[Previous] | [Session 90] | [Next]
Yoram Lithwick, P. Goldreich (Caltech)
Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of interstellar electron density fluctuations. Although this spectrum is suggestive of turbulence, there is little theoretical understanding of compressible turbulence in magnetized plasmas. We calculate the spectrum of density fluctuations by extending the theory of incompressible magnetohydrodynamic (MHD) turbulence given by Goldreich & Sridhar (1995) to include the effects of compressibility and particle transport. Our most important results are as follows.
\noindent (1) Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfvén waves. Since the shear Alfvén waves have a Kolmogorov spectrum, so do the density fluctuations.
\noindent (2) Density fluctuation amplitudes constrain the nature of MHD turbulence in the interstellar medium. Slow mode density fluctuations are inversely proportional to \beta, the ratio of the gas pressure to the magnetic pressure. Entropy mode density fluctuations are suppressed by cooling when the cascade timescale is longer than the cooling timescale. These constraints suggest that either \beta is of order unity or the outer scale of the turbulence is very small.
\noindent (3) A high degree of ionization is required for the cascade to survive damping by neutrals and extend to small lengthscales. Regions that are insufficiently ionized only produce density fluctuations on lengthscales larger than the neutral damping scale. They may account for the excess of power that is found on large scales.
\noindent (4) Both the entropy mode and the slow mode are damped on lengthscales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant lengthscale is that transverse to the magnetic field. Thus the cut-off lengthscale for density fluctuations is significantly smaller than the proton mean free path.
\noindent (5) The Alfvén mode is critically damped at the transverse lengthscale of the proton gyroradius, and thus cascades to smaller lengthscales than either the slow mode or the entropy mode.
The author(s) of this abstract have provided an email address for comments about the abstract: yoram@tapir.caltech.edu