Astronomy and Astrophysics – Astrophysics
Scientific paper
1994-08-08
Astronomy and Astrophysics
Astrophysics
13 pages, Written in LATEX, using aaspp.sty
Scientific paper
10.1086/175583
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.
Brada Rafael
Milgrom Mordehai
No associations
LandOfFree
Finite Disks with Power-Law Potentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Finite Disks with Power-Law Potentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite Disks with Power-Law Potentials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-684817