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

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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