Theory of axisymmetric magnetohydrodynamic flows - Disks

Abstract

A general theory is developed for relativistic, steady, axisymmetric, ideal magnetohydrodynamic flows around a black hole or a rotating magnetized star. The theory leads to an autonomous second-order partial differential equation - a Grad-Shafranov equation - for the magnetic flux function psi(r,z). One limit of this equation gives the familiar Grad-Shafranov equation which describes the equilibrium of axisymmetric fusion plasmas. Another limit gives the equation describing general nonmagnetic flows of matter with angular momentum. A further limit gives the "pulsar equation" of Scharlemann, Wagoner, and Michel for relativistic plasma flows around an aligned, rotating, magnetized neutron star. Applications of the theory are made to thin, magnetized disks around a Schwarzschild black hole and around an aligned, rotating, magnetized star.