Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves

Abstract

Spiral galaxies and their rotation curves have key characteristics of differentially spinning objects. Oblate spheroid shapes are a consequence of spin and reasonably describe galaxies, indicating that their matter is distributed in gravitationally interacting homeoidal shells. Here, previously published equations describing differentially spinning oblate spheroids with radially varying density are applied to 51 galaxies, mostly spirals. A constant volumetric density (ρ, kg m−3) is assumed for each thin homeoid in these formulae, after Newton, which is consistent with RCs being reported simply as a function of equatorial radius r. We construct parameter-free inverse models that uniquely specify mass inside any given r, and thus directly constrain ρ vs. r solely from velocity v (r) and galactic aspect ratios (assumed as 1:10 for spirals when data are unavailable). Except for their innermost zones, ρ is proven to be closely proportional to rn, where the statistical average of n for all 36 spirals studied is −1.80 ± 0.40. Our values for interior densities compare closely with independently measured baryon density in appropriate astronomical environments: for example, calculated ρ at galactic edges agrees with independently estimated ρ of intergalactic media (IGM). Our finding that central densities increase with galaxy size is consistent with behavior exhibited by diverse self-gravitating entities. Our calculated mass distributions are consistent with visible luminosity and require no non-baryonic component.