Mining the SPARC Galaxy Database: Finding "Hidden Variables" in the Baryonic Tully-Fisher Relation

Abstract: The Baryonic Tully-Fisher Relation (BTFR) links baryonic mass of rotationally supported galaxies to their flat disk velocities. A popular form of the BTFR linked to MOND is based on an empirically determined characteristic acceleration, a0 that serves as the constant of proportionality. In this work, we propose an alternative, parametric form of the BTFR employing individual galactic properties from the SPARC galaxy database. Based on this data we find that a precise mass-velocity correlation is possible taking into account galactic disk radius and two dynamical related properties; mass discrepancy and disk surface density. We find no need to invoke a characteristic acceleration constant although its ansatz can be extracted and compared to several recent analyses also arguing against the MOND interpretation of a0. This improved BTFR finding has ramifications for the Radial Acceleration Relation (RAR) as well. Rather than a universal relation that describes the dynamics of all rotationally-supported galaxies, we find the RAR consists of a statistically distributed family of curves, reflecting the unique properties attributed to individual galaxies.