Self-Consistent Direct Method for Chemical Abundances in High-z Galaxies with JWST
The unprecedented rest-frame UV and optical coverage provided by JWST enables simultaneous constraints on the electron density (n$_{\rm e}$) and temperature (T$_{\rm e}$) of ionized gas in galaxies at z>5. We present a self-consistent direct method based on multiple OIII]1661,66) and [OIII] ($\lambda$4363, and $\lambda$5007) transitions to characterize the physical conditions of the high-ionization zone. This new approach is insensitive to a wide range of n$_{\rm e}$ due to the high critical densities of the OIII] and [OIII] transitions. Applying this technique to six galaxies at z=5-9, we find electron densities up to n$_{\rm e}$$\sim 3\times 10^{5}$ cm$^{-3}$ and temperatures of T$_{\rm e}$ $\sim 20,000$ K in systems at $z>6$. Accounting for these self-consistent densities changes the derived T$_{\rm e}$ and modifies the inferred metallicities by up to 0.29 dex relative to previous estimates. We discuss the reported N/O overabundances in the high-$z$ galaxies from our sample, which arise entirely from the high N$^{3+}$/H$^{+}$ values inferred from NIV] lines. We point out that a T$_{\rm e}$-stratification, in which the N$^{3+}$ zone has a slightly higher T$_{\rm e}$ than T$_{\rm e}$([OIII]), could substantially reduce the inferred N/O. Quantitatively, if T$_{\rm e}$(N$^{3+}$) were 10\% higher than T$_{\rm e}$([OIII]), this could induce a systematic overestimation of N$^{3+}$/O$^{2+}$ of nearly 50\%. 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 N$^{2+}$/O$^{2+}$ place these galaxies closer to $z\sim0$ systems in the N/O-O/H plane. Future JWST programs with larger and more diverse samples will be essential to test the universality and robustness of these results.