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

在这项研究中，我们成功地发展了一个新的公式的结构的轴对称和固定结构的强磁化旋转的恒星，并获得了一个新的数字代码根据该公式。用该程序计算了磁化旋转星的多种平衡位形。我们还发展了一个新的稳定性公式，目前正在编制一个数值程序用于稳定性分析。关于轴对称和静止磁化旋转星，从20世纪50年代开始，许多研究者已经开始研究它们。然而，只有平衡配置已被那些配置只有极向磁场考虑到强场。然而，只有极向场的位形被认为是不稳定的。因此，它已被要求建立平衡配置与极向和环向磁场。关键是要找到 ...更多信息 为了发展一种新的计算极向和环向磁场平衡位形的数值格式，我们找到了电流密度的一般表达式：j=（κ+ κ 'v）H+φω+ρ（μ+ κ' v）e_φ其中j，H，ω，ρ，e_φ分别为电流密度，磁场，涡度，质量密度，转动方向的单位矢量。这里，κ，φ，μ和Ω是矢势φ分量的任意函数，利用这个表达式，我们成功地得到了（1）强磁化均匀自转星，（2）强磁化差自转星和（3）强磁化旋光星，它们都具有极向和环向磁场。从这些平衡位形得到的最重要的结果与轴对称定态的一般位形的磁场分布有关：即磁场的扭曲环面分布是磁平衡星的最一般位形。它们由类偶极向场和围绕轴对称轴的几何环面螺旋的环面场组成。应该强调的是，这种扭曲的环面结构的磁场已经获得了动力学模拟Brauithwaite和Spruit。因此，这些扭曲的环面结构被认为是稳定的和一般的磁场分布的轴对称恒星。少

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