Limits to Ionization-Parameter Mapping as a Diagnostic of HII Region
  Optical Depth
  We employ ionization-parameter mapping (IPM) to infer the optical depth of
HII regions in the northern half of M33. We construct [OIII]$\lambda
5007$/[OII]$\lambda 3727$ and [OIII]$\lambda 5007$/[SII]$\lambda 6724$ ratio
maps from narrow-band images continuum-subtracted in this way, from which we
classify the HII regions by optical depth to ionizing radiation, based on their
ionization structure. This method works relatively well in the low metallicity
regime, $12 + \log(\rm O/H) \leq 8.4$, where [OIII]$\lambda\lambda4949,5007$ is
strong. However, at higher metallicities, the method breaks down due to the
strong dependence of the [OIII]$\lambda\lambda4959,5007$ emission lines on the
nebular temperature. Thus, although O$^{++}$ may be present in metal-rich HII
regions, these commonly used emission lines do not serve as a useful indicator
of its presence, and hence, the O ionization state. In addition, IPM as a
diagnostic of optical depth is limited by spatial resolution. We also report a
region of highly excited [OIII] extending over an area $\sim$ 1 kpc across and
[OIII]$\lambda5007$ luminosity of $4.9\pm 1.5\times10^{38}$ erg/s, which is
several times higher than the ionizing budget of any potential sources in this
portion of the galaxy. Finally, this work introduces a new method for continuum
subtraction of narrow-band images based on the dispersion of pixels around the
mode of the diffuse-light flux distribution. In addition to M33, we demonstrate
the method on C III]$\lambda$1909 imaging of Haro~11, ESO 338-IG004, and
Mrk~71.
