Two-fluid ambipolar diffusion for molecular clouds with realistic heating and cooling

Molecular clouds are composed of a mix of ions and neutral gas, which interact differently with magnetic fields. We present a thorough analysis of the eigenstructure of the system of equations that describe the evolution of both ions and neutrals in the presence of a magnetic field, and with a physically motivated equation of state with heating and cooling. We show that the wave structure of the two-fluid equations with an adiabatic equation of state parallels that of the isothermal system. In particular, the same wave families exist in both isothermal and adiabatic systems, and the scales on which the waves are dissipated are unchanged. For typical molecular cloud parameters, the gravitational collapse is carried by the slow wave, just as it was in the isothermal case. There are, however, several interesting points of difference as well. In particular, the presence of cooling and radiative effects reduces the Jeans scale and furthermore increases the damping rates and reduces the phase velocity of several families of waves near the Jeans scale. The magnetohydrodynamic waves can re-emerge on scales significantly smaller than the ambipolar dissipation scale, as the neutrals and ions become completely decoupled from each other. This allows for the possibility of extremely small scale turbulence and thus lends plausibility to the idea that a small-scale dynamo can be sustained on scales smaller than the ambipolar diffusion scale.