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Magnetic field fluctuations in anisotropic, supersonic turbulence
Monthly Notices of the Royal Astronomical Society ( IF 4.8 ) Pub Date : 2020-08-06 , DOI: 10.1093/mnras/staa2257
James R Beattie 1 , Christoph Federrath 1 , Amit Seta 1
Affiliation  

The rich structure that we observe in molecular clouds is due to the interplay between strong magnetic fields and supersonic (turbulent) velocity fluctuations. The velocity fluctuations interact with the magnetic field, causing it too to fluctuate. Using numerical simulations, we explore the nature of such magnetic field fluctuations, $\vec{\delta B}$, over a wide range of turbulent Mach numbers, $\mathcal{M} = 2 - 20$ (i.e., from weak to strong compressibility), and Alfven Mach numbers, $\mathcal{M}_{\text{A}0} = 0.1 - 100$ (i.e., from strong to weak magnetic mean fields, $B_0$). We derive a compressible quasi-static fluctuation model from the magnetohydrodynamical (MHD) equations and show that velocity gradients parallel to the mean magnetic field give rise to compressible modes in sub-Alfvenic flows, which prevents the flow from becoming two-dimensional, as is the case in incompressible MHD turbulence. We then generalise an analytical model for the magnitude of the magnetic fluctuations to include $\mathcal{M}$, and find $|\vec{\delta B}| = \delta B = c_s\sqrt{\pi\rho_0}\mathcal{M}\mathcal{M}_{\text{A}0}$, where $c_s$ is the sound speed and $\rho_0$ is the mean density of gas. This new relation fits well in the strong $B$-field regime. We go on to study the anisotropy between the perpendicular ($ B_{\perp}$) and parallel ($ B_{\parallel}$) fluctuations and the mean-normalised fluctuations, which we find follow universal scaling relations, invariant of $\mathcal{M}$. We provide a detailed analysis of the morphology for the $\delta B_{\perp}$ and $\delta B_{\parallel}$ probability density functions and find that eddies aligned with $B_0$ cause parallel fluctuations that reduce $B_{\parallel}$ in the most anisotropic simulations. We discuss broadly the implications of our fluctuation models for magnetised gases in the interstellar medium.

中文翻译:

各向异性、超音速湍流中的磁场波动

我们在分子云中观察到的丰富结构是由于强磁场和超音速(湍流)速度波动之间的相互作用。速度波动与磁场相互作用,导致磁场也发生波动。使用数值模拟,我们探索了这种磁场波动的性质,$\vec{\delta B}$,在大范围的湍流马赫数 $\mathcal{M} = 2 - 20$(即,从弱到强压缩性)和阿尔文马赫数,$\mathcal{M}_{\text{A}0} = 0.1 - 100$(即,从强磁场到弱磁场,$B_0$)。我们从磁流体动力学 (MHD) 方程中推导出可压缩的准静态波动模型,并表明平行于平均磁场的速度梯度会在亚阿尔芬尼流中产生可压缩模式,这可以防止流动变成二维的,就像不可压缩的 MHD 湍流一样。然后我们将磁涨落幅度的分析模型推广到包括 $\mathcal{M}$,并找到 $|\vec{\delta B}| = \delta B = c_s\sqrt{\pi\rho_0}\mathcal{M}\mathcal{M}_{\text{A}0}$,其中 $c_s$ 是声速,$\rho_0$ 是声速气体的平均密度。这种新关系非常适合强大的 $B$ 领域制度。我们继续研究垂直($ B_{\perp}$)和平行($ B_{\parallel}$)波动和均值归一化波动之间的各向异性,我们发现它们遵循通用标度关系,$\数学{M}$。我们对 $\delta B_{\perp}$ 和 $\delta B_{\parallel}$ 概率密度函数的形态进行了详细分析,发现与 $B_0$ 对齐的涡流会导致平行波动,从而减少 $B_{\在最各向异性的模拟中并行}$。我们广泛讨论了我们的波动模型对星际介质中磁化气体的影响。
更新日期:2020-08-06
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