SIMBAD references

We present an analysis of the rest-frame optical spectra of 22 [O III]$\lambda$4363 detected galaxies in the redshift range $1.65 \le z \le 7.92$ (with $\langle z\rangle = 4.05$) from JWST/NIRSpec medium-resolution observations taken as part of the EXCELS survey. To supplement these high-redshift sources, we also consider a sample of 782 local [O III]$\lambda$4363 detected galaxies from the DESI Early Data Release. Our analysis demonstrates that many strong-line calibrations are biased in the early Universe due to the systematic evolution in ionization conditions with redshift. However, the recently introduced $\widehat {R}$ calibration mostly removes the dependence on ionization state and can be considered a largely redshift-independent calibration. In a similar spirit, we introduce a new strong-line diagnostic, $\widehat {RNe}$ (using [O II]$\lambda \lambda$3726,3729, [Ne III]$\lambda$3869 and H $\gamma$), which can be used to robustly estimate metallicities when the [O III]$\lambda$5007 is redshifted out of the wavelength range of JWST/NIRSpec at $z > 9.5$. We also show that strong-line diagnostics using the [N II]$\lambda$6584 emission line are likely to be biased at high redshift due to a moderate enhancement in the average N/O abundance ratios (at fixed O/H) in these sources. Finally, we discuss the location of our new [O III]$\lambda$4363 detected galaxies at $z\simeq 4$ on the mass-metallicity plane and investigate the redshift evolution of the fundamental metallicity relation (FMR). We find tentative evidence for an increasing deviation from the FMR at $z > 4$, which might indicate fundamental differences in the baryon cycle at these redshifts. However, more data are required as our high-redshift constraints are still based on a relatively small sample of galaxies and the significance of the deviation is strongly dependent on the assumed form of the FMR.