Analytic solution of a magnetized tori with magnetic polarization around Kerr black holes

Abstract

We present the first family of magnetically polarized equilibrium tori around a Kerr black hole. The models were obtained in the test fluid approximation by assuming that the tori is a linear media, making it is possible to characterize the magnetic polarization of the fluid through the magnetic susceptibility χm. The magnetohydrodynamic (MHD) structure of the models was solved by following the Komissarov approach, but with the aim of including the magnetic polarization of the fluid, the integrability condition for the magnetic counterpart was modified. We build two kinds of magnetized tori depending on whether the magnetic susceptibility is constant in space or not. In the models with constant χm, we find that the paramagnetic tori ( χm > 0) are more dense and less magnetized than the diamagnetic ones ( χm < 0) in the region between the inner edge, rin, and the center of the disk, rc; however, we find the opposite behavior for r > rc. Now, in the models with non-constant χm, the tori become more magnetized than the Komissarov solution in the region where ∂χm/∂r < 0, and less magnetized when ∂χm/∂r > 0. Nevertheless, it is worth mentioning that in all solutions presented in this paper the magnetic pressure is greater than the hydrodynamic pressure. These new equilibrium tori can be useful for studying the accretion of a magnetic media onto a rotating black hole.