A present prevailing open problem planetary nebulae research, and photoionized gaseous nebulae research at large, is the systematic discrepancies in ionic abundances derived from recombination and collisionally excited lines in many H II regions and planetary nebulae. Peimbert (1967) proposed that these discrepancies were due to temperature fluctuations in the plasma, but the amplitude of such fluctuations remain unexplained by standard phtoionization modeling. In this letter we show that large amplitude temperature oscillations are expected to form in gaseous nebulae photoionized by short-period binary stars. Such stars yield periodically varying ionizing radiation fields, which induce periodic oscilla- tions in the heating-minus-cooling function across the nebula. For flux oscillation periods of a few days any temperature perturbations in the gas with frequencies similar to those of the ionizing source will undergo resonant amplification. In this case, the rate of growth of the perturbations increases with the amplitude of the variations of the ionizing flux and with decreasing nebular equilibrium temperature. We also present a line ratios diagnostic plot that combines [O III] collisional lines and O II recombination lines for diagnosing equilibrium and fluctuation am- plitude temperatures in gaseous nebulae. When applying this diagnostic to the planetary nebula M 1-42 we find an equilibrium temperature of ~6000 K and a resonant temperature fluctuation amplitude (Trtf ) of ~4000 K. This equilibrium temperature is significantly lower than the temperature estimated when temperature perturbations are ignored.
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