The origin of the MOND critical acceleration scale

Abstract

The irrefutable successes of MOND are predicated upon the idea that a critical gravitational acceleration scale, $a_0$, exists. But, beyond its role in MOND, the question: 'Why should a critical gravitational acceleration scale exist at all?' remains unanswered. There is no deep understanding about what is going on. Over roughly the same period that MOND has been a topic of controversy, Baryshev, Sylos Labini, Pietronero and others have been arguing, with equal controversy in earlier years, that, on medium scales at least, material in the universe is distributed in a quasi-fractal $D\approx 2$ fashion. There is a link: if the idea of a quasi-fractal $D \approx 2$ universe on medium scales is taken seriously then there is an associated characteristic mass surface density scale, $\Sigma_F$ say, and an associated characteristic gravitational acceleration scale, $a_F = 4 \pi G \Sigma_F$. If, furthermore, the quasi-fractal structure is taken to include the inter-galactic medium, then it is an obvious step to consider the possibility that $a_0$ and $a_F$ are the same thing. Subsequently, via a modern geometric realization of the Leibniz-Mach worldview, we obtain a detailed theoretical understanding of how galaxy disks should interact with a $D\approx 2$ quasi-fractal IGM. This understanding takes the form of a superficially unremarkable scaling relationship which, used with standard photometric mass-modelling applied to SPARC data, shows that $a_F \approx 1.2\times 10^{-10}\, mtrs/sec^2$ is explicitly embedded in that data. Since the scaling relationship also gives rise to the Baryonic Tully-Fisher Relationship, but with $a_0$ replaced by $a_F$, we are led unambiguously to the conclusion that $a_0$ and $a_F$ are, in reality, one and the same thing.