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Stellar population models produce radiation fields that ionize oxygen up toO+2, defining the limit of standard HII region models (<54.9 eV). Yet, someextreme emission line galaxies, or EELGs, have surprisingly strong emissionoriginating from much higher ionization potentials. We present UV-HST/COS andoptical-LBT/MODS spectra of two nearby EELGs that have very-high-ionizationemission lines (e.g., HeII 1640,4686 CIV 1548,1550, [FeV] 4227, [ArIV]4711,4740). We define a 4-zone ionization model that is augmented by avery-high-ionization zone, as characterized by He+2 (>54.4 eV).  The 4-zone model has little to no effect on the measured total nebularabundances, but does change the interpretation of other EELG properties: wemeasure steeper central ionization gradients, higher volume-averaged ionizationparameters, and higher central T_e, n_e, and logU values. Traditional 3-zoneestimates of the ionization parameter can under-estimate the average log U byup to 0.5 dex. Additionally, we find a model-independent dichotomy in theabundance patterns, where the alpha/H-abundances are consistent but N/H, C/H,and Fe/H are relatively deficient, suggesting these EELGs are alpha/Fe-enrichedby >3 times. However, there still is a high-energy ionizing photon productionproblem (HEIP^3). Even for such alpha/Fe-enrichment and very-high log Us,photoionization models cannot reproduce the very-high-ionization emission linesobserved in EELGs.

Characterizing Extreme Emission Line Galaxies I: A Four-Zone Ionization Model for Very-High-Ionization Emission