  We conduct a statistical analysis of 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 (CEERS) survey. The sample consists of
48 galaxies with spectroscopic redshifts z=2.7-6.3 which are largely
representative of typical star-forming galaxies at these redshifts. The [SII]
6718, 6733 doublet is used to estimate electron densities (n_e), and
dust-corrected Ha luminosities are used to compute total ionizing photon rates
(Q). Using composite spectra of galaxies in bins of [OIII]/[OII] (i.e., O32) as
a proxy for U, we determine that galaxies with higher O32 have <n_e> ~ 500
cm^-3 that are at least a factor of ~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 of all available strong rest-frame optical
emission lines is used to simultaneously constrain U and oxygen abundance
(Z_neb). We find a large spread in 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 (Sigma_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 Sigma_SFR (or gas density) may influence U,
including variations in n_e and Q that are tied to metallicity and gas density,
internal dust extinction of ionizing photons, and the effects of gas density on
the volume filling fraction of dense clumps in HII regions and the escape
fraction of ionizing photons. Based on these considerations, we conclude that
gas density may play a more central role than metallicity in modulating U at
these redshifts.
