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

Photoionization produces supra-thermal electrons, electrons with much more energy than is found in a thermalized gas at electron temperatures characteristic of nebulae. The presence of these high energy electrons may solve the long-standing 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, if they survive long enough to affect diagnostic emission lines. The presence of these non-Maxwellian distribution electrons is usually designated by the term kappa. Here we use well-established methods to 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 establish that supra thermal electrons will have disappeared into the Maxwellian velocity distribution long before they affect the collisionally excited forbidden and recombination lines that are used for deriving abundances relative to hydrogen. The electron velocity distribution in nebulae should be closely thermal.