Turbulent thermal conduction in the solar transition region

Emission measures ℰ(T) derived from EUV observations of the lower solar transition region (LTR; 4.3 ≲ log T ≲ 5.3) indicate that there is far more material in that temperature range than can be explained within the steady single flux-tube scenario if the classical energy transfer and loss mechanisms are adopted. This suggests that some mechanism may be operating which reduces the temperature gradient. We investigate the inclusion of a turbulent thermal conductivity κ_T = Φρ_p ul in a one-dimensional model, where u is the rms microvelocity in one direction, l is the mixing length, and Φ is a constant of order unity. Athay has inferred from observational evidence that u ≃ 20(T/10⁵)^1/2 km s^-1, but the temperature dependence of the mixing length is uncertain, although it appears likely that it should decrease with increasing T. If we assume l ∝ T^-α, it is shown that near-perfect agreement with the observed emission measures is obtained for α = 3/2, both as regards the slope d log ℰ/d log T ≈ -3 in the LTR, and the upturn at the top of this range. It is argued that the upturn results from the transition between the dominance of turbulent conductivity in the LTR and of classical conductivity in the upper transition region (UTR).