# Radial Acceleration and Tully-Fisher Relations in Conformal Gravity

## TL;DR

This paper demonstrates that conformal gravity can naturally explain the Radial Acceleration Relation and the Tully-Fisher relation in spiral galaxies without invoking dark matter, supported by an expanded empirical dataset.

## Contribution

It shows how conformal gravity accounts for galaxy rotation curves and the Radial Acceleration Relation without dark matter, extending previous empirical analyses.

## Key findings

- Conformal gravity reproduces the Radial Acceleration Relation.
- The empirical Tully-Fisher relation emerges naturally in conformal gravity.
- Expanded dataset confirms the universality of the acceleration relation.

## Abstract

In 2016 McGaugh, Lelli and Schombert established a universal Radial Acceleration Relation for centripetal accelerations in spiral galaxies. Their work showed a strong correlation between observed centripetal accelerations and those predicted by luminous Newtonian matter alone. Through the use of the fitting function that they introduced, mass discrepancies in spiral galaxies can be constrained in a uniform manner that is completely determined by the baryons in the galaxies. Here we present a new empirical plot of the observed centripetal accelerations and the luminous Newtonian expectations, which more than doubles the number of observed data points considered by McGaugh et al. while retaining the Radial Acceleration Relation. If this relation is not to be due to dark matter, it would then have to be due to an alternate gravitational theory that departs from Newtonian gravity in some way. In this paper we show how the candidate alternate conformal gravity theory can provide a natural description of the Radial Acceleration Relation, without any need for dark matter or its free halo parameters. We discuss how the empirical Tully-Fisher relation follows as a consequence of conformal gravity.