Newtonian Fractional-Dimension Gravity and Disk Galaxies

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.

23 pages, including 6 figures: references added and other minor changes after peer review. Final version to be published in The European Physical Journal Plus, Springer

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Cited by in corpus (11)

• Newtonian Fractional-Dimension Gravity and Rotationally Supported Galaxies
• Newtonian Fractional-Dimension Gravity and MOND
• Newtonian Fractional-Dimension Gravity and Disk Galaxies
• Emergence of fractal cosmic space from fractional quantum gravity
• Gravitational potential and galaxy rotation curves in multi-fractional spacetimes
• Elongated Gravity Sources as an Analytical Limit for Flat Galaxy Rotation Curves
• Newtonian Fractional-Dimension Gravity and the External Field Effect
• Newtonian Fractional-Dimension Gravity and Galaxies without Dark Matter
• The $\kappa$-model under test of the SPARC database
• Isothermal spheres in general relativity and Horava-type gravity
• Relativistic Fractional-Dimension Gravity