Density Profiles of 51 Galaxies from ParameterFree 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 parameterfree 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 r^{n}, 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 selfgravitating entities. Our calculated mass distributions are consistent with visible luminosity and require no nonbaryonic component.
 Publication:

Galaxies
 Pub Date:
 February 2020
 DOI:
 10.3390/galaxies8010019
 Bibcode:
 2020Galax...8...19C
 Keywords:

 inverse models;
 rotation curves;
 galactic density;
 galactic mass;
 galactic luminosity;
 Newtonian gravitation;
 dark matter