SIMBAD references

We present a systematic study for ionization state of inter-stellar medium in galaxies at z = 0- with ∼ 140000 Sloan Digital Sky Survey (SDSS) galaxies and 108 intermediate- to high-redshift galaxies from the literature, using an ionization parameter sensitive line ratio of [OIII]λ5007/[OII]λ3727 and photoionization models. We confirm that z ∼ 2-3 galaxies show an [OIII]/[OII] ratio significantly higher than a typical star-forming galaxy of SDSS by a factor of ≳ 10, and the photoionization models reveal that these high-z galaxies have an ionization parameter of log(qion/cm/s) ∼ 7.6-9.0, a factor of ∼ 4-10 higher than local galaxies. For galaxies at any redshift, we identify a correlation between the [OIII]/[OII] ratio and galaxy global properties of star formation rate (SFR), stellar mass (M*), and metallicity (Z). We extend the fundamental metallicity relation (FMR) and develop the fundamental ionization relation (FIR), a four-dimensional relation of ionization parameter, SFR, M*, and Z. The intermediate- and high-z galaxies up to z ≃ 3 follow the FIR defined with the local galaxies, in contrast with the FMR whose possible evolution from z ∼ 2 to 3 is reported. We find that the FMR evolution of z ∼ 2-3 appears, if one omits ionization parameter differences, and that the FMR evolution does not exist for an average metallicity solution of z ∼ 3 galaxies with a high-ionization parameter. Interestingly, all of two local Lyman-continuum emitting galaxies (LyC leakers) have a high [OIII]/[OII] ratio, indicating a positive correlation between [OIII]/[OII] and ionizing photon escape fraction (fesc), which is successfully explained by our photoionization models. Because [OIII]/[OII] ratios of z ∼ 2-3 galaxies, especially Lyα emitters (LAEs), are comparable to, or higher than, those of the local LyC leakers, these high-z galaxies are candidates of Lyman-continuum emitting objects. A strong Lyα emission can coexist with a large fesc of ≲ 0.8, and the increasing fraction of LAEs towards high-z reconciles the picture of cosmic reionization whose major ionizing sources are faint galaxies having intrinsically bright Lyα emission.