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Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas

Lithwick, Yoram and Goldreich, Peter (2001) Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas. Astrophysical Journal, 562 (1). pp. 279-296. ISSN 0004-637X. doi:10.1086/323470.

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Radio wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible magnetohydrodynamic (MHD) turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows: 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. 2. Observed density fluctuation amplitudes constrain the nature of MHD turbulence in the interstellar medium. Slow mode density fluctuations are suppressed when the magnetic pressure is less than the gas pressure. Entropy mode density fluctuations are suppressed by cooling when the cascade timescale is longer than the cooling timescale. These constraints imply either that the magnetic and gas pressures are comparable or that the outer scale of the turbulence is very small. 3. A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small length scales. Regions that are insufficiently ionized produce density fluctuations only on length scales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. 4. Provided that the thermal pressure exceeds the magnetic pressure, both the entropy mode and the slow mode are damped on length scales 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 length scale is that transverse to the magnetic field. Thus, the cutoff length scale for density fluctuations is significantly smaller than the proton mean free path. 5. The Alfvén mode is critically damped at the transverse length scale of the proton gyroradius and thus cascades to smaller length scales than either the slow mode or the entropy mode.

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Additional Information:© 2001 The American Astronomical Society. Received 2001 June 21; accepted 2001 July 24. We thank Jason Maron for analyzing some of his simulations for us, for showing us how to use his numerical code, and for informative discussions. We thank the referee, Ben Chandran, for a very helpful report. Research reported in this paper was supported by NSF grant 94-14232.
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Subject Keywords:ISM: kinematics and dynamics - MHD - turbulence
Issue or Number:1
Record Number:CaltechAUTHORS:20130225-113105156
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Official Citation:Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas Yoram Lithwick and Peter Goldreich 2001 ApJ 562 279
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37114
Deposited By: Tony Diaz
Deposited On:25 Feb 2013 21:18
Last Modified:09 Nov 2021 23:26

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