A solution for galactic disks with Yukawian gravitational potential

TL;DR

This paper develops a new analytical method to compare Yukawian and Newtonian gravitational potentials in galactic disks, enabling constraints on graviton mass from galactic rotation curves, which are more restrictive than solar system bounds.

Contribution

It introduces a novel solution for galactic rotation curves with Yukawian potential, facilitating direct comparison with Newtonian models and constraining graviton mass.

Findings

Yukawian potential models can be directly compared to Newtonian ones.

Strong limits on graviton mass are derived from galactic rotation curves.

The graviton mass must be much less than 10^{-59} g for typical galactic scales.

Abstract

We present a new solution for the rotation curves of galactic disks with gravitational potential of the Yukawa type. We follow the technique employed by Toomre in 1963 in the study of galactic disks in the Newtonian theory. This new solution allows an easy comparison between the Newtonian solution and the Yukawian one. Therefore, constraints on the parameters of theories of gravitation can be imposed, which in the weak field limit reduce to Yukawian potentials. We then apply our formulae to the study of rotation curves for a zero-thickness exponential disk and compare it with the Newtonian case studied by Freeman in 1970. As an application of the mathematical tool developed here, we show that in any theory of gravity with a massive graviton (this means a gravitational potential of the Yukawa type), a strong limit can be imposed on the mass (m_g) of this particle. For example, in order to obtain a galactic disk with a scale length of b ~ 10 kpc, we should have a massive graviton of m_g << 10^{-59} g. This result is much more restrictive than those inferred from solar system observations.