Temperature fluctuations in HII 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 t(2) 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 cosmic rays. We show that a very small amount of cold gas is sufficient to account for t(2) values typically inferred for H II regions.