Mass distribution in rotating thin-disk galaxies according to Newtonian dynamics

TL;DR

This paper introduces a numerical method to determine mass distribution in rotating thin-disk galaxies from their rotation curves using Newtonian dynamics, showing consistency with observed galaxy profiles.

Contribution

The paper develops a boundary-element method to accurately compute mass distributions from rotation curves, including effects of central bulges and extended outer regions.

Findings

Mass density profiles follow an exponential decay similar to observed brightness.

Including a bulge slightly increases total mass but redistributes mass toward the center.

Rotation velocities outside the galactic edge decrease and approach Keplerian decline.

Abstract

An accurate computational method is presented to determine the mass distribution in a rotating thin-disk galaxy from given rotation curve by applying Newtonian dynamics for an axisymmetrically rotating thin disk of finite size with or without a central spherical bulge. The governing integral equation for mass distribution, resulting from the balance between the Newtonian gravitational force and centrifugal force due to rotation at every point on the disk, is transformed via a boundary-element method into a linear algebra matrix equation that can be solved numerically for rotation curves with a wide range of shapes. To illustrate the effectiveness of this computational method, mass distributions in several mature spiral galaxies are determined from their measured rotation curves. All the surface mass density profiles predicted by our model exhibit approximately a common exponential law of decay, qualitatively consistent with the observed surface brightness distributions. When a central spherical bulge is present, the total galactic mass increases only slightly but the mass distribution in the galaxy is altered in such a way that the periphery mass density is reduced while more mass appears toward the galactic center. By extending the computational domain beyond the galactic edge, we can determine rotation velocity outside the cut-off radius which appears to continuously decrease and gradually approach the Keplerian rotation velocity out over twice the cut-off radius. Am examination of the circular orbit stability suggests that galaxies with flat or increasing rotation velocities with radius are more stable than those with decreasing rotation velocities especially in the region near the galactic edge. Our results demonstrate the fact that Newtonian dynamics can be adequate for describing the observed rotation behavior of mature spiral galaxies.