Bridging Optical and Far-Infrared Emission-Line Diagrams of Galaxies from Local to the Epoch of Reionization: Characteristic High [O III] 88 $\mu \mathrm{m}$/SFR at $z>6$

We present photoionization modeling of galaxy populations at $z\sim 0$, $2$, and $>6$ to bridge optical and far-infrared (FIR) emission-line diagrams. We collect galaxies with measurements of optical and/or FIR ([O III] 88 $\mu \mathrm{m}$ and [C II] 158 $\mu \mathrm{m}$) emission line fluxes and plot them on the [O III]$\lambda 5007\mathrm{/}\mathrm{H}\beta$–[N II]$\lambda 6585\mathrm{/}\mathrm{H}\alpha$ (BPT) and L([O III]88)/SFR–L([C II]158)/SFR diagrams, where SFR is the star-formation rate and L([O III]88) and L([C II]158) are the FIR line luminosities. We aim to explain the galaxy distributions on the two diagrams with photoionization models that employ three nebular parameters: the ionization parameter $U$, hydrogen density $n_{\text{H}}$, and gaseous metallicity $Z_{\text{gas}}$. Our models successfully reproduce the nebular parameters of local galaxies, and then predict the distributions of the $z\sim 0$, $2$, and $>6$ galaxies on the diagrams. The predicted distributions illustrate the redshift evolution on all the diagrams; e.g., [O III]$\mathrm{/}\mathrm{H}\beta$ and [O III]88/[C II]158 ratios continuously decrease from $z>6$ to $0$. Specifically, the $z>6$ galaxies exhibit $\sim \text{\hspace{0.17em}⁣}0.5$ dex higher $U$ than low-redshift galaxies at a given $Z_{\text{gas}}$ and show predicted flat distributions on the BPT diagram at $\log [\mathrm{O}\mathrm{I}\mathrm{I}\mathrm{I}]\mathrm{/}\mathrm{H}\beta =0.5$-$0.8$. We find that some of the $z>6$ galaxies exhibit high L([O III]88)/SFR ratios. To explain these high ratios, our photoionization models require a low stellar-to-gaseous metallicity ratio or bursty/increasing star-formation history at $z>6$. The James Webb Space Telescope will test the predictions and scenarios for the $z>6$ galaxies proposed by our photoionization modeling.