Galaxies Rotation Curves in the Grumiller's Modified Gravity

TL;DR

This paper tests Grumiller's modified gravity against galaxy rotation curves, finding a universal Rindler acceleration that fits most data well within 40 kpc, offering an alternative to dark matter and MOND.

Contribution

It demonstrates that a universal Rindler acceleration in Grumiller's gravity can effectively explain galaxy rotation curves without dark matter.

Findings

Six out of eight galaxies fit well within 40 kpc using the universal Rindler acceleration.

The average Rindler acceleration is approximately 0.30×10^{-10} m/s^2.

The theory's fit is comparable to MOND but with a different acceleration scale.

Abstract

The effective potential in the Grumiller's modified gravity [D. Grumiller, Phys. Rev. Lett {\bf 105}, 211303 (2010)] includes the Newtonian potential and a Rindler term. The fitting to the rotation curve data of eight galaxies suggests a universal Rindler acceleration $a\approx 0.30\times 10^{-10}$ m s$^{-2}$. We do a two-parameter fit first, with the mass-to-light ratio ($\Upsilon_*$) and the Rindler acceleration ($a$) as free parameters. It is found that the data of six out of the eight galaxies fit well with the prediction of theory in the range $0\lesssim r \lesssim 40$ kpc, although the theoretical curves show a tendency of arising beyond this range. The Rindler accelerations of the six well-fitted galaxies have the same magnitude, with an average value $\bar{a}\approx0.30\times 10^{-10}$ m s$^{-2}$. Inspired by this fact, we then carry out a one-parameter ($\Upsilon_*$) fit to the six galaxies, with $a$ fixed at $\bar{a}$, and find that the theory can still reproduce the observation. The value of Rindler acceleration we get here is a quarter of that of Milgrom's MOND. For the rest two galaxies, NGC5055 and DDO154, the fitting results are significantly improved if the photometric scale length ($h$) is included as another free parameter.