吸积盘星磁层顶的开尔文-亥姆霍兹不稳定性
Kelvin-Helmholtz Instability of the Magnetopause of Disc-Accreting Stars
摘要：
本文研究了一个快速旋转的、超音速的、致密的吸积盘和一个缓慢旋转的低密度磁化星磁层之间的磁层顶的短波长稳定性。磁层顶是一个强烈的剪切层，在短径向距离内，方位角速度、密度和磁场都有快速变化，因此Kelvin-Helmholtz（KH）不稳定性可能是重要的。等离子体动力学处理使用非相对论，可压缩（等熵）磁流体力学。为了使等离子体波的速度保持小于光速，必须包括位移电流。我们主要关注的情况下，一个明星的偶极子磁场对齐，使磁场是轴向的磁盘中面和垂直的磁盘流速。然而，我们也给出了结果的情况下，磁场是在一个任意角度的流速。在排列偶极子情况下，当KH波沿垂直于磁场的方位角方向传播时，磁层顶最不稳定，而磁场则倾向于稳定平行于它传播的波，波的相速度是圆盘物质的相速度。不稳定性饱和的准线性理论导致磁层顶密度和温度起伏的波数（$k$）功率谱$\propto k^{-1}$，它给出了穿过磁层顶的质量吸积和角动量流入率。在自洽条件下，这个质量吸积率将等于离磁层顶很远的圆盘吸积率。
英文摘要：
This work investigates the short wavelength stability of the magnetopause between a rapidly-rotating, supersonic, dense accretion disc and a slowly-rotating low-density magnetosphere of a magnetized star. The magnetopause is a strong shear layer with rapid changes in the azimuthal velocity, the density, and the magnetic field over a short radial distance and thus the Kelvin-Helmholtz (KH) instability may be important. The plasma dynamics is treated using non-relativistic, compressible (isentropic) magnetohydrodynamics. It is necessary to include the displacement current in order that plasma wave velocities remain less than the speed of light. We focus mainly on the case of a star with an aligned dipole magnetic field so that the magnetic field is axial in the disc midplane and perpendicular to the disc flow velocity. However, we also give results for cases where the magnetic field is at an arbitrary angle to the flow velocity. For the aligned dipole case the magnetopause is most unstable for KH waves propagating in the azimuthal direction perpendicular to the magnetic field which tends to stabilize waves propagating parallel to it. The wave phase velocity is that of the disc matter. A quasi-linear theory of the saturation of the instability leads to a wavenumber ($k$) power spectrum $\propto k^{-1}$ of the density and temperature fluctuations of the magnetopause, and it gives the mass accretion and angular momentum inflow rates across the magnetopause. For self-consistent conditions this mass accretion rate will be equal to the disc accretion rate at large distances from the magnetopause.
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