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
Οmβ. 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 Οmβ, we find that the paramagnetic tori (Οmβ>0) are
more dense and less magnetized than the diamagnetic ones (Οmβ<0) in the
region between the inner edge, rinβ, and the center of the disk, rcβ;
however, we find the opposite behavior for r>rcβ. Now, in the models with
non-constant Οmβ, the tori become more magnetized than the Komissarov
solution in the region where βΟmβ/βr<0, and less
magnetized when βΟmβ/βr>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.Comment: 7 pages, 15 .pdf figures, 1 table, Accepted for publication in
Astronomy & Astrophysics (A&A