The Third Law of Galactic Rotation

TL;DR

This paper reviews the relationship between galaxy dynamics and baryonic matter, highlighting a universal mass discrepancy-acceleration relation that suggests a natural law governing galaxy rotation, challenging traditional dark matter models.

Contribution

It provides an empirical calibration of the mass discrepancy-acceleration relation and formulates how dark matter distribution relates to baryonic surface brightness, supporting a universal force law.

Findings

Mass-to-light ratio increases with decreasing luminosity and surface brightness.

The mass discrepancy correlates with acceleration, consistent with a single force law.

Dark matter halo shapes depend on baryonic distribution, not fitting simple cusp or core models.

Abstract

I review the connection between dynamics and the baryonic mass distribution in rotationally supported galaxies. The enclosed dynamical mass-to-light ratio increases with decreasing galaxy luminosity and surface brightness. The correlation with surface brightness appears to be the more fundamental, with the dependence on luminosity following simply from the weaker correlation between luminosity and surface brightness. In addition to this global relation, there is also a local relation between the amplitude of the mass discrepancy and the acceleration predicted by the observed distribution of baryons. I provide an empirical calibration of this mass discrepancy-acceleration relation. The data are consistent with the operation of a singe effective force law in disk galaxies, making this relation tantamount to a natural law. I further provide formulae by which the radial dark matter distribution can be estimated from surface photometry. The form of the dark matter halo depends uniquely on the distribution of baryons in each galaxy, and in general is neither a cusp nor a core. It remains difficult to see how galaxy formation models can reproduce the observed behavior, which is uniquely predicted by MOND.