A New Interpretation of the Mass-Temperature Relation and Mass Calibration of Galaxy Clusters Based on the Fundamental Plane

TL;DR

This paper reinterprets the mass-temperature relation of galaxy clusters using the fundamental plane, revealing that it reflects cluster core structure and not virial equilibrium, and proposes a new calibration method based on this insight.

Contribution

It introduces a new interpretation of the mass-temperature relation based on the fundamental plane, accounting for cluster structure and mass accretion effects.

Findings

The mass-temperature relation reflects cluster core structure, not virial equilibrium.

The intrinsic scatter in concentration-mass relation explains cluster distribution on the FP.

X-ray and lensing data are consistent in the fundamental plane analysis.

Abstract

Observations and numerical simulations have shown that the relation between the mass scaled with the critical density of the universe and the X-ray temperature of galaxy clusters is approximately represented by $M_\Delta \propto T_X^{3/2}$ (e.g. $\Delta=500$). This relation is often interpreted as evidence that clusters are in virial equilibrium. However, the recently discovered fundamental plane (FP) of clusters indicates that the temperature of clusters primarily depends on a combination of the characteristic mass $M_s$ and radius $r_s$ of the Navarro-Frenk-White profile rather than $M_\Delta$. Moreover, the angle of the FP revealed that clusters are not in virial equilibrium because of continuous mass accretion from the surrounding matter. By considering both the FP and the mass dependence of the cluster concentration parameter, we show that this paradox can be solved and the relation $M_\Delta \propto T_X^{3/2}$ actually reflects the central structure of clusters. We also find that the intrinsic scatter in the halo concentration-mass relation can largely account for the spread of clusters on the FP. We also show that X-ray data alone form the FP and the angle and the position are consistent with those of the FP constructed from gravitational lensing data. We demonstrate that a possible shift between the two FPs can be used to calibrate cluster masses obtained via X-ray observations.