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.
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