A test of galaxy cluster fundamental plane for the X-COP sample

TL;DR

This study tests the galaxy cluster fundamental plane using the X-COP sample, finding a tight relation between temperature, mass, and radius that aligns with theoretical expectations.

Contribution

It provides the first detailed analysis of the fundamental plane for the X-COP galaxy cluster sample, confirming its tightness and consistency with theoretical models.

Findings

The fundamental plane has a dispersion of about 0.02 dex.

Best-fit parameters are between virial and self-similar expectations.

Results are consistent with previous analyses of the CLASH sample.

Abstract

We test the galaxy cluster fundamental plane using the X-COP sample of 12 clusters. The fundamental plane is given by the relation $T_X \propto M_s^{\alpha} r_s^{\beta}$, where $T_X$, $M_s$, and $r_s$ correspond to the gas temperature, NFW halo mass, and scale radius, respectively. We did this analysis using two different temperatures: the error-weighted temperature in $(50-500)h^{-1}$ kpc as well as the mass-weighted temperature in the same range. With both these temperatures, we find a very tight fundamental plane with dispersion of about 0.02 dex. The best-fit values for $\alpha$ and $\beta$ are in-between those expected from virial equilibrium and self-similarity solution for secondary infall and collapse, with $\alpha$ being closer to the virial expectation. Our best-fit values are also consistent with a recent re-analyses of the fundamental plane for the CLASH sample, after excluding the hottest clusters.