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arXiv · astro-ph/9408025

Finite Disks with Power-Law Potentials

R. Brada·M. Milgrom
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Abstract

We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff at some radius Ro. First we discuss circular disks whose circular rotation speed v is proportional to r^alpha, with any alpha> -1/2. The surface-density of the disks is expressed in terms of hypergeometric functions of 1-(Ro/r)^2. We give closed expressions for the full 3-D potentials in terms of hypergeometric functions of two variables. We express the potential and acceleration in the plane at r>Ro, and along the rotation axis, in terms of simple hypergeometric functions. All the multipoles of the disk are given. We then generalize to non-axisymmetric disks. The potential in the midplane is given in terms of the hypergeometric function of two variables. For integer values of 2 alpha the above quantities are given in more elementary terms. All these results follow straightforwardly from formulae we derive for the general, cutoff, power-law, triaxial ellipsoid.

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R. Brada, M. Milgrom. 1994-08-08. Finite Disks with Power-Law Potentials. https://doi.org/10.1086/175583

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