# Fundamental plane of elliptical galaxies in $f(R)$ gravity: the role of luminosity

## TL;DR

This paper demonstrates that a modified gravity theory, specifically $f(R)$ gravity with a power-law form, can accurately reproduce the fundamental plane of elliptical galaxies without requiring dark matter, linking photometric and gravitational parameters.

## Contribution

It shows that $f(R)$ gravity, especially the $R^n$ model, can explain elliptical galaxy dynamics and the fundamental plane relation without dark matter.

## Key findings

- $f(R)$ gravity reproduces observed fundamental plane coefficients.
- $R^n$ gravity fits elliptical galaxy data well.
- Dark matter is not necessary in this model.

## Abstract

The global properties of elliptical galaxies are connected through the so-called fundamental plane of ellipticals, which is an empirical relation between their parameters: effective radius, central velocity dispersion and mean surface brightness within the effective radius. We investigated the relation between the parameters of the fundamental plane equation and the parameters of modified gravity potential $f(R)$. With that aim, we compared theoretical predictions for circular velocity in $f(R)$ gravity with the corresponding values from a large sample of observed elliptical galaxies. Besides, we consistently reproduced the values of coefficients of the fundamental plane equation as deduced from observations, showing that the photometric quantities like mean surface brightness are related to gravitational parameters. We show that this type of modified gravity, especially its power-law version - $R^n$, is able to reproduce the stellar dynamics in elliptical galaxies. Also, it is shown that $R^n$ gravity fits the observations very well, without need for a dark matter.