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arXiv 0812.1541astro-ph
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极向和环向混合磁场中薄Keplerian圆盘的Hall平衡

Hall equilibrium of thin Keplerian disks embedded in mixed poloidal and toroidal magnetic fields

Yuri M. Shtemler, Michael Mond, Gunther Rudiger

摘要:

本文用渐近展开法研究了轴对称稳态弱电离Hall-MHD Keplerian薄圆盘的小圆盘长宽比ε。该模型在ε中的主导阶中包含了磁场的方位角分量和极向分量。磁盘结构是由一个适当的梯度-Shafranov方程的极向通量函数,其中涉及两个任意函数的环向和极向电流的极向通量函数。通量函数关于中平面是对称的,并且在接近水平的圆盘边缘处满足一定的边界条件。边界条件模拟了原始磁场和类偶极磁场的组合效应。通过将相关方程进一步扩展为与霍尔参数成反比的附加小参数δ,获得了霍尔平衡的解析解。结果表明,霍尔平衡盘可分为两类:一类是小半径(Rd ~δ^0)的开普勒盘,另一类是大半径(Rd > δ^k,k > 0)的开普勒盘.所提出的数值例子表明,丰富和各种各样的磁和密度配置,可以实现霍尔MHD平衡下。

英文摘要:

Axisymmetric steady-state weakly ionized Hall-MHD Keplerian thin disks are investigated by using asymptotic expansions in the small disk aspect ratio ε. The model incorporates the azimuthal and poloidal components of the magnetic fields in the leading order in ε. The disk structure is described by an appropriate Grad-Shafranov equation for the poloidal flux function ψthat involves two arbitrary functions of ψfor the toroidal and poloidal currents. The flux function is symmetric about the midplane and satisfies certain boundary conditions at the near-horizontal disk edges. The boundary conditions model the combined effect of the primordial as well as the dipole-like magnetic fields. An analytical solution for the Hall equilibrium is achieved by further expanding the relevant equations in an additional small parameter δthat is inversely proportional to the Hall parameter. It is thus found that the Hall equilibrium disks fall into two types: Keplerian disks with (i) small (Rd ~δ^0) and (ii) large (Rd > δ^k, k > 0) radius of the disk. The numerical examples that are presented demonstrate the richness and great variety of magnetic and density configurations that may be achieved under the Hall-MHD equilibrium.

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