A New 3D Potential-Density Basis Set

TL;DR

This paper introduces a new set of bi-orthogonal potential-density basis functions for modeling 3D stellar systems, utilizing spherical Bessel functions for the radial component.

Contribution

The paper presents a novel basis set with specific properties suitable for representing the density and gravitational fields of stellar systems.

Findings

Demonstrates the shape of basis functions for latitudinal Fourier number l=2

Discusses properties of the basis functions

Provides integral forms of radial components using spherical Bessel functions

Abstract

A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of spherical Bessel functions. We discuss the properties of our basis functions and demonstrate their shapes for the latitudinal Fourier number $l=2$.