Magnetized tori with magnetic polarization around Kerr black holes: Variable angular momentum discs

Analytical models of magnetized, geometrically thick disks are relevant to understand the physical conditions of plasma around compact objects and to explore its emitting properties. This has become increasingly important in recent years in the light of the Event Horizon Telescope observations of Sgr A$^*$ and M87. Models of thick disks around black holes usually consider constant angular momentum distributions and do not take into account the magnetic response of the fluid to applied magnetic fields. We present a generalization of our previous work on stationary models of magnetized accretion disks with magnetic polarization (Pimentel et al. 2018). This extension is achieved by accounting for non-constant specific angular momentum profiles, done through a two-parameter ansatz for those distributions. We build a large number of new equilibrium solutions of thick disks with magnetic polarization around Kerr black holes, selecting suitable parameter values within the intrinsically substantial parameter space of the models. We study the morphology and the physical properties of those solutions, finding qualitative changes with respect to the constant angular momentum tori solutions (Pimentel et al. 2018). However, the dependences found on the angular momentum distribution or on the black hole spin do not seem to be strong. Some of the new solutions, however, exhibit a local maximum of the magnetization function, absent in standard magnetized tori. Due to the enhanced development of the magneto-rotational instability as a result of magnetic susceptibility, those models might be particularly well-suited to investigate jet formation through general-relativistic MHD simulations. The new equilibrium solutions reported here can be used as initial data in numerical codes to assess the impact of magnetic susceptibility in the dynamics and observational properties of black hole-thick disk systems.