Variable Modified Newtonian Mechanics III: Milky Way Rotational Curve

Abstract

For a point mass residing in an expanding universe, within General Relativity (GR), a new metric [1} is found to lead to a cosmological background dependent MOND-like acceleration in addition to the Newtonian acceleration. In [2], we study the monolithic evolution of a spherical overdensity at recombination in this combined acceleration, called VMOND. Under reasonable relaxation assumptions we find that a massive spherical galaxy with a stable core can from at $z>7$. For galaxy mass $M=10^{10.5}M_{\odot}$ and a realistic initial overdensity, the model late time MOND acceleration $a_0^{VM}(r)$ at radius r takes on values similar to the canonical MOND acceleration $a_0$ at large radius r. In this work, we consider an idealised model of rotating galaxy formation in which a Milky Way mass overdensity under VMOND monolithically evolves into a virialised sphere. We assume that this virialised sphere is given an uniform systematic angular velocity which equilibriates into a flat disk according to Mestel's analysis \cite{mestel}. We apply Mestel to o the Mestel's disk potential due to the flatten virialised sphere under VMOND to calculate the rotational curve at $17.77kpc-27.30kpc$, We find that the model combined acceleration leads to a Baryonic Tully-Fisher Relation (BTFR) with radius dependent acceleration $a_0^{VM}(25kpc)\sim O(a_0)$. The model rotational velocity in the same radius range matches Gaia DR3 measurements very closely.