Ionization state of inter-stellar medium in galaxies: evolution, SFR-M*-Z dependence, and ionizing photon escape

We present a systematic study for ionization state of inter-stellar medium in galaxies at z = 0- with similar to 140 000 Sloan Digital Sky Survey (SDSS) galaxies and 108 intermediate-to high-redshift galaxies from the literature, using an ionization parameter sensitive line ratio of [O III]lambda 5007/[O II]lambda 3727 and photoionization models. We confirm that z similar to 2-3 galaxies show an [O III]/[O II] ratio significantly higher than a typical star-forming galaxy of SDSS by a factor of greater than or similar to 10, and the photoionization models reveal that these high-z galaxies have an ionization parameter of log (q(ion)/cm s(-1)) similar to 7.6-9.0, a factor of similar to 4-10 higher than local galaxies. For galaxies at any redshift, we identify a correlation between the [O III]/[O II] ratio and galaxy global properties of star formation rate (SFR), stellarmass (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 similar or equal to 3 follow the FIR defined with the local galaxies, in contrast with the FMR whose possible evolution from z similar to 2 to 3 is reported. We find that the FMR evolution of z similar to 2-3 appears, if one omits ionization parameter differences, and that the FMR evolution does not exist for an average metallicity solution of z similar to 3 galaxies with a high-ionization parameter. Interestingly, all of two local Lyman-continuum emitting galaxies (LyC leakers) have a high [O III]/[O II] ratio, indicating a positive correlation between [O III]/[O II] and ionizing photon escape fraction (f(esc)), which is successfully explained by our photoionization models. Because [O III]/[O II] ratios of z similar to 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. A strong Ly alpha emission can coexist with a large f(esc) of less than or similar to 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 Ly alpha emission.