The Tight Empirical Relation between Dark Matter Halo Mass and Flat Rotation Velocity for Late-Type Galaxies

Abstract: We present a new empirical relation between galaxy dark matter halo mass (${\rm M_{halo}}$) and the velocity along the flat portion of the rotation curve (${\rm V_{flat}}$), derived from 120 late-type galaxies from the SPARC database. The orthogonal scatter in this relation is comparable to the observed scatter in the baryonic Tully-Fisher relation (BTFR), indicating a tight coupling between total halo mass and galaxy kinematics at $r\ll R_{\rm vir}$. The small vertical scatter in the relation makes it an extremely competitive estimator of total halo mass. We demonstrate that this conclusion holds true for different priors on $M_*/L_{[3.6\mu]}$ that give a tight BTFR, but requires that the halo density profile follows DC14 rather than NFW. We provide additional relations between ${\rm M_{halo}}$ and other velocity definitions at smaller galactic radii (i.e. ${\rm V_{2.2}}$, ${\rm V_{eff}}$, and ${\rm V_{max}}$) which can be useful for estimating halo masses from kinematic surveys, providing an alternative to abundance matching. Furthermore, we constrain the dark matter analog of the Radial Acceleration Relation and also find its scatter to be small, demonstrating the fine balance between baryons and dark matter in their contribution to galaxy kinematics.