Mass-Temperature relation in $\Lambda$CDM and modified gravity

TL;DR

This paper derives a refined mass-temperature relation for galaxy clusters considering various physical effects, showing deviations from classical models and comparing it with modified gravity theories, concluding it is not a good test for such theories.

Contribution

The study introduces an improved model for the mass-temperature relation that includes angular momentum, dynamical friction, and external pressure effects, and compares it with modified gravity models.

Findings

Mass-temperature relation deviates from classical $M \,\propto \, T^{3/2}$ behavior.

Relation shows a break at 3--4 keV and steepens at lower temperatures.

Mass-temperature relation in $\,\Lambda$CDM$\ and modified gravity models are similar.

Abstract

We derive the mass-temperature relation using an improved top-hat model and a continuous formation model which takes into account the effects of the ordered angular momentum acquired through tidal-torque interaction between clusters, random angular momentum, dynamical friction, and modifications of the virial theorem to include an external pressure term usually neglected. We show that the mass-temperature relation differs from the classical self-similar behavior, $M \propto T^{3/2}$, and shows a break at $3--4$ keV, and a steepening with a decreasing cluster temperature. We then compare our mass-temperature relation with those obtained in the literature with $N$-body simulations for $f(R)$ and symmetron models. We find that the mass-temperature relation is not a good probe to test gravity theories beyond Einstein's general relativity, because the mass-temperature relation of the $\Lambda$CDM model is similar to that of the modified gravity theories.