New biorthogonal potential--density basis functions

TL;DR

This paper introduces a new set of biorthogonal potential-density basis functions derived from spherical Bessel functions, designed for modeling three-dimensional stellar systems with finite central values and specific fall-off behaviors.

Contribution

The authors develop a novel analytical basis set of potential-density functions that are complete, biorthogonal, and suitable for soft-centered stellar systems, expanding on existing basis sets.

Findings

The new basis functions have finite central values and specific fall-off rates.

They effectively model spherical and oblate galaxy profiles.

Performance tests show good expansion accuracy for galaxy models.

Abstract

We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to $r^{-(1+l)}$ and $r^{-(4+l)}$ at large radii where $l$ is the latitudinal quantum number of spherical harmonics. The lowest order term associated with $l=0$ is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modeling of three dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models.