Does the Fundamental Metallicity Relation Evolve with Redshift? I: the Correlation Between Offsets from the Mass-Metallicity Relation and Star Formation Rate

The scatter about the mass-metallicity relation (MZR) has a correlation with the star formation rate (SFR) of galaxies. The lack of evidence of evolution in correlated scatter at z less than or similar to 2.5 leads many to refer to the relationship between mass, metallicity, and SFR as the Fundamental Metallicity Relation (FMR). Yet, recent high-redshift (z > 3) JWST observations have challenged the fundamental (i.e. redshift-invariant) nature of the FMR. In this work, we show that the cosmological simulations Illustris, IllustrisTNG, and Evolution and Assembly of GaLaxies and their Environment (EAGLE) all predict MZRs that exhibit scatter with a secondary dependence on SFR up to z = 8. We introduce the concept of a 'strong' FMR, where the strength of correlated scatter does not evolve with time, and a 'weak' FMR, where there is some time evolution. We find that each simulation analysed has a statistically significant weak FMR - there is non-negligible evolution in the strength of the correlation with SFR. Furthermore, we show that the scatter is reduced an additional similar to 10-40 per cent at z greater than or similar to 3 when using a weak FMR, compared to assuming a strong FMR. These results highlight the importance of avoiding coarse redshift binning when assessing the FMR.