Galactic Rotation Described with Various Thin-Disk Gravitational Models
  For mature spiral galaxies, the rotation velocities quickly increase from the galactic center and achieve a constant velocity from the core to the periphery. This dynamic behavior is described by models balancing Newtonian gravitational and centrifugal forces in rotating thin axisymmetric disks. Freeman's disk assumes a mass density decreasing exponentially with radius which correctly produces rotational velocities which increase from the galactic center to a maximum near the outer core, but then decreases out to the periphery contrary to measurements. Mestel's disk assumes a mass distribution decreasing more slowly (inversely with radius) that yields a constant rotational velocity across the entire disk, but has an unrealistic central mass singularity and does not describe the core rotation properly. Thus combine the Freeman and Mestel disks to utilize their strengths and eliminate their deficiencies. Utilize the Freeman formula for the central core, and the Mestel formula beyond the core to the galactic rim. This combined model produces rotation curves comparable to the measurements of mature spiral galaxies. For a more general thin-disk model, we develop an alternative computational method to solve for the mass density distributions for various measured rotation curves We compute radial mass densities that balance the Newtonian gravitational and centrifugal forces at every point. The computational solutions show mass densities which decrease approximately exponentially in the central core (similar to Freeman), and transition to a slower inverse radial decrease (similar to Mestel) to the periphery. Thus these diverse approaches yield similar results and are mutaully self-consistent with Newtonian gravity/dynamics. 
James Q. Feng and C. F. Gallo