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 can not 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 \leq M _ { S } \leq 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 , \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 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 \epsilon \sim 2.9 \times 10 ^ { -2 } , 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 .