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Astrophysical Hydromagnetic Turbulence

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Abstract

Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich–Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.

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Notes

  1. The Reynolds number \(\mathit{Re}\equiv L_{\mathrm{f}}V/\nu=(V/L_{\mathrm{f}})/(\nu/L^{2}_{\mathrm{f}})\) characterizes the ratio of the eddy turnover rate \(\tau^{-1}_{\mathrm{eddy}}=V/L_{\mathrm{f}}\) and the viscous dissipation rate \(\tau_{\mathrm{dis}}^{-1}=\eta/L^{2}_{\mathrm{f}}\). Therefore large values of Re correspond to negligible viscous dissipation of large eddies over the cascading time τ casc which is equal to τ eddy in Kolmogorov turbulence.

  2. The arguments in Eyink et al. (2011) should be distinguished from the arguments based on attempted renormalization of the effective magnetic Reynolds numbers in Blackman and Field (2008). Eyink et al. (2011) do not introduce artificial “turbulent diffusivities” but appeal to the established and tested concept of Richardson diffusion.

  3. For the single-scale model, L RR∼30L and the diffusion over distance Δ takes L RR/Lss steps, i.e. Δ2∼L RR L, which decreases the corresponding diffusion coefficient \(\kappa_{e,{\rm single}}\sim\Delta^{2}/\delta t\) by a factor 30.

  4. The resonant scattering is happening on the magnetic scales of the order of the cosmic ray gyroradius. If the Alfvénic eddies are strongly elongated, the particles interacts with many eddies within its radius and the scattering effect is dramatically reduced. Scattering efficiency and the acceleration efficiencies are closely related for the second order Fermi acceleration of cosmic rays by turbulence (see Schlickeiser 2002).

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Acknowledgements

We thank Andre Balogh for providing an inspiring atmosphere at the International Space Science Institute in Bern in 2012, which has led to new collaborations and scientific progress. Computing resources were provided by the Swedish National Allocations Committee at the Center for Parallel Computers at the Royal Institute of Technology in Stockholm and the High Performance Computing Center North in Umeå. This work was supported in part by the European Research Council under the AstroDyn Research Project No. 227952 and the Swedish Research Council under the project grants 621-2011-5076 and 2012-5797. A.L. acknowledges the support of the NSF grant AST-1212096, the NASA grant NNX09AH78G, the Vilas Associate Award as well as the support of the NSF Center for Magnetic Self-Organization. In addition, A.L. thanks the International Institute of Physics (Natal, Brazil) for its hospitality during the work on this review.

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  1. Nordita, KTH Royal Institute of Technology, Stockholm University, Roslagstullsbacken 23, 10691, Stockholm, Sweden

    A. Brandenburg

  2. Department of Astronomy, Stockholm University, 10691, Stockholm, Sweden

    A. Brandenburg

  3. Department of Astronomy, University of Wisconsin-Madison, 475 N. Charter St., Madison, WI, 53706, USA

    A. Lazarian

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Brandenburg, A., Lazarian, A. Astrophysical Hydromagnetic Turbulence. Space Sci Rev 178, 163–200 (2013). https://doi.org/10.1007/s11214-013-0009-3

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