The abundance discrepancy factor and t^2 in nebulae: are non-thermal electrons the culprits?

We discuss recent claims that the free electrons in ionized nebulae may not have a significantly Maxwellian velocity distribution. Supra-thermal electrons, electrons with much more energy than is encountered at electron temperatures found in nebulae, may solve the t^2/ADF puzzle, the observations that abundances obtained from recombination and collisionally excited lines do not agree, and that different temperature indicators give different results. These non-Maxwellian electrons can be designated by the kappa formalism. We show that the distance over which heating rates change are much longer than the distance supra-thermal electrons can travel, and that the timescale to thermalize these electrons are much shorter than the heating or cooling timescales. These estimates show that supra-thermal electrons will have disappeared into the Maxwellian velocity distribution long before they affect the collisionally-excited forbidden and recombination lines, so the electron velocity distribution will be closely thermal.