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- · arXiv e-print (arXiv:1011.6350)
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| Title: |
| Three-Dimensional Simulations of MHD Turbulence Behind Relativistic Shock Waves and Their Implications for GRBs |
| Authors: |
| Inoue, Tsuyoshi; Asano, Katsuaki; Ioka, Kunihito |
| Publication: |
| eprint arXiv:1011.6350 |
| Publication Date: |
| 11/2010 |
| Origin: |
| ARXIV |
| Keywords: |
| Astrophysics - High Energy Astrophysical Phenomena |
| Comment: |
| 13 pages, 12 figures. Submitted to ApJ |
| Bibliographic Code: |
| 2010arXiv1011.6350I |
Abstract
Relativistic astrophysical phenomena such as gamma-ray bursts (GRBs) and active galactic nuclei often require long-lived strong magnetic field that cannot be achieved by shock compression alone. Here, we report on three-dimensional special-relativistic magnetohydrodynamic (MHD) simulations that we performed using a second-order Godunov-type conservative code, to explore the amplification and decay of macroscopic turbulence dynamo excited by the so-called Richtmyer-Meshkov instability (RMI; a Rayleigh-Taylor type instability). This instability is an inevitable outcome of interactions between shock and ambient density fluctuations. We find that the magnetic energy grows exponentially in a few eddy turnover times, because of field-line stretching, and then, following the decay of kinetic turbulence, decays with a temporal power-law exponent of -0.7. The magnetic-energy fraction can reach $epsilon_B \sim$ 0.1 but depends on the initial magnetic field strength, which can diversify the observed phenomena. We find that the magnetic energy grows by at least two orders of magnitude compared to the magnetic energy immediately behind the shock. This minimum degree of the amplification does not depend on the amplitude of the initial density fluctuations, while the growth timescale and the maximum magnetic energy depend on the degree of inhomogeneity in the density. The transition from Kolmogorov cascade to MHD critical balance cascade occurs at $\sim$ 1/10th the initial inhomogeneity scale, which limits the maximum synchrotron polarization to less than 2%. New results include the avoidance of electron cooling with RMI turbulence, the turbulent photosphere model via RMI, the shallow decay of the early afterglow from RMI, and the impossibility of the relativistic turbulent model by Narayan & Kumar because of fast shock dissipation.
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