The ultraviolet CII lines as a diagnostic of kappa-distributed electrons in planetary nebulae

Abstract

Non-Maxwellian $\kappa$ electron energy distributions (EEDs) have been proposed in recent years to resolve the so-called ``electron temperature and abundance discrepancy problem'' in the study of planetary nebulae (PNe). Thus the need to develop diagnostic tools to determine from observations the EED of PNe is raised. Arising from high energy levels, the ultraviolet (UV) emission lines from PNe present intensities that depend sensitively on the high-energy tail of the EED. In this work, we investigate the feasibility of using the \ion{C}{2}]$\lambda$2326/\ion{C}{2}$\lambda$1335 intensity ratios as a diagnostic of the deviation of the EED from the Maxwellian distribution (as represented by the $\kappa$ index). We use a Maxwellian decomposition approach to derive the theoretical $\kappa$-EED-based collisionally excited coefficients of \ion{C}{2}, and then compute the \ion{C}{2} UV intensity ratio as a function of the $\kappa$ index. We analyze the archival spectra acquired by the {\it International Ultraviolet Explorer} and measure the intensities of \ion{C}{2} UV lines from 12 PNe. By comparing the observed line ratios and the theoretical predictions, we can infer their $\kappa$ values. With the Maxwellian-EED hypothesis, the observed \ion{C}{2}]$\lambda$2326/\ion{C}{2}$\lambda$1335 ratios are found to be generally lower than those predicted from the observed optical spectra. This discrepancy can be explained in terms of the $\kappa$ EED. Our results show that the $\kappa$ values inferred range from 15 to infinity, suggesting a mild or modest deviation from the Maxwellian distribution. However, the $\kappa$-distributed electrons are unlikely to exist throughout the whole nebulae. A toy model shows that if just about 1--5 percent of the free electrons in a PN had a $\kappa$-EED as small as $\kappa=3$, it would be sufficient to account for the observations.