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arXiv 0811.3638astro-ph
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Kelvin-Helmholtz不稳定性的三维相对论MHD模拟:湍流发电机对磁场的放大

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

Weiqun Zhang, Andrew MacFadyen, Peng Wang

摘要:

相对论外流(包括伽马射线暴(GRB)和活动星系核(AGN))的磁场强度比天真地预期的要大几个数量级。我们提出了三维相对论磁流体力学(MHD)模拟演示放大和饱和的磁场的宏观湍流发电机触发的开尔文-亥姆霍兹剪切不稳定性。我们发现,由于不稳定性的非线性发展导致的湍流速度场的场线的拉伸和折叠,电磁能量的快速增长。利用伽玛暴内震和余辉晚期的相关条件,我们得到了电磁能部分对$ε_B \sim 5 \times 10^{-3}$的放大。该值在剪切消散后缓慢衰减,并且似乎在很大程度上与初始场强无关。发电机运行所需的条件是存在速度剪切和一些种子磁化,这两者都是常见的。我们还发现,湍流动能频谱的情况下研究服从Kolmogorov的5/3定律,电磁能谱基本上是平坦的,在小尺度的电磁能量的大部分。

英文摘要:

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 $ε_B \sim 5 \times 10^{-3}$. 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.

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