Wednesday, January 23, 2013

1301.5233 (Niall Ryan)

Galactic Disc Rotation: Analytic models and asymptotic results    [PDF]

Niall Ryan
This paper outlines an exact analytic model for self-gravitating disc galaxies. The model is capable of describing thin, cylindrically symmetric discs with very general rotation curves, including curves with finite flat sections. With the rotation curve represented using piecewise polynomials, the corresponding disc density can be written as a sum of known power series. These series are also used to investigate the properties of the model. The method allows for the rapid generation and fitting of discs to rotation curves. Several example models are presented, and the results of the analysis are confirmed by numerical simulation. Relationships between the asymptotic behaviours of disc velocity and density are also derived, placing necessary restrictions on the velocity profiles of finite mass galaxies, and showing the link between flat rotation curves and "exponential" declines in radial density. A major result of the analysis is the confirmation of slow O(1/r) convergence as a general property of disc mass profiles. This leads to the phenomenon of mass "hinterlands"; sparse outer regions, coplanar with the disc, lying beyond the flat velocity sections, but which can contain large fractions or even the majority of the total disc mass. This counterintuitive property has implications for the problem of missing mass in spiral galaxies and in galactic clusters.
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