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 H II regions in the northern half of M33. We construct [O III]λ5007/[O II]λ3727 and [O III]λ5007/[S II]λ6724 ratio maps from narrowband images continuum-subtracted in this way, from which we classify the H II regions by optical depth to ionizing radiation, based on their ionization structure. This method works relatively well in the low-metallicity regime, $12+\mathrm{log}({\rm{O}}/{\rm{H}})\leqslant 8.4$ 12+log(O/H)≤8.4 , where [O III]λ λ4959, 5007 is strong. However, at higher metallicities, the method breaks down due to the strong dependence of the [O III]λ λ4959, 5007 emission lines on the nebular temperature. Thus, although O⁺⁺ may be present in metal-rich H II 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 [O III] extending over an area ~1 kpc across and [O III]λ5007 luminosity of 4.9 ± 1.5 × 10³⁸ erg s^-1, 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 narrowband 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]λ1909 imaging of Haro 11, ESO 338-IG004, and Mrk 71.