Temperature Fluctuations in Photoionized Nebulae

Recombination lines in gaseous nebulae frequently yield parent-ion abundances that are several times larger than abundances derived from forbidden lines. One possible explanation for this discrepancy is the presence of temperature fluctuations. We examine temperature fluctuations in model nebulae by utilizing Peimbert\u27s t2 parameter. We have run large grids of models, varying the stellar temperature and the total hydrogen density. We consider two abundance sets: The first uses typical planetary nebulae abundances, while the second examines the effect of increasing the metals and grains by a factor of 3. We also consider both a constant density distribution and one which varies sinusoidally with radius. We examine the method of deriving t2 observationally, which uses measured [O III] and Balmer temperatures. We find that this derived t2 shows no correlation with the t2 based on the integral definition. We discuss the reasons for this discrepancy, which include nonvalidity of some of the basic assumptions and theoretical and observational difficulties with the Balmer temperature. We find that, in high-metallicity objects especially, noncollisional contributions to [O III] λ4363 can significantly affect the derived temperature. We argue that while temperature fluctuations may result in non-negligible abundance corrections in some objects, they are insufficient to resolve the abundance discrepancy