Bridging Optical and Far-infrared Emission-line Diagrams of Galaxies from Local to the Epoch of Reionization: Characteristic High [O III] 88 μm/SFR at z > 6

We present photoionization modeling of galaxy populations at z ∼ 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 μm and [C II] 158 μm) emission-line fluxes and plot them on the [O III]λ5007/Hβ-[N II]λ6585/Hα (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 nH, and gaseous metallicity Z_gas. Our models successfully reproduce the nebular parameters of local galaxies, and then predict the distributions of the z ∼ 0, 2, and >6 galaxies in the diagrams. The predicted distributions illustrate the redshift evolution on all the diagrams; e.g., [O III]/Hβ and [O III]₈₈/[C II]₁₅₈ ratios continuously decrease from z > 6 to 0. Specifically, the z > 6 galaxies exhibit ∼0.5 dex higher U than low-redshift galaxies at a given Z_gas and show predicted flat distributions on the BPT diagram at log[O III]/Hβ = 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. JWST will test the predictions and scenarios for the z > 6 galaxies proposed by our photoionization modeling.