Fine-Scale Temperature Fluctuations in the Orion Nebula and the t² Problem^*

We present a high spatial resolution map of the columnar electron temperature (T_c) of a region to the southwest of the Trapezium in the Orion Nebula. This map was derived from Hubble Space Telescope images that isolated the primary lines of H I for determination of the local extinction and of the [O III] lines for determination of T_c. Although there is no statistically significant variation of T_c with distance from the dominant ionizing star, θ¹ Ori C, we find small-scale variations in the plane of the sky down to a few arcseconds, which are compatible with the variations inferred from comparing the value of T_e derived from forbidden and recombination lines, commonly known as the t² problem. We present other evidence for fine-scale variations in conditions in the nebula, these being variations in the surface brightness of the nebula, fluctuations in radial velocities, and ionization changes. From our T_c map and other considerations we estimate that t² = 0.028 ± 0.006 for the Orion Nebula. Shadowed regions behind clumps close to the ionization front can make a significant contribution to the observed temperature fluctuations, but they cannot account for the t² values inferred from several methods of temperature determination. It is shown that an anomalous broadening of nebular emission lines appears to have the same sense of correlation as the temperature anomalies, although a causal link is not obvious.