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arXiv 1707.09419astro-ph.HEgr-qc
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r模不稳定性对磁场放大的限制

Limits on Magnetic Field Amplification from the r-Mode Instability

John L. Friedman, Lee Lindblom, Luciano Rezzolla, Andrey I. Chugunov

摘要:

在微扰论的二阶条件下,旋转恒星的不稳定r模包括增长的微分旋转,其形式和增长率由引力辐射反应决定。在没有磁场的情况下,流体单元的角速度呈指数增长,直到模式达到其非线性饱和振幅并且在饱和之后保持非零。在背景磁场的情况下,差分旋转卷起并放大场,并且考虑大模式振幅的先前工作表明放大可能抑制不稳定性。然而,背景磁场将与增加微分旋转相对应的饱和的与时间无关的扰动转变为特征频率为阿尔文频率的扰动。如在先前的研究中所发现的,我们认为磁场的增长是急剧限制的饱和振幅的不稳定模式。然而,与以前的工作相比,我们表明,如果振幅很小,即,10^(-4)量级,那么磁场增长的极限就足够严格,足以防止能量损失到磁场中,从而阻尼或显著改变具有正常内部的新生中子星和内部为II型超导体的冷星中的不稳定r模。我们首先展示了一个玩具模型的结果,然后我们使用一个更真实的旋转中子星模型获得了类似的磁场增长上限。我们的分析依赖于假设,有没有边际不稳定的扰动,这可能不成立时,差分旋转导致磁旋转不稳定。

英文摘要:

At second order in perturbation theory, the unstable r-mode of a rotating star includes growing differential rotation whose form and growth rate are determined by gravitational-radiation reaction. With no magnetic field, the angular velocity of a fluid element grows exponentially until the mode reaches its nonlinear saturation amplitude and remains nonzero after saturation. With a background magnetic field, the differential rotation winds up and amplifies the field, and previous work where large mode amplitudes were considered suggests that the amplification may damp out the instability. A background magnetic field, however, turns the saturated time-independent perturbations corresponding to adding differential rotation into perturbations whose characteristic frequencies are of order the Alfvén frequency. As found in previous studies, we argue that magnetic- field growth is sharply limited by the saturation amplitude of an unstable mode. In contrast to previous work, however, we show that if the amplitude is small, i.e., of order 10^(-4), then the limit on the magnetic-field growth is stringent enough to prevent the loss of energy to the magnetic field from damping or significantly altering an unstable r-mode in nascent neutron stars with normal interiors and in cold stars whose interiors are type II superconductors. We show this result first for a toy model, and we then obtain an analogous upper limit on magnetic field growth using a more realistic model of a rotating neutron star. Our analysis depends on the assumption that there are no marginally unstable perturbations, and this may not hold when differential rotation leads to a magnetorotational instability.

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