通过核塌缩超新星中的寄生不稳定性终止磁旋转不稳定性
Termination of the magnetorotational instability via parasitic instabilities in core-collapse supernovae
摘要：
磁旋转不稳定性（MRI）可以是一个强大的机制放大的磁场在核心坍缩超新星。最初的弱磁场是否可以被这种不稳定性放大到动态相关的强度仍然是一个争论的问题。主要的不确定性之一涉及终止不稳定性增长的过程。Kelvin-Helmholtz和撕裂模式类型的寄生不稳定性被认为在此过程中起着至关重要的作用，破坏了MRI通道流并淬灭了磁场放大。我们进行了二维和三维剪切盘模拟的差分旋转质子中子星层在非理想磁流体力学前所未有的高数值精度，发现开尔文-亥姆霍兹寄生模式占主导地位的撕裂模式在大的流体动力学和磁雷诺数的制度，遇到接近表面的质子中子星。它们还确定了MRI指数增长期间可达到的最大磁场应力。我们的结果是一致的寄生不稳定性理论的基础上的局部稳定性分析。为了正确地模拟Kelvin-Helmholtz不稳定性，需要非常高的数值分辨率。使用九阶空间重建方案，我们发现，每个MRI通道至少有8个网格区域是必要的，以模拟MRI的生长阶段，并达到约10%的增长率的准确性，而超过60个区域，每个通道需要实现收敛的结果在MRI终止的磁应力值。
英文摘要：
The magnetorotational instability (MRI) can be a powerful mechanism amplifying the magnetic field in core-collapse supernovae. Whether initially weak magnetic fields can be amplified by this instability to dynamically relevant strengths is still a matter of debate. One of the main uncertainties concerns the process that terminates the growth of the instability. Parasitic instabilities of both Kelvin-Helmholtz and tearing-mode type have been suggested to play a crucial role in this process, disrupting MRI channel flows and quenching magnetic field amplification. We perform two-dimensional and three-dimensional sheering-disc simulations of a differentially rotating protoneutron star layer in non-ideal magnetohydrodynamics with unprecedented high numerical accuracy, finding that Kelvin-Helmholtz parasitic modes dominate tearing modes in the regime of large hydrodynamic and magnetic Reynolds numbers, as encountered close to the surface of protoneutron stars. They also determine the maximum magnetic field stress achievable during the exponential growth of the MRI. Our results are consistent with the theory of parasitic instabilities based on a local stability analysis. To simulate the Kelvin-Helmholtz instabilities properly, a very high numerical resolution is necessary. Using ninth-order spatial reconstruction schemes, we find that at least eight grid zones per MRI channel are necessary to simulate the growth phase of the MRI and reach an accuracy of ~10 per cent in the growth rate, while more than ~60 zones per channel are required to achieve convergent results for the value of the magnetic stress at MRI termination.
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