Analytical Potential-Density Pairs for Flat Rings and Toroidal Structures

TL;DR

This paper develops analytical potential-density pairs for flat rings and toroidal structures, enabling easier modeling of such systems in astrophysics, and calculates their dynamical properties like circular velocity and oscillation frequencies.

Contribution

It introduces new elementary function-based potential-density pairs for flat rings and toroidal structures, expanding analytical tools for astrophysical modeling.

Findings

Potential-density pairs for flat rings are derived using elementary functions.

Dynamical properties such as circular velocity are calculated for these structures.

Examples of three-dimensional toroidal potential-density pairs are presented.

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.