# Metallicity has followed local gravitational potential of galaxies since z=3

## TL;DR

This study demonstrates that galaxy metallicity has been governed by local gravitational potential since z=3, supported by observational data showing consistent velocity dispersion patterns in galaxy halos.

## Contribution

It provides the first observational test confirming that metallicity follows local gravitational potential since high redshift, using absorption and emission data across galaxy halos.

## Key findings

- Metallicity correlates with local gravitational potential since z=3.
- Velocity dispersion profiles match the predicted steep decline with impact parameter.
- Absorption data supports a model of multiple sub-clouds in galaxy halos.

## Abstract

The MZ relation between stellar mass (M*) and metallicity (Z) of nearby galaxies has been described as both a global and local property, i.e. valid also on sub-galaxy scales. Here we show that Z has remained a local property, following the gravitational potential, since z=3. In absorption the MZ relation has been well studied, and was in place already at z=5.1. A recent absorption study of GRB galaxies revealed a close match to Damped Ly{\alpha} (DLA) galaxies, surprising due to their vastly different impact parameters and leading the authors to suggest that local metallicity follows the local gravitational potential. In this paper we formulate an observational test of this hypothesis. The test, in essence, forms a prediction that the velocity dispersion of the absorbing gas in galaxy halos, normalized by the central velocity dispersion, must follow a steep log scale slope of -0.015 dex/kpc as a function of impact parameter out to at least 20-30 kpc. We then compile an archival data and literature based sample of galaxies seen in both emission and absorption suitable for the test, and find that current data confirm the hypothesis out to 40-60 kpc. In addition we show that the distribution of the velocity offsets between z em and z abs favours a model where DLA systems are composed of individual sub-clouds distributed along the entire path through the halo, and disfavours a model where they are one single cloud with a bulk motion and internal sub-structure.