Potential-density pairs for bent bars

TL;DR

This paper introduces a method for modeling bent thin bars with small curvature, producing exact Laplace solutions and three-dimensional potential-density pairs relevant for galactic structures.

Contribution

It presents a novel approach using Legendre polynomial combinations to generate exact solutions for bent bar potentials and extends to 3D and non-axisymmetric matter distributions.

Findings

Exact solutions for bent bar potentials using Legendre polynomials

Generation of non-singular 3D potential-density pairs

Application to galactic bar models with spiral arms

Abstract

A method is presented to bend a thin massive line when the curvature is small. The procedure is applied to a homogeneous thin bar with two types of curvatures. One of them mimics a galactic bar with two spiral arms at its tips. It is showed that if the bending function is a linear combination of Legendre polynomials, then the bent potential is an exact solution of the Laplace equation. A transformation is applied on the thin bent bars to generate three-dimensional potential-density pairs without singularities. The potentials of the thin bent bars are also used to generate non-axisymmetric planar distributions of matter.