Simple and accurate modelling of the gravitational potential produced by thick and thin exponential disks

TL;DR

This paper introduces simple, fully analytical models of gravitational potential for exponential disks, adaptable to various thicknesses and scales, enabling faster and accurate simulations of galactic dynamics.

Contribution

The authors develop a new method combining three Miyamoto-Nagai disks to model exponential disks with adjustable thickness and scale, improving speed and simplicity over previous models.

Findings

Models deviate less than 0.4% from true exponential mass distribution within 4 scalelengths.

Models are fully analytical and differentiable at all points.

Applicable to a wide range of galaxy types, including the Milky Way and dwarf galaxies.

Abstract

We present accurate models of the gravitational potential produced by a radially exponential disk mass distribution. The models are produced by combining three separate Miyamoto-Nagai disks. Such models have been used previously to model the disk of the Milky Way, but here we extend this framework to allow its application to disks of any mass, scalelength, and a wide range of thickness from infinitely thin to near spherical (ellipticities from 0 to 0.9). The models have the advantage of simplicity of implementation, and we expect faster run speeds over a double exponential disk treatment. The potentials are fully analytical, and differentiable at all points. The mass distribution of our models deviates from the radial mass distribution of a pure exponential disk by <0.4% out to 4 disk scalelengths, and <1.9% out to 10 disk scalelengths. We tabulate fitting parameters which facilitate construction of exponential disks for any scalelength, and a wide range of disk thickness (a user-friendly, web-based interface is also available). Our recipe is well suited for numerical modelling of the tidal effects of a giant disk galaxy on star clusters or dwarf galaxies. We consider three worked examples; the Milky Way thin and thick disk, and a disky dwarf galaxy.