Figuring Out Gas & Galaxies In Enzo (FOGGIE) VIII: Complex and Stochastic Metallicity Gradients at z > 2

Gas-phase metallicity gradients are a crucial element in understanding the chemical evolution of galaxies. We use the FOGGIE simulations to study the metallicity gradients ($\nabla Z$) of six Milky Way-like galaxies throughout their evolution. FOGGIE galaxies generally exhibit steep negative gradients for most of their history, with only a few short-lived instances reaching positive slopes that appear to arise mainly from interactions with other galaxies. FOGGIE concurs with other simulation results but disagrees with the robust observational finding that flat and positive gradients are common at $z>1$. By tracking the metallicity gradient at a rapid cadence of simulation outputs ($\sim 5$--10 Myr), we find that theoretical gradients are highly stochastic: the FOGGIE galaxies spend $\sim 30-50$\% of their time far away from a smoothed trajectory inferred from analytic models or other, less high-cadence simulations. This rapid variation makes instantaneous gradients from observations more difficult to interpret in terms of physical processes. Because of these geometric and stochastic complications, we explore non-parametric methods of quantifying the evolving metallicity distribution at $z > 1$. We investigate how efficiently non-parametric measures of the 2-D metallicity distribution respond to metal production and mixing. Our results suggest that new methods of quantifying and interpreting gas-phase metallicity will be needed to relate trends in upcoming high-$z$ {\it JWST} observations with the underlying physics of gas accretion, expulsion, and recycling in early galaxies.