Exploring the Relationship Between Stellar Mass, Metallicity, and Star Formation Rate at $z \sim 2.3$ in KBSS-MOSFIRE

The metal enrichment of a galaxy is determined by the cycle of baryons in outflows, inflows, and star formation. The relative contribution and timescale of each process sets the relationship between stellar mass, metallicity, and the star formation rate (SFR). In the local universe, galaxies evolve in an equilibrium state where the timescales on which SFR and metallicity vary are comparable, and define a surface in mass-metallicity-SFR space known as the Fundamental Metallicity Relation (FMR). However, high-redshift observations suggest that this state of equilibrium may not persist throughout cosmic time. Using galaxies from the Keck Baryonic Structure Survey (KBSS) observed with MOSFIRE, we explore the relationship between stellar mass, gas-phase oxygen abundance, and SFR at $z \sim 2.3$. Across strong-line calibrations and SFR calculation methods, KBSS galaxies are inconsistent with the locally-defined FMR. We use both parametric and non-parametric methods of exploring a mass-metallicity-SFR relation. When using a parametric approach, we find no significant reduction mass-metallicity relation scatter when folding in SFR as a third parameter, although a non-parametric approach reveals that there could be a weak, redshift-dependent anticorrelation between residual gas-phase oxygen abundance, and SFR. Injection-recovery tests show that a significant reduction in scatter requires a stronger anticorrelation between SFR and residual metallicity. Our results suggest that the local FMR may not persist to $z \sim 2.3$, implying that $z \sim 2.3$ galaxies may not be in the equilibrium state described by the FMR and are more similar to higher redshift galaxies.