Analytical potential-density pairs for bars

TL;DR

This paper develops analytical models of thin and softened bar-shaped mass distributions in Newtonian gravity, exploring their equilibrium and stability properties for rotating configurations.

Contribution

It introduces a method to construct potential-density pairs for bars with specific density profiles, including singular and softened models, using an identity relating Einstein solutions to Newtonian potentials.

Findings

Analytical models for thin and softened bars are derived.

Equilibrium points and stability of test particles in rotating bars are analyzed.

Models provide insights into gravitational dynamics of bar-shaped structures.

Abstract

An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally thin bars with a given linear density profile. By means of a suitable transformation, softened bars that are free of singularities are also obtained. As an application we study the equilibrium points and stability for the motion of test particles in the gravitational field for three models of rotating bars.