Modeling the Newtonian Dynamics for Rotation Curve Analysis of Thin-Disk
  Galaxies
  We present an efficient, robust computational method for modeling the
Newtonian dynamics for rotation curve analysis of thin-disk galaxies. For a
disk galaxy with a typical flat rotation curve, our modeling results show that
the surface mass density monotonically decreases from the galactic center
toward periphery, according to Newtonian dynamics. In a large portion of the
galaxy, the surface mass density follows an approximately exponential law of
decay with respect to the galactic radial coordinate. Yet the radial scale
length for the surface mass density seems to be generally larger than that of
the measured brightness distribution, suggesting an increasing mass-to-light
ratio with the radial distance in a disk galaxy. In a nondimensionalized form,
our mathematical system contains a dimensionless parameter which we call the
"galactic rotation number" that represents the gross ratio of centrifugal force
and gravitational force. The value of this galactic rotation number is
determined as part of the numerical solution. Through a systematic
computational analysis, we have illustrated that this galactic rotation number
remains within $\pm 10%$ of 1.70 for a wide variety of rotation curves. This
implies that the total mass in a disk galaxy is proportional to $V_0^2\,R_g$,
with $V_0$ denoting the characteristic rotation velocity and $R_g$ the radius
of the galactic disk. The predicted total galactic mass of the Milky Way is in
good agreement with the star-count data.
