One cloud is not enough: extreme conditions bias chemical abundances in high-redshift galaxies

Abstract: Since its launch, JWST has opened an unprecedented opportunity to characterise the ionised ISM of high-redshift galaxies using well-established rest-frame UV/optical diagnostics from the local Universe. At the same time, these observations challenge the validity of such classical methods when applied to the extreme environments typical at high redshift. We present an in-depth analysis of the ISM in three representative case studies at $z=2 - 6$ (MARTA 4327, the Sunburst Arc and RXCJ2248-ID) conducted within a multi-cloud photoionisation modelling framework (HOMERUN). We show that even a small fraction of unresolved high-density clumps can contribute more than half of the observed flux of auroral lines, while only negligibly to standard optical density tracers. As a result, $T_{\mathrm{e}}$-method metallicities can be underestimated by $\sim 0.15 - 0.3$ dex, as for MARTA 4327. By modelling rest-frame UV and optical data, we demonstrate that discrepancies between abundances obtained from diagnostics tracing different zones do not necessarily imply chemical inhomogeneities. In RXCJ2248-ID, the disagreement between UV and optical N/O may naturally arise from ionisation and density structure alone. In contrast, we find evidence for genuine chemical stratification in the Sunburst Arc, where a component enriched in nitrogen coexists with a chemically normal one. Finally, we argue that very-high-ionisation lines may be explained within a pure star-formation scenario invoking matter-bounded regions. However, in the case of RXCJ2248-ID, we cannot rule out a minor contribution from an AGN based solely on the observed fluxes. These results indicate that classical diagnostics can be significantly biased in high-redshift galaxies and that self-consistent, physically motivated tools are therefore essential to properly interpret the complex ISM conditions and chemical enrichment in the early Universe.