Eur. Phys. J. Plus (2021) 136: 183
https://doi.org/10.1140/epjp/s13360-021-01165-w

Regular Article

Newtonian fractional-dimension gravity and disk galaxies

Loyola Marymount University, 90045, Los Angeles, CA, USA

^a gvarieschi@lmu.edu http://gvarieschi.lmu.build

Received: 5 November 2020
Accepted: 27 January 2021
Published online: 5 February 2021

Abstract

This paper continues previous work on a novel alternative model of gravity, based on the theory of fractional-dimension spaces applied to Newton’s law of gravitation. In particular, our Newtonian fractional-dimension gravity is now applied to axially symmetric structures, such as thin/thick disk galaxies described by exponential, Kuzmin, or other similar mass distributions. As in the case of spherically symmetric structures, which was studied in previous work on the subject, we examine a possible connection between our model and modified Newtonian dynamics, a leading alternative gravity model, which accounts for the observed properties of galaxies and other astrophysical structures without requiring the dark matter hypothesis. By relating the MOND acceleration constant $a_0\simeq 1.2\times {10}^{-10}\text{m}{\text{s}}^{-2}$ to a natural scale length $l_0$ of our model, namely $a_0\approx \mathrm{GM}/l_0^2$ for a galaxy of mass M, and by using the empirical Radial Acceleration Relation, we are able to explain the connection between the observed radial acceleration $g_{\mathrm{obs}}$ and the baryonic radial acceleration $g_{\mathrm{bar}}$ in terms of a variable local dimension D. As an example of this methodology, we provide a detailed rotation curve fitting for the case of the field dwarf spiral galaxy NGC 6503.