Impact of Rastall gravity on hydrostatic mass of galaxy clusters

TL;DR

The paper addresses the hydrostatic mass bias observed in galaxy clusters within the standard Newtonian framework and tests Rastall gravity as a potential alternative to dark matter on cluster scales. It derives the Rastall-modified hydrostatic mass by formulating the TOV equation in Rastall gravity and taking its Newtonian limit to obtain a $m(r)$ expression with explicit $\\lambda$-dependent corrections. Two observational tests are performed: (i) a DM-free scenario where Rastall hydrostatic mass is fitted to baryonic mass, and (ii) a DM-present scenario where Rastall hydrostatic mass is compared to lensing mass to assess bias alleviation. For ten clusters in the baryonic-mass test, the best-fit slope is $M=1.07\\pm0.11$ at $\\lambda=1.14\\times10^{-1}$, with unity within the uncertainty, while standard gravity yields $M=8.24\\pm0.86$; for five clusters in the lensing-mass test, $M=1.01\\pm0.16$ at $\\lambda=1.69\\times10^{-3}$, again near unity, indicating substantial alleviation of the hydrostatic-mass bias. Overall, Rastall gravity shows statistical favorability in addressing mass discrepancies on cluster scales, but larger cluster samples are needed to tighten constraints on the Rastall parameter $\\lambda$.

Abstract

Galaxy clusters are the largest virialized structures in the Universe and are predominantly dominated by dark matter. The hydrostatic mass and the mass obtained from gravitational lensing measurements generally differ, a discrepancy known as the hydrostatic mass bias. In this work, we derive the hydrostatic mass of galaxy clusters within the framework of Rastall gravity and investigate its implications under two scenarios: (i) the absence of dark matter and (ii) the existence of dark matter. In the first scenario, Rastall gravity effectively reduces the hydrostatic mass, bringing it closer to the observed baryonic mass. The best linear fit yields a slope $\mathbf{M}=1.07\pm0.11$, indicating a near one-to-one correspondence between the two masses. In the second scenario, Rastall gravity helps to alleviate the hydrostatic mass bias. The linear fit between the Rastall hydrostatic mass and the observed lensing mass results in a best-fit slope $\mathbf{M}=1.01\pm0.16$, which is very close to unity. These results suggest that Rastall gravity provides a statistically favorable framework for addressing mass discrepancies in galaxy clusters.

Figures (2)

• Figure 1: (a) Linear fit to the relation between the hydrostatic masses according to standard non-Rastall gravity and the observed baryonic masses, (b) the likelihood function for parameter $\mathbf{M}$ in standard non-Rastall gravity, (c) linear fit to the relation between the hydrostatic masses according to Rastall gravity with $\lambda=9.55\times10^{-2}$ and the observed baryonic masses, (d) the likelihood function for parameter $\mathbf{M}$ in Rastall gravity for $\lambda=9.55\times10^{-2}$, (e) linear fit to the relation between the hydrostatic masses according to Rastall gravity with $\lambda=1.14\times10^{-1}$ and the observed baryonic masses, and (f) the likelihood function for parameter $\mathbf{M}$ in Rastall gravity for $\lambda=1.14\times10^{-1}$.
• Figure 2: (a) Linear fit to the relation between the hydrostatic masses according to standard non-Rastall gravity and the observed lensing masses, (b) the likelihood function for parameter $\mathbf{M}$ in standard non-Rastall gravity, (c) linear fit to the relation between the hydrostatic masses according to Rastall gravity with $\lambda=1.49\times10^{-3}$ and the observed baryonic masses, (d) the likelihood function for parameter $\mathbf{M}$ in Rastall gravity for $\lambda=1.49\times10^{-3}$, (e) linear fit to the relation between the hydrostatic masses according to Rastall gravity with $\lambda=1.69\times10^{-3}$ and the observed baryonic masses, and (f) the likelihood function for parameter $\mathbf{M}$ in Rastall gravity for $\lambda=1.69\times10^{-3}$.