  The temperature of the gas in molecular clouds is a key determinant of the
characteristic mass of star formation. Ambipolar diffusion (AD) is considered
one of the most important heating mechanisms in weakly ionized molecular
clouds. In this work, we study the AD heating rate using 2-fluid turbulence
simulations and compare it with the overall heating rate due to turbulent
dissipation. We find that for observed molecular clouds, which typically have
Alfven Mach numbers of ~1 (Crutcher 1999) and AD Reynolds numbers of ~20 (McKee
et al. 2010), about 70% of the total turbulent dissipation is in the form of AD
heating. AD has an important effect on the length scale where energy is
dissipated: when AD heating is strong, most of the energy in the cascade is
removed by ion-neutral drift, with a comparatively small amount of energy
making it down to small scales. We derive a relation for the AD heating rate
that describes the results of our simulations to within a factor of two.
Turbulent dissipation, including AD heating, is generally less important that
cosmic-ray heating in molecular clouds, although there is substantial scatter
in both.
