Three-dimensional solutions of the magnetohydrostatic equations: Rigidly rotating magnetized coronae in spherical geometry
Three-dimensional solutions of the magnetohydrostatic equations: Rigidly rotating magnetized coronae in spherical geometry
复制标题
磁流体静力学方程的三维解：球形几何中刚性旋转的磁化日冕
DOI：
10.1051/0004-6361/201014887
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发表时间：
2010
影响因子：
6.5
通讯作者：
Al-Salti N
中科院分区：
文献类型：
--
作者：
Al-Salti N
磁流体静力学（MHS）平衡常用于模拟天体物理等离子体，例如行星磁层或磁化恒星的日冕。然而，找到现实的三维解决方案的MHS方程是困难的，只有少数已知的解析解，甚至找到数值解是远远不容易的AimsWe扩展的结果，以前的文件上的三维解决方案的MHS方程周围刚性旋转的大规模的圆柱体的刚性旋转的大规模的领域更现实的情况下。一个明显的应用是模型的快速旋转的stars.MethodsWe使用了一些简化的假设，以减少MHS方程到一个单一的椭圆形偏微分方程的pseudo-potentialU，从所有的物理量，如磁场，等离子体的压力和密度，可以推导出微分的冠状面的封闭场线区域。最重要的假设是平稳的共同旋转的参考框架，一种特殊形式的电流密度，并忽略outflows.ResultsIn本文中，我们证明了标准的方法可以用来找到数值解的基本方程的理论。我们提出了三个简单的不同情况下的中心球的表面上的磁场边界条件，对应于一个对齐的偶极场，一个非对齐的偶极场，和一个位移偶极场。我们的研究结果表明，它应该有可能在未来使用这种方法，而不会显着增加对计算资源的需求，以改善旋转磁层和日冕的位场模型。
ContextMagnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy.AimsWe extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars.MethodsWe used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potentialU, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows.ResultsIn this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.