Exact Solutions and Approximations of Mond Fields of Disk Galaxies

TL;DR

This paper derives exact and approximate solutions for the gravitational fields and rotation curves of disk galaxies within the MOND framework, providing analytical tools for modeling galaxy dynamics.

Contribution

It presents the first analytic solutions for MOND gravitational fields of Kuzmin disks and disk-plus-bulge models, along with improved approximations for rotation curves.

Findings

Exact solutions for Kuzmin disks and disk-plus-bulge models.

A simple algebraic relation between MOND and Newtonian potentials.

An improved approximation for MOND rotation curves using Newtonian data.

Abstract

We Consider models of thin disks (with and without bulges) in the Bekenstein-Milgrom formulation of MOND as a modification of Newtonian gravity. Analytic solutions are found for the full gravitational fields of Kuzmin disks, and of disk-plus-bulge generalizations of them. For all these models a simple algebraic relation between the MOND potential field and the Newtonian potential holds everywhere outside the disk. We give exact expressions for the rotation curves for these models. We also find that the algebraic relation is a very good approximation for exponential disks. The algebraic relation outside the disk is then extended into the disk to derive an improved approximation for the MOND rotation curve of disk galaxies that requires only knowledge of the Newtonian curve and the surface density.