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.