Galactic Rotation Described with Thin-Disk Gravitational Model

TL;DR

This paper presents a gravitational thin-disk model to accurately describe spiral galaxy rotation profiles, deriving mass distributions that align with observed data and suggesting more baryonic matter in outer regions than previously thought.

Contribution

The study introduces a novel integral equation approach for modeling galaxy rotation using a thin-disk gravitational framework with a new galactic rotation parameter.

Findings

Calculated total galactic masses agree with observational data.

Mass distributions decrease exponentially in the core, consistent with prior models.

Outer disk regions contain more baryonic mass than traditionally estimated.

Abstract

The measured rotation velocity profiles of mature spiral galaxies are successfully described with a gravitational model consisting of a thin axisymmetric disk of finte radius. The disk is assumed uniformly thin but with variable radial mass density. The governing integral equation is based on mechanical balance between Newtonian gravitational and centrifugal forces (due to galaxy rotation) at each and every point in a finite set of concentric rings. The nondimensionalized mathematical system contains a dimensionless parameter we call ``galactic rotation parameter'' which concisely crystallizes perspective. Computational solutions are obtained for the radial mass distributions that satisfy the measured rotational velocity profiles. Together with a constraint equation for mass conservation, the galactic rotational parameter is also determined from which the total galactic mass is calculated from measured galactic radii and maximum rotation velocities. These calculated total galactic masses are in good agreement with data. Our deduced exponentially decreasing mass distributions in the central galactic core are in agreement with almost all others. However our mass distributions differ toward the galactic periphery with more ordinary baryonic mass in these outer disk regions which are cooler with lower opactiy/emissivity (and thus darker).