Generalized T_e([O iii])-T_e(He i) Discrepancies in Ionized Nebulae: Possible Evidence of Case B Deviations and Temperature Inhomogeneities

The physics of recombination lines in the He i singlet system is expected to be relatively simple, supported by accurate atomic models. We examine the intensities of He i singlets λ3614, λ3965, λ5016, λ6678, and λ7281 and the triplet He i λ5876 in various types of ionized nebulae and compare them with theoretical predictions to test the validity of the “Case B” recombination scenario and the assumption of thermal homogeneity. Our analysis includes 85 spectra from Galactic and extragalactic H ii regions, 90 from star-forming galaxies, and 218 from planetary nebulae, all compiled by the Deep Spectra of Ionized Regions Database Extended (DESIRED-E) project. By evaluating the ratios He i λ7281/λ6678 and He i λ7281/λ5876, we determine T_e(He i) and compare it with direct measurements of T_e([O iii] λ4363/λ5007). We find that T_e(He i) is systematically lower than T_e([O iii]) across most objects and nebula types. Additionally, we identify a correlation between the abundance discrepancy factor (ADF(O²⁺)) and the difference T_e([O iii]) - T_e(He i) for planetary nebulae. We explore two potential explanations: photon loss from n¹P → 1¹S transitions and temperature inhomogeneities. Deviations from “Case B” may indicate photon absorption by H i rather than He i and/or generalized ionizing photon escape, highlighting the need for detailed consideration of radiative transfer effects. If temperature inhomogeneities are widespread, identifying a common physical phenomenon affecting all ionized nebulae is crucial. Our results suggest that both scenarios can contribute to the observed discrepancies.