The Bower Reservoir Relation: Newtonian Disk Structure Predicts the Residual Speed–Gas Fraction Trend in Disk Galaxies

Abstract

Real atomic-gas disks in nearby spiral and irregular galaxies are systematically more extended than their stellar disks. At fixed total baryonic mass, a larger gas fraction therefore places a greater share of the mass in the more extended component. Using only the standard, zero-free-parameter Freeman (1970) formula for the circular velocity of exponential disks, together with published stellar and HI sizes and masses from the SPARC sample, this purely structural difference is shown to produce a residual rotation-speed trend with gas fraction whose sign, statistical significance, and strength match or exceed the empirical residual–gas-fraction correlation measured across four independent surveys. The relation is therefore not an independent empirical finding that requires a separate dynamical explanation; it is the expected Newtonian consequence of the observed relative sizes of stellar and gas disks. The structural (size) signature is independently confirmed on six surveys spanning six telescopes, environments from dense clusters to cosmic voids, and two separate superclusters, with the strongest result in the Perseus–Pisces Supercluster (r = 0.70, p = 3.7 × 10⁻⁹). Environmental processes that preferentially remove the outer, high-angular-momentum gas (most clearly ram-pressure stripping in clusters) naturally amplify the speed residual, consistent with the stronger effect observed in denser environments. An explicit quantitative law is derived and cross-validated. The result is quantitative, parameter-free, and falsifiable with any new sample that supplies stellar mass, gas mass, stellar size, gas size, and a reliable rotation speed.