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Theory and Applications of Non-relativistic and Relativistic Turbulent Reconnection

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Magnetic Reconnection

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 427))

Abstract

Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers of the flows. Therefore, the theories intended for describing astrophysical reconnection should not ignore the effects of turbulence. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also the outflows from magnetic reconnection induce turbulence affecting the rate of turbulent reconnection. Thus turbulence must be accounted for any realistic astrophysical reconnection set up. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources and gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach. We also argue that the tearing reconnection transfers to fully turbulent reconnection in 3D astrophysically relevant settings with realistically high Reynolds numbers.

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Notes

  1. 1.

    In addition, the mean free path of particles can also be constrained by the instabilities developed on the collisionless scales of plasma (see Schekochihin et al. 2009; Lazarian and Beresnyak 2006; Brunetti and Lazarian 2011), while ensures that compressible motions can also survive collisionless damping.

  2. 2.

    Thus, weak turbulence has a limited, i.e. [L i , L i M A 2] inertial range and at small scales it transits into the regime of strong turbulence. We should stress that weak and strong are not the characteristics of the amplitude of turbulent perturbations, but the strength of non-linear interactions (see more discussion in Cho et al. 2003) and small scale Alfvénic perturbations can correspond to a strong Alfvénic cascade.

  3. 3.

    One can obtain the force-free condition from Maxwell’s equations and the energy-momentum equation: \(\partial _{\mu }T_{( f)}^{\nu \mu } = -F_{\nu \mu }J^{\mu } = 0\). Here, F ν μ is the electromagnetic field tensor.

  4. 4.

    The basic idea of the model was first discussed by Sweet and the corresponding paper by Parker refers to the model as “Sweet model”.

  5. 5.

    The magnetic field wandering was discussed for an extended period to explain the diffusion of cosmic rays perpendicular to the mean magnetic field, but, as was shown in Lazarian and Yan (2014), those attempts employed scalings that were erroneous even for the hypothetical Kolmogorov turbulence of magnetic fields, for which they were developed.

  6. 6.

    Incidentally, this can explain the formation of density fluctuations on scales of thousands of AU, that are observed in the ISM.

  7. 7.

    Thus we can expect that the theory of imbalanced relativistic MHD can be also very similar to Beresnyak and Lazarian (2008) model.

  8. 8.

    This may indicates a relation similar to one predicted by Galtier and Banerjee (2011), i.e. that the compressible component is proportional to B 0 2, exists even in relativistic MHD turbulence.

  9. 9.

    Although collisionless reconnection can also provide fast reconnection rate around 0. 3c, it is still unclear if the collisionless reconnection rate can be applied to the MHD scale.

  10. 10.

    We note that this process will also occur in pure turbulent environments, i.e., without the presence of large scale magnetic discontinuities formed by coherent flux tubes of opposite polarity, but in such cases, the absence of the large scale converging flux tubes will also allow for catch-up collisions, where particles lose energy to the magnetic fluctuations rather than gaining. In such a case, the process is more like a second-order Fermi acceleration (Kowal et al. 2012).

  11. 11.

    It was shown in Lazarian and Yan (2014) that the mathematical formulation of the field wandering is an error in the classical papers, but this does not diminish the importance of the idea. In fact, the diffusion perpendicular to magnetic field by charged particles that follow magnetic field lines was an important impetus for one of the authors towards the idea of turbulent reconnection.

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Acknowledgements

AL acknowledges the NSF grant AST 1212096, a distinguished visitor PVE/CAPES appointment at the Physics Graduate Program of the Federal University of Rio Grande do Norte and thanks the INCT INEspao and Physics Graduate Program/UFRN for hospitality. Final work on the review were done in a stimulating atmosphere of Bochum University during the visit supported by the Humboldt Foundation. GK acknowledges support from FAPESP (grants no. 2013/04073-2 and 2013/18815-0). EMGDP: Brazilian agencies FAPESP (2013/10559-5) and CNPq (306598/2009-4). JC acknowledges support from the National Research Foundation of Korea (NRF-2013R1A1A2064475).

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Authors and Affiliations

  1. Department of Astronomy, University of Wisconsin, Madison, WI, USA

    A. Lazarian

  2. Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, São Paulo, SP, Brazil

    G. Kowal

  3. Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

    M. Takamoto

  4. Instituto de Astronomia, Geofísica e Ciencias Atmosfericas, Universidade de Sao Paulo, São Paulo, SP, Brazil

    E. M. de Gouveia Dal Pino

  5. Department of Astronomy and Space Science, Chungnam National University, Daejeon, Korea

    J. Cho

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  1. A. Lazarian
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  2. G. Kowal
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  3. M. Takamoto
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  4. E. M. de Gouveia Dal Pino
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  5. J. Cho
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Correspondence to A. Lazarian .

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Editors and Affiliations

  1. INPE, São José dos Campos, Brazil

    Walter Gonzalez

  2. University of Chicago, CHICAGO, Illinois, USA

    Eugene Parker

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Lazarian, A., Kowal, G., Takamoto, M., de Gouveia Dal Pino, E.M., Cho, J. (2016). Theory and Applications of Non-relativistic and Relativistic Turbulent Reconnection. In: Gonzalez, W., Parker, E. (eds) Magnetic Reconnection. Astrophysics and Space Science Library, vol 427. Springer, Cham. https://doi.org/10.1007/978-3-319-26432-5_11

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