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Development of numerical scheme for equilibrium structures and their stability analysis of strongly magnetized rotating stars

强磁化旋转星平衡结构数值方案的开发及其稳定性分析

基本信息

批准号：
16540235
负责人：
ERIGUCHI Yoshiharu
金额：
$ 2.24万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540235/
关键词：
rotating stars magnetar equilibrium states poloidal magnetic fields toroidal magnetic fields stability 磁気回転星

项目摘要

In this investigation we have succeeded in developing a new formulation of structures of axisymmetric and stationary structures of strongly magnetized rotating stars and obtaining a new numerical code according to the formulation. By using the numerical code we have obtained many kinds of equilibrium configurations of magnetized rotating stars. We also have developed a new stability formulation and are now constructing a numerical code for the stability analysis.Concerning axisymmetric and stationary magnetized rotating stars, many researchers have studied them from 1950's. However, only equilibrium configurations obtained have been those for configurations with only poloidal magnetic fields by taking the strong fields into account. Nevertheless, configurations with poloidal fields only have been considered to be unstable. Thus it has been required to construct equilibrium configurations with both poloidal and toroidal magnetic fields. It is a crucial point to find an expression of the … More electric current density in order to develop a new numerical scheme for equilibrium configurations with poloidal and toroidal magnetic fields.In this investigation, we have found the general expression for the electric current density as follows :j=(κ+φ'v)H+φω+ρ(μ+Ω'v)e_φwhere j, H, ω, ρ and, e_φ are the current density, the magnetic field, the vorticity, the mass density, the unit vector in the rotational direction, respectively. Here, κ, φ, μ and Ω are arbitrary functions of the φ component of the vector potential.By using this expression, we have succeeded in obtaining (1) strongly magnetized and uniformly rotating stars, (2) strongly magnetized and differentially rotating stars and (3) strongly magnetized rotating stars with meridional circulations with both poloidal and toroidal magnetic fields. The most important result obtained from these equilibrium configurations is connected with the magnetic field distributions of general configurations for axisymmetric stationary states : i.e. twisted torus distributions of the magnetic fields are the most general configurations for the magnetic equilibrium stars. They consist of the dipole-like poloidal fields and the toroidal fields which spiral around geometrical tori around an axisymmetric axis. It should be stressed that this kind of twisted torus structures of the magnetic fields have been obtained by dynamical simulations by Brauithwaite and Spruit. Thus these twisted torus structures are considered to be stable and general distributions of the magnetic fields for stationary axisymmetric stars. Less

在这项研究中，我们成功地开发了强磁化旋转星的轴对称结构和静止结构的新公式，并根据该公式获得了新的数字代码。利用数值代码我们得到了磁化旋转星的多种平衡构型。我们还开发了一种新的稳定性公式，现在正在构建用于稳定性分析的数值代码。关于轴对称和静止磁化旋转星，许多研究人员从 1950 年代开始就对它们进行了研究。然而，仅获得的平衡构型是通过考虑强场而仅具有极向磁场的构型。然而，仅具有极向场的构型被认为是不稳定的。因此，需要构建具有极向和环形磁场的平衡配置。为了开发一种新的极向和环形磁场平衡构型的数值方案，找到电流密度的表达式是关键点。在本研究中，我们发现电流密度的一般表达式如下：j=(κ+φ'v)H+φω+ρ(μ+Ω'v)e_φ，其中 j、H、ω、ρ 和 e_φ 是电流分别为密度、磁场、涡度、质量密度、旋转方向的单位矢量。这里，κ、φ、μ和Ω是矢量势的φ分量的任意函数。通过使用这个表达式，我们成功地获得了（1）强磁化且均匀旋转的恒星，（2）强磁化且差动旋转的恒星和（3）具有极向和环形磁场的子午环流的强磁化旋转恒星。从这些平衡配置中获得的最重要的结果与轴对称静止状态的一般配置的磁场分布有关：即磁场的扭曲环面分布是磁平衡星的最一般配置。它们由类偶极子极向场和围绕轴对称轴围绕几何环面螺旋的环形场组成。需要强调的是，这种扭曲的磁场环面结构是由Brauithwaite和Spruit通过动力学模拟得到的。因此，这些扭曲的环面结构被认为是静止轴对称恒星磁场的稳定且普遍的分布。较少的