The KLEVER survey: Nitrogen abundances at $z\sim$2 and probing the existence of a fundamental nitrogen relation

We present a comparison of the nitrogen-to-oxygen ratio (N/O) in 37 high-redshift galaxies at $z\sim$2 taken from the KMOS Lensed Emission Lines and VElocity Review (KLEVER) Survey with a comparison sample of local galaxies, taken from the Sloan Digital Sky Survey (SDSS). The KLEVER sample shows only a mild enrichment in N/O of $+$0.1 dex when compared to local galaxies at a given gas-phase metallicity (O/H), but shows a depletion in N/O of $-$0.36 dex when compared at a fixed stellar mass (M$_*$). We find a strong anti-correlation in local galaxies between N/O and SFR in the M$_*$-N/O plane, similar to the anti-correlation between O/H and SFR found in the mass-metallicity relation (MZR). We use this anti-correlation to construct a fundamental nitrogen relation (FNR), analogous to the fundamental metallicity relation (FMR). We find that KLEVER galaxies are consistent with both the FMR and the FNR. This suggests that the depletion of N/O in high-$z$ galaxies when considered at a fixed M$_*$ is driven by the redshift-evolution of the mass-metallicity relation in combination with a near redshift-invariant N/O-O/H relation. Furthermore, the existence of an fundamental nitrogen relation suggests that the mechanisms governing the fundamental metallicity relation must be probed by not only O/H, but also N/O, suggesting pure-pristine gas inflows are not the primary driver of the FMR, and other properties such as variations in galaxy age and star formation efficiency must be important.