Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas

Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum ofdensity fluctuations in the ionized interstellar medium. Although this densityspectrum is suggestive of turbulence, no theory relevant to its interpretationexists. We calculate the density spectrum in turbulent magnetized plasmas byextending the theory of incompressible MHD turbulence given by Goldreich &Sridhar to include the effects of compressibility and particle transport. Ourmost important results are as follows. (1) Density fluctuations are due to theslow mode and the entropy mode. Both modes are passively mixed by the cascadeof shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum,so do the density fluctuations. (2) Observed density fluctuation amplitudesimply either that the magnetic and gas pressures are comparable, or that theouter scale of the turbulence is very small. (3) A high degree of ionization isrequired for the cascade to survive damping by neutrals and thereby to extendto small lengthscales. Regions that are insufficiently ionized produce densityfluctuations only on lengthscales larger than the neutral damping scale. Theseregions may account for the excess of power that is found on large scales. (4)Both the entropy mode and the slow mode are damped on lengthscales below thatat which protons can diffuse across an eddy during the eddy's turnover time.Consequently, eddies whose extents along the magnetic field are smaller thanthe proton collisional mean free path do not contribute to the densityspectrum. However, in MHD turbulence eddies are highly elongated along themagnetic field. From an observational perspective, the relevant lengthscale isthat transverse to the magnetic field. Thus the cut-off lengthscale for densityfluctuations is significantly smaller than the proton mean free path.Comment: 19 pages, 2 figures, submitted to Ap