A self-consistent direct method for chemical abundances in high-z galaxies with JWST

The unprecedented rest-frame UV and optical coverage provided by James Webb Space Telescope (JWST) enables simultaneous constraints on the electron density (ne ) and temperature (Te ) of ionized gas in galaxies at z > 5. We present a self-consistent direct method based on multiple O iii] (λλ1661, 1666) and [O iii] (λλ4363, 5007) transitions to characterize the physical conditions of the high-ionization zone. This new approach is insensitive to a wide range of ne due to the high critical densities of the O iii] and [O iii] transitions. Applying this technique to six galaxies at z ∼ 5–9, we find electron densities up to ne ∼ 3 × 105 cm−3 and temperatures of Te ∼ 20 000 K in systems at z > 6. Accounting for these self-consistent densities changes the derived Te and modifies the inferred metallicities by up to 0.29 dex relative to previous
estimates. We discuss the reported N/O overabundances in our high-z sample, driven by the high N3+ /H+ ratios inferred from the N iv] lines. We point out that a Te -stratification, in which the N3+ zone has a slightly higher Te than Te ([O iii]),
could substantially reduce the inferred N/O. Quantitatively, if Te (N3+ ) were 10 per cent higher than Te ([O iii]), this could induce a systematic overestimation of N3+ /O2+ of nearly 50 per cent. Classical N/O diagnostics such as N+ /O+ , due to their critical densities, can significantly impact the inferred N/O abundance in the presence of high-density gas, whereas N2+ /O2+ place these galaxies closer to z ∼ 0 systems in the N/O–O/H plane. While promising, this method accounts for density inhomogeneities but not Te fluctuations, and relies on UV atomic data in the high-ne regime. Future JWST programs will be key to testing its robustness.