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

Far–ultraviolet (FUV) photons expel electrons from interstellar dust grains and the excess kinetic energy of the electrons is converted into gas thermal energy through collisions. This photoelectric heating is believed to be the main heating mechanism in cool HI clouds. The heating rate cannot be directly measured, but it can be estimated through observations of the [CII] line emission, since this is believed to be the main coolant in regions where the photoelectric effect dominates the heating. Furthermore, the 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 of the density distribution in HI clouds. The density distributions are obtained as the result of numerical simulations of compressible magneto–hydrodynamic turbulence, with rms sonic Mach numbers of the flow ranging from subsonic to highly supersonic, 0.6 ≤ MS ≤ 10. The FIR intensities are solved with detailed radiative transfer calculations. The [CII] line radiation is estimated assuming local thermodynamic equilibrium where the [CII] line cooling equals the FUV absorption multiplied by the unknown efficiency of the photoelectric heating, ǫ. 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 ǫ should not depend on the rms Mach number of the turbulence. The comparison of the models with the empirical data from translucent, high latitude clouds yields an estimate of the photoelectric heating efficiency of ǫ ∼2.9×10, based on the dust model of Li & Draine. This value confirms previous theoretical predictions. The observed correlation between [CII] and FIR emission contains a large scatter, even within individual clouds. Our models show that most of the scatter can be understood as resulting from the highly fragmented density field in turbulent HI clouds. The scatter can be reproduced with density distributions from supersonic turbulence, while subsonic turbulence fails to generate the observed scatter. Subject headings: ISM: clouds — radio lines: ISM — infrared: ISM — radiative transfer — ISM: dust — ISM: kinematics and dynamics 1