A Dimensional Analysis of the Galactic Baryonic Tully-Fisher Relation with Comparison to MOND and Dark Matter Halo Dynamics

Abstract: Most rotationally-supported galaxies strictly follow the Baryonic Tully-Fisher Relation (BFTR) linking circular velocity with baryon content. This firmly established empirical relationship is currently thought to have origins in either modified gravity or dark matter halo effects. In this work, we construct a physically-based version of the BFTR founded on known scaling relations, disk dynamics (acceleration, jerk and snap) that also reveals the foundational elements responsible for this phenomenology. We employ the Milky Way galaxy as an exemplar to quantitatively compare the two leading theories against this improved version. Additionally, a dimensionless variant of the BFTR is also provided which may permit its use as an analytic tool to aid in the understanding of galactic dynamics.