Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

Abstract

The Kuzmin-Toomre family of discs is used to construct potential-density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular orbits are calculated for these structures. A few examples of three-dimensional potential-density pairs of "inflated" flat rings (toroidal mass distributions) are presented.

25 pages, 11 figures, accepted for publication in MNRAS

References in corpus (6)

• On the stability of general relativistic geometric thin disks
• Exact density-potential pairs from the holomorphic Coulomb field
• Chaotic and regular motion around generalized Kalnajs discs
• Exact density-potential pairs from complex shifted axisymmetric systems
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• Static axisymmetric rings in general relativity: How diverse they are
• Orbital perturbations due to massive rings
• Integrability of motion around galactic razor-thin disks
• A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates
• Black hole encircled by a thin disk: fully relativistic solution
• Interior potential of a toroidal shell from pole values
• Relativistic ring models
• Analytical potential-density pairs from complex-shifted Kuzmin-Toomre discs
• Analytical potential-density pairs for bars