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

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 Lyα (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.