层流磁转流对太阳内部磁场的极约束
Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow
摘要：
只有在所有纬度（包括极冠）的对流区以下，才能有效地解释太阳观测到的差异自转所需的全球尺度内部磁场。轴对称非线性MHD解表明，这种约束可以由每一极上的非常弱的下降流U~10^{-5}cm/s引起。这种下降流与日震证据相一致。所有三个组成部分的磁场衰减指数与高度在一个薄的“磁约束层”位于底部的速跃层。在现实的参数值下，限制层的厚度约为太阳半径的10^{-3}。除了斜压效应和稳定的热分层，解决方案考虑到稳定的成分分层的氦沉降层，如果目前在今天的太阳，和小扩散率的氦通过氢，chi。相对于磁扩散率的小值chi产生双边界层结构，其中较小垂直尺度的“氦子层”夹在氦沉降层的顶部和限制层的其余部分之间。使用半解析和纯数值，有限差分技术的解决方案。约束层流动是磁旋的极好的近似。更确切地说，主要的力平衡是在洛伦兹力、科里奥利力、压力梯度力和浮力之间，相对加速度和粘性力可以忽略不计。这是尽管运动粘度略大于卡。我们将讨论如何限制层在每个极点可能适合到一个全球性的动态图片的太阳速跃层。这张照片，反过来，提出了一个新的见解，早期的太阳和太阳锂耗尽的长期之谜。
英文摘要：
The global-scale interior magnetic field needed to account for the Sun's observed differential rotation can be effective only if confined below the convection zone in all latitudes, including the polar caps. Axisymmetric nonlinear MHD solutions are obtained showing that such confinement can be brought about by a very weak downwelling flow U~10^{-5}cm/s over each pole. Such downwelling is consistent with the helioseismic evidence. All three components of the magnetic field decay exponentially with altitude across a thin "magnetic confinement layer" located at the bottom of the tachocline. With realistic parameter values, the thickness of the confinement layer ~10^{-3} of the Sun's radius. Alongside baroclinic effects and stable thermal stratification, the solutions take into account the stable compositional stratification of the helium settling layer, if present as in today's Sun, and the small diffusivity of helium through hydrogen, chi. The small value of chi relative to magnetic diffusivity produces a double boundary-layer structure in which a "helium sublayer" of smaller vertical scale is sandwiched between the top of the helium settling layer and the rest of the confinement layer. Solutions are obtained using both semi-analytical and purely numerical, finite-difference techniques. The confinement-layer flows are magnetostrophic to excellent approximation. More precisely, the principal force balances are between Lorentz, Coriolis, pressure-gradient and buoyancy forces, with relative accelerations and viscous forces negligible. This is despite the kinematic viscosity being somewhat greater than chi. We discuss how the confinement layers at each pole might fit into a global dynamical picture of the solar tachocline. That picture, in turn, suggests a new insight into the early Sun and into the longstanding enigma of solar lithium depletion.
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