paper

Three-Dimensional Relativistic MHD Simulations of the Kelvin-Helmholtz Instability: Magnetic Field Amplification by a Turbulent Dynamo

arXiv:0811.3638 · doi:10.1088/0004-637X/692/1/L40

Abstract

Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Using conditions relevant for GRB internal shocks and late phases of GRB afterglow, we obtain amplification of the electromagnetic energy fraction to . This value decays slowly after the shear is dissipated and appears to be largely independent of the initial field strength. The conditions required for operation of the dynamo are the presence of velocity shear and some seed magnetization both of which are expected to be commonplace. We also find that the turbulent kinetic energy spectrum for the case studied obeys Kolmogorov's 5/3 law and that the electromagnetic energy spectrum is essentially flat with the bulk of the electromagnetic energy at small scales.

arXiv commentaccepted for publication in ApJL; high-resolution version available at http://cosmo.nyu.edu/~wqzhang/publications/kh.pdf; movies of simulations available at http://cosmo.nyu.edu/~wqzhang/movies/

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