Temperature fluctuations in H II regions: t2 for the two-phase model

Aims: We investigate temperature fluctuations in H II regions in terms of a two-phase model, which assumes that the nebular gas consists of a hot and a cold phase. Methods: We derive general formulae for T([O III), the [O III] forbidden line temperature, and T(H I), the hydrogen Balmer jump temperature, in terms of the temperatures of the hot and cold phases, T_h and T_c. Results: For large temperature differences, the values of t2 required to account for the observed difference between T([O III]) and T(H I) are much lower than those deduced using the classical formulae that assume random and small amplitude temperature fluctuations. One should therefore be cautious when using a two-phase model to account for empirically derived $t^2$ values. We present a correction of a recent work by Giammanco & Beckman, who use a two-phase model to estimate the ionization rate of H II regions by cosmicrays. We show that a very small amount of cold gas is sufficient to account for t2 values typically inferred for H II regions.