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Galaxies 2014, 2(2), 199-222; doi:10.3390/galaxies2020199

Mass Distribution in Rotating Thin-Disk Galaxies According to Newtonian Dynamics

*  and
Superconix Inc., 2440 Lisbon Avenue, Lake Elmo, MN 55042, USA
* Author to whom correspondence should be addressed.
Received: 13 February 2014 / Revised: 31 March 2014 / Accepted: 8 April 2014 / Published: 14 April 2014
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An accurate computational method is presented for determining the mass distribution in a mature spiral galaxy from a 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 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, quantitatively consistent with the observed surface brightness distributions. When a central spherical bulge is present, 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 the rotation velocity outside the cut-off radius, which appears to continuously decrease and to gradually approach the Keplerian rotation velocity out over twice the cut-off radius. An examination of circular orbit stability suggests that galaxies with flat or rising rotation velocities are more stable than those with declining 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.
Keywords: Newtonian dynamics; disk galaxy; mass distribution; rotation curve Newtonian dynamics; disk galaxy; mass distribution; rotation curve
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Feng, J.Q.; Gallo, C.F. Mass Distribution in Rotating Thin-Disk Galaxies According to Newtonian Dynamics. Galaxies 2014, 2, 199-222.

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