Origins of Extreme Emission-Line Ratios in z > 3 Galaxies: Insights from the Lumen Model

Abstract: Optical emission-line ratios in star-forming galaxies at $z \sim 3$-8, such as [OIII]/H$β$ and [OIII]/[OII], are strongly offset from those at $z \sim 0$-2, pointing to more extreme ionization and ISM conditions in the early Universe. To constrain the physical origin of these offsets, we developed Lumen, a framework for modelling nebular emission from spatially distributed HII regions in cosmological simulations. We apply Lumen to IllustrisTNG50, validate its predictions at low redshift, and test a suite of proposed mechanisms for producing extreme line ratios at $z = 3$-8. We focus on the [NII]/H$α$ versus [OIII]/H$β$ (N2-BPT) diagram, the [SII]/H$α$ versus [OIII]/H$β$ (S2-VO87) diagram, and the [OIII]/[OII] versus ([OII]+[OIII])/H$β$ (O32-R23) diagram. We find that $α$-enhancement alone cannot explain the bulk of observations. Moderate offsets emerge from the combined effects of $α$-enhancement, a higher IMF upper-mass cutoff, and AGN contributions. The most extreme [OIII]/H$β$ and [OIII]/[OII] values require high ionization parameters powered by massive star clusters of $\gtrsim 10<sup>5$-$10<sup>6\,\mathrm{M}_\odot$, consistent with recent JWST observations. Reproducing the highest [NII]/H$α$ ratios additionally requires enhanced nitrogen abundances. Although gas densities of $n \sim 10<sup>4\,\mathrm{cm}<sup>{-3}$ can boost several diagnostic ratios, they suppress [SII]/H$α$ and are therefore in tension with current observations. Overall, models combining harder ionizing spectra, elevated ionization parameters from massive star clusters, and enhanced nitrogen abundances reproduce the observed high-$z$ galaxy population across the N2-BPT, S2-VO87, and O32-R23 diagrams. This successful model also motivates new demarcation lines for star-forming galaxies in the N2-BPT and S2-VO87 diagrams.