Ambipolar Drift Heating in Turbulent Molecular Clouds

Although thermal pressure is unimportant dynamically in most molecular gas,the temperature is an important diagnostic of dynamical processes and physicalconditions. This is the first of two papers on thermal equilibrium in molecularclouds. We present calculations of frictional heating by ion-neutral (orambipolar) drift in three-dimensional simulations of turbulent, magnetizedmolecular clouds. We show that ambipolar drift heating is a strong function of position in aturbulent cloud, and its average value can be significantly larger than theaverage cosmic ray heating rate. The volume averaged heating rate per unitvolume due to ambipolar drift, H_AD ~ |JxB|^2 ~ B^4/L_B^2, is found to dependon the rms Alfvenic Mach number, M_A, and on the average field strength, asH_AD ~ M_A^2<|B|>^4. This implies that the typical scale of variation of themagnetic field, L_B, is inversely proportional to M_A, which we alsodemonstrate.Comment: 37 pages, 9 figures include