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 $z\lesssim2.5$ 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 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 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 ~10-40% at $z\gtrsim3$ 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.