The THESAN-ZOOM project: Mystery N/O more -- uncovering the origin of peculiar chemical abundances and a not-so-fundamental metallicity relation at $3<z<12$

We present an analysis of metallicities and chemical abundances at $3<z<12$ in the THESAN-ZOOM simulations. We find that smoothly curved gas-phase and stellar mass-metallicity relations (MZR) are already in place at $z\approx12$ and evolve slowly ($\sim$0.2 dex increase for gas, $\sim$0.4 dex increase for stars at a fixed stellar mass) down to $z=3$, governed largely by the efficiency with which galaxies retain their metals, rather than gas fraction. The canonical fundamental metallicity relation (FMR) survives in stars but breaks down and inverts for gas in low-mass galaxies ($M_\ast\lesssim10^{9}\mathrm{M_\odot}$) due to regular dilution by low-metallicity gas inflow. We find broad agreement of gas-phase N/O, Fe/O, and C/O with high-redshift observations, including the presence of nitrogen-rich galaxies (NRGs; $\log(\mathrm{N/O})>-0.6$) without the need for exotic yields in our chemical network. Instead, bursty star formation naturally generates order-of-magnitude excursions in N/O on $\lesssim$100 Myr timescales due to temporally differential galactic winds; after a starburst, stellar feedback expels gas, leaving a large population of asymptotic-giant-branch stars to dominate the enrichment of the relatively low-mass interstellar medium. NRGs lie below the main sequence and typically exhibit $\mathrm{EW}[H$β$]\lesssim40$ Å, in apparent tension with observed high-EW NRGs. This tension is reconciled if observed NRGs are in the initial stages of a subsequent starburst, illuminating previously enriched gas, which is supported by the finding of high SFR surface density nitrogen-rich giant molecular clouds.