Correlation between the gas-phase metallicity and ionization parameter in extragalactic HII regions

The variations of the metallicity and ionization parameter in HII regions are usually thought to be the dominant factors that produce the variations we see in the observed emission line spectra. There is an increasing amount of evidence that these two quantities are physically correlated, although the exact form of this correlation is debatable in the literature. Simulated emission line spectra from photoionized clouds provide important clues about the physical conditions of HII regions and are frequently used for deriving metallicities and ionization parameters. Through a systematic investigation on the assumptions and methodology used in applying photoionization models, we find that the derived correlation has a strong dependence on the choice of model parameters. On the one hand, models that give consistent predictions over multiple emission-line ratios would yield a positive correlation between metallicity and ionization parameter for the general population of HII regions. On the other hand, models that are inconsistent with the data locus in the line-ratio space would yield discrepant correlations when different subsets of line ratios are used in the derivation. The correlation between metallicity and ionization parameter has a secondary dependence on the star formation rate (SFR) surface density, with the higher SFR regions showing higher ionization parameter but weaker correlations. The existence of the positive correlation contradicts the wind-driven bubble model for HII regions. We explore assumptions in the models and conclude that there is a potential bias associated with the geometry. However, this is still insufficient to explain the correlation. Mechanisms that suppress the dynamical influence of stellar winds in realistic HII regions might be the key to solve this puzzle, which require more sophisticated combinations of dynamical models and photoionization models to test.