Newtonian Fractional Gravity and Disk Galaxies. (arXiv:2008.04737v1 [gr-qc])

Newtonian Fractional Gravity and Disk Galaxies. (arXiv:2008.04737v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Varieschi_G/0/1/0/all/0/1">Gabriele U. Varieschi</a>

This paper continues previous work on a possible alternative model of
gravity, based on fractional calculus applied to Newton’s law of gravitation.
In particular, our Newtonian Fractional Gravity (NFG) is now applied to
axially-symmetric stellar 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 NFG and Modified
Newtonian Dynamics (MOND), a leading alternative gravity model, which accounts
for the observed properties of galaxies and other astrophysical structures
without requiring the dark matter (DM) 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 $l_{0}$ in NFG, namely $a_{0} approx
GM/l_{0}^{2}$ for a galaxy of mass $M$, and by using the empirical Radial
Acceleration Relation (RAR), 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.

This paper continues previous work on a possible alternative model of
gravity, based on fractional calculus applied to Newton’s law of gravitation.
In particular, our Newtonian Fractional Gravity (NFG) is now applied to
axially-symmetric stellar 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 NFG and Modified
Newtonian Dynamics (MOND), a leading alternative gravity model, which accounts
for the observed properties of galaxies and other astrophysical structures
without requiring the dark matter (DM) 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 $l_{0}$ in NFG, namely $a_{0} approx
GM/l_{0}^{2}$ for a galaxy of mass $M$, and by using the empirical Radial
Acceleration Relation (RAR), 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.

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