Scaling Relations of Mass, Velocity and Radius for Disk Galaxies

Abstract

I demonstrate four tight correlations of total baryonic mass, velocity and radius for a set of nearby disk galaxies: the Mass-Velocity relation $ Mt \propto V^4$; the Mass-Radius relation $ Mt \propto R^2$; the Radius-Velocity relation $R \propto V^2$; and the Mass-Radius-Velocity relation $ Mt \propto R V^2$. The Mass-Velocity relation is the familiar Baryonic Tully-Fisher relation(BTFR) and versions of the other three relations, using magnitude rather than baryonic mass, are also well known. These four observed correlations follow from a pair of more fundamental relations. First, the centripetal acceleration at the edge of the stellar disk is proportional to the acceleration predicted by Newtonian physics and secondly, this acceleration is a constant which is related to Milgrom's constant. The two primary relations can be manipulated algebraically to generate the four observed correlations and allow little room for dark matter inside the radius of the stellar disk. The primary relations do not explain the velocity of the outer gaseous disks of spiral galaxies which do not trace the Newtonian gravitational field of the observed matter.