmetry and a known profile for the anisotropy parameter of the galaxy velocity dispersions. We test the method with a numerically simulated galaxy cluster and galaxies identified therein. We extract a projected velocity-dispersion profile from the simulated cluster and pass it through our algorithm, showing that the deviation between the true and the reconstructed gravitational potential is less then 10% within approximately 1.2 Mpc/h from the cluster centre.