Differential rotation of a nonspherical polytropic star

A. A. Bobnev

Abstract
A single parameter family of solutions 0f MHD equations for an ideal and perfectly conducting gas has been constructed. Here, the ratio between the inertia forces and the hydrodynamic pressure forces is small and the ϕ - component of H is absent with r,Θ,ϕ being the spherical coordinates. The solution satisfying the principle of minimum integral electromagnetic energy (in our case, we neglected the electric energe as compared with the magnetic one) was chosen from the infinite set of all the solutions. Using this approach, the magnetic field of the star was shown to be solely defined by the characteristic parameter of differential rotation, while the perturbed radius of the star surface depends on the characteristic angular velocity, too. A polynomial dependence of the star surface angular velocity squared and the perturbed radius of the star surface on sin²Θ has been established. Figs 5, refs 5.