Can the Kappa-distributed Electron Energies Account for the Intensity Ratios of O ii Lines in Photoionized Gaseous Nebulae?

A vexing puzzle in the study of planetary nebulae and H ii regions is that the plasma diagnostic results based on collisionally excited lines systematically differ from those based on recombination lines. A fairly speculative interpretation is the presence of nonthermal electrons with the so-called κ energy distributions, yet there is little observational evidence to verify or disprove this hypothesis. In this paper, we examine the influence of κ-distributed electrons on the emissivities of O ii recombination lines using an approximate method, where the rate coefficients for a κ distribution are computed by summing Maxwellian-Boltzmann rate coefficients with appropriate weights. The results show that if invoking κ-distributed electrons, the temperatures derived from the [O iii] (λ4959 + λ5007)/λ4363 ratios could coincide with those estimated from the O ii λ4649/λ4089 ratios. However, the estimated temperatures and κ values are not in agreement with those obtained through comparing the [O iii] (λ4959 + λ5007)/λ4363 ratios and the hydrogen recombination spectra, suggesting that the electron energy is unlikely to follow the κ-distributions over a global scale of the nebular regions. Nevertheless, based on this observation alone, we cannot definitely rule out the presence of κ-distributed electrons in some microstructures within nebulae.