Potentials of axisymmetric razor-thin disks

Fuente: arXiv
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Main Author: An, J.
Format: Preprint
Published: 2026
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author An, J.
author_facet An, J.
contents We investigate the gravitational potentials generated by axisymmetric, razor-thin disks. Within certain limitations, the potential on one side of the disk is shown to be equivalent to the potential produced by a linear mass distribution along the axis perpendicular to the disk. We first establish the connection between two mass distributions that generate the same potential. We then consider all disk surface density profiles that produce the potential equivalent to those generated by linear mass distributions, specifically those defined by the elementary beta distribution and its relatives on the interval $[0,1]$, $[1,\infty)$ or $[0,\infty)$. These families of models are important because the potentials in all cases are given by, at most, a single real quadrature of elementary functions of the coordinates, and furthermore, many cases result in closed-form expressions. The potential of many realistic disks may be constructed from some combinations of these disk models.
format Preprint
id arxiv_https___arxiv_org_abs_2604_13091
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Potentials of axisymmetric razor-thin disks
An, J.
Classical Physics
Astrophysics of Galaxies
We investigate the gravitational potentials generated by axisymmetric, razor-thin disks. Within certain limitations, the potential on one side of the disk is shown to be equivalent to the potential produced by a linear mass distribution along the axis perpendicular to the disk. We first establish the connection between two mass distributions that generate the same potential. We then consider all disk surface density profiles that produce the potential equivalent to those generated by linear mass distributions, specifically those defined by the elementary beta distribution and its relatives on the interval $[0,1]$, $[1,\infty)$ or $[0,\infty)$. These families of models are important because the potentials in all cases are given by, at most, a single real quadrature of elementary functions of the coordinates, and furthermore, many cases result in closed-form expressions. The potential of many realistic disks may be constructed from some combinations of these disk models.
title Potentials of axisymmetric razor-thin disks
topic Classical Physics
Astrophysics of Galaxies
url https://arxiv.org/abs/2604.13091