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Testing the true nature of black holes - the no-hair hypothesis - will becomeincreasingly more precise in the next few years as new observational data iscollected in both the gravitational wave channel and the electromagneticchannel. In this paper we consider numerically generated spacetimes of Kerrblack holes with synchronised scalar hair and build stationary models ofmagnetized thick disks (or tori) around them. Our approach assumes that thedisks are not self-gravitating, they obey a polytropic equation of state, thedistribution of their specific angular momentum is constant, and they aremarginally stable, i.e. the disks completely fill their Roche lobe. Moreover,contrary to existing approaches in the literature, our models arethermodinamically relativist, as the specific enthalpy of the fluid can adoptvalues significantly larger than unity. We study the dependence of themorphology and properties of the accretion tori on the type of black holeconsidered, from purely Kerr black holes with varying degrees of spinparameter, namely from a Schwarzschild black hole to a nearly extremal Kerrcase, to Kerr black holes with scalar hair with different ADM mass and horizonangular velocity. Comparisons between the disk properties for both types ofblack holes are presented. The sequences of magnetized, equilibrium disksmodels discussed in this study can be used as initial data for numericalrelativity codes to investigate their dynamical (non-linear) stability and usedin tandem with ray-tracing codes to obtain synthetic images of black holes(i.e. shadows) in astrophysically relevant situations where the light source isprovided by an emitting accretion disk.

Magnetized accretion disks around Kerr black holes with scalar hair - I. Constant angular momentum disks