Recovering the fundamental plane of galaxies by $f(R)$ gravity

TL;DR

This paper demonstrates that $f(R)$ gravity, specifically the power-law form, can successfully reproduce the fundamental plane of galaxies without dark matter, linking gravitational modifications to galaxy properties.

Contribution

It shows that $f(R)$ gravity with Noether symmetries can recover galaxy scaling relations, providing an alternative to dark matter explanations.

Findings

The fundamental plane can be derived from $f(R)$ gravity.

The scale-length $r_c$ is proportional to the galaxy's effective radius.

Gravity may behave differently at various astrophysical scales.

Abstract

The fundamental plane (FP) of galaxies can be recovered in the framework of $f(R)$ gravity avoiding the issues related to dark matter to fit the observations. In particular, the power-law version $f(R)\propto R^n$, resulting from the existence of Noether symmetries for $f(R)$, is sufficient to implement the approach. In fact, relations between the FP parameters and the corrected Newtonian potential, coming from $R^n$, can be found and justified from a physical point of view. Specifically, we analyze the velocity distribution of elliptical galaxies and obtain that $r_c$, the scale-length depending on the gravitational system properties, is proportional to $r_e$, the galaxy effective radius. This fact points out that the gravitational corrections induced by $f(R)$ can lead photometry and dynamics of the system. Furthermore, the main byproduct of such an approach is that gravity could work in different ways depending on the scales of self-gravitating systems.