The magnitude of heating of the Diffuse Ionized Gas of the interstellar medium by Landau damping of turbulence

I consider the dissipation of interstellar magnetohydrodynamic turbulence by Landau damping, and the associated heating of the interstellar gas, as a function of the wave distribution function and the plasma (beta). The paper particularly addresses the contention of Lerche & Schlickeiser (2001, LS) that previous treatments of these features were incorrect, and produced expressions which were substantially in error, leading to qualitatively incorrect estimates for turbulent heating of the interstellar medium. Lerche and Schickeiser are correct in noting that the exact expression for the heating rate by dissipation through Landau damping requires integration of the product 2(gamma)PB over all wavenumber space, where (gamma) is the fast magnetosonic wave damping rate, and PB is the magnetic turbulence spatial power spectrum. However, this exact expression yields numerical results which differ little from the previously used expressions, when evaluated for the same turbulence properties. If turbulence in the Diffuse Ionized Gas (DIG) phase of the interstellar medium consisted of fast mode magnetosonic waves, the heat input due to dissipation would exceed the cooling rate by at least 2 to 3 orders of magnitude. This fact may be demonstrated by the formulas in LS as well as previous papers on this topic. Lowering the theoretical rate for heat input requires rather extreme assumptions about the nature of this turbulence, such as very large and seemingly improbable anisotropy factors.