  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 yield a positive correlation between the
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 yield discrepant correlations when different subsets of line
ratios are used in the derivation. The correlation between the metallicity and
ionization parameter has a secondary dependence on the 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 solving this puzzle, though more sophisticated combinations
of dynamical models and photoionization models to test are required.
