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Paper: A Thin-Disk Gravitational Model for Galactic Rotation
Volume: 413, 2nd Crisis in Cosmology Conference, CCC-2
Page: 289
Authors: Gallo, C. F.; Feng, J. Q.
Abstract: A gravitational model is presented consisting of an axisymmetric thin disk of finite radius, capable of describing the measured rotational velocity profiles (i.e., the rotation curves) of mature spiral galaxies. Without loss of generality, the disk is assumed to have a uniform thickness but with a mass density variable in the radial coordinate. The governing integral equation, based on mechanical balance between Newtonian gravitational force and centrifugal force due to galaxy rotation at each and every point on the disk, is solved numerically to determine the radial mass density distribution for a given rotation curve. The nondimensionalized mathematical system contains a dimensionless parameter which we call the "galactic rotation number'' that represents the ratio of centrifugal force and gravitational force. Together with a constraint equation for mass conservation, the value of the galactic rotation number can be determined as part of the numerical solution. With a known value of the galactic rotation number, the total galactic mass can be calculated from measured galactic radii and maximum rotation velocities. The predicted total galactic masses are in good agreement with star-count data. Our computed mass density shows a rapid decrease within the central core followed by a slower nearly exponential decay outward from the galactic center and then takes a sharp drop at the galatic edge. However our predicted mass densities show generally slower decaying rates toward the galactic periphery than that of measured brightness, consistent with more ordinary baryonic mass in the outer disk regions which are cooler with lower emissivity (and thus darker).
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