# Vertical dynamics of disk galaxies in MOND

## TL;DR

This study compares the vertical dynamics of disk galaxies under MOND and Newtonian gravity with dark matter, finding that differences in vertical velocity dispersion are often too subtle for current observations to distinguish.

## Contribution

It provides a detailed analysis of vertical kinematics in disk galaxies under MOND and Newtonian models, highlighting the challenges in observationally discriminating between the two.

## Key findings

- Deep-MOND disks can have much larger vertical velocity dispersions than Newtonian models.
- High-surface density disks show reduced differences, complicating observational discrimination.
- Current observations may not be sufficient to distinguish between MOND and dark matter models.

## Abstract

We investigate the possibility of discriminating between Modified Newtonian Dynamics (MOND) and Newtonian gravity with dark matter, by studying the vertical dynamics of disk galaxies. We consider models with the same circular velocity in the equatorial plane (purely baryonic disks in MOND and the same disks in Newtonian gravity embedded in spherical dark matter haloes), and we construct their intrinsic and projected kinematical fields by solving the Jeans equations under the assumption of a two-integral distribution function. We found that the vertical velocity dispersion of deep-MOND disks can be much larger than in the equivalent spherical Newtonian models. However, in the more realistic case of high-surface density disks this effect is significantly reduced, casting doubts on the possibility of discriminating between MOND and Newtonian gravity with dark matter by using current observations.