The Ultraviolet C ii Lines as a Diagnostic of κ-distributed Electrons in Planetary Nebulae

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