A JWST/NIRSpec Exploration of the Connection between Ionization Parameter, Electron Density, and Star-formation-rate Surface Density in z = 2.7-6.3 Galaxies

We examine the factors responsible for the variation in the ionization parameter (U) of high-redshift star-forming galaxies based on medium-resolution JWST/NIRSpec observations obtained by the Cosmic Evolution Early Release Science survey. The sample consists of 48 galaxies with redshifts z _spec = 2.7-6.3, which are largely representative of typical galaxies at these redshifts. The [S II] λ λ6718, 6733 doublet is used to estimate electron densities (n _e ), and dust-corrected Hα luminosities are used to compute ionizing photon rates (Q). Using composite spectra of galaxies in bins of [O III] λ λ4960, 5008/[O II] λ λ3727, 3730 (O32) as a proxy for U, we determine that galaxies with higher O32 have <n _e > ≃ 500 cm^-3 that are ≳5 × larger than that of lower-O32 galaxies. We do not find a significant difference in <Q> between low- and high-O32 galaxies. Photoionization modeling indicates a large spread in $\mathrm{log}U$ of ≈1.5 dex at a fixed Z _neb. On the other hand, the data indicate a highly significant correlation between U and star-formation-rate surface density (Σ_SFR), which appears to be redshift invariant at z ~ 1.6-6.3, and possibly up to z ~ 9.5. We consider several avenues through which metallicity and Σ_SFR (or gas density) may influence U, including variations in n _e and Q, internal dust extinction of ionizing photons, and the effects of gas density on the volume filling fraction. Based on these considerations, we conclude that gas density may play a more central role than metallicity in modulating U at these redshifts.