Ionization State of Inter-Stellar Medium in Galaxies: Evolution, SFR-M_star-Z Dependence, and Ionizing Photon Escape

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 [OIII]5007/[OII]3727 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 (M_star), 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_star, 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)