Criss, R.E.; Hofmeister, A.M. Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves. Galaxies2020, 8, 19.
Criss, R.E.; Hofmeister, A.M. Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves. Galaxies 2020, 8, 19.

Criss, R.E.; Hofmeister, A.M. Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves. Galaxies2020, 8, 19.
Criss, R.E.; Hofmeister, A.M. Density Profiles of 51 Galaxies from Parameter-Free Inverse Models of Their Measured Rotation Curves. Galaxies 2020, 8, 19.

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. Previously published equations describing differentially spinning oblate spheroids with radially varying density are here applied to 51 galaxies, mostly spirals. A constant volumetric density (rho, kg m-3) is assumed for each thin homeoid in these formulae, after Newton, which is consistent with RC 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 rho vs. r solely from velocity v(r) and galactic aspect ratios (assumed as 1:10 when data are unavailable). Except for their innermost zones, rho is proven to be closely proportional to rn, where n for all 36 spirals studied equals -1.80±0.40. Our values for interior densities compare closely with independently measured baryon density in appropriate astronomical environments: for example, calculated rho at galactic edges agrees with estimated rho 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. Empirical luminosity-velocity relationships for galaxies, such as the Tully-Fisher rule, originate in Newtonian physics.

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