Photoelectric heating and [CII] cooling in translucent clouds: results for cloud models based on simulations of compressible MHD turbulence

The photoelectric heating is believed to be the main heating mechanism in cool HI clouds. The heating rate can be estimated through observations of the [CII] line emission, since this is the main coolant in regions where the photoelectric effect dominates the heating. Comparison of the [CII] emission with the far-infrared (FIR) emission allows to constrain the efficiency of the photoelectric heating, using model calculations that take into account the strength of the radiation field. Recent [CII] observations carried out with the ISO satellite have made this study possible. In this work we study the correlation between FUV absorption and FIR emission using three-dimensional models. The density distributions are obtained with numerical simulations of compressible magneto-hydrodynamic turbulence, with rms sonic Mach numbers 0.6<M<10. The FIR intensities are solved with detailed radiative transfer calculations. The [CII] line radiation is estimated assuming the [CII] line cooling equals the FUV absorption multiplied by the efficiency of the photoelectric heating, epsilon. The average ratio between the predicted [CII] and FIR emissions is found to be remarkably constant between different models, implying that the derived values of epsilon should not depend on the rms Mach number. The comparison with empirical data from translucent, high latitude clouds yields an estimate of the photoelectric heating efficiency of 2.9 10^-2. This value confirms previous theoretical predictions. Our models show that most of the scatter in the observed [CII] and FIR intensities can be understood as a result of the highly fragmented density field in turbulent HI clouds. The scatter can be reproduced with models with supersonic turbulence, while subsonic turbulence fails to generate the observed scatter.