Newtonian Fractional-Dimension Gravity and Disk Galaxies

TL;DR

This paper extends a fractional-dimension gravity model to disk galaxies, linking it with MOND and explaining galaxy rotation curves without dark matter by relating local dimension to observed accelerations.

Contribution

It introduces a fractional-dimension gravity model for disk galaxies and connects it with MOND, providing a new framework to explain galactic dynamics without dark matter.

Findings

Successfully applied the model to fit the rotation curve of NGC 6503.

Established a relation between the MOND acceleration constant and the model's scale length.

Demonstrated the connection between observed and baryonic accelerations via local dimension variations.

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 $a_{0} \simeq 1.2 \times 10^{ -10}\mbox{m}\thinspace \mbox{s}^{ -2}$ to a natural scale length $l_{0}$ of our model, namely $a_{0} \approx GM/l_{0}^{2}$ 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 $g_{obs}$ and the baryonic radial acceleration $g_{bar}$ 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.