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