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We present a systematic study for ionization state of inter-stellar medium in galaxies at z=0-3 with ~140, 000 SDSS galaxies and 108 intermediate to high redshift galaxies from the literature, using an ionization-parameter sensitive line ratio of OIII5007/OII3727 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^-1) ~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 (Mₛtar), 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, Mₛtar, 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 Ly-alpha 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. (abridged)
Nakajima et al. (2014) studied this question.