Stationary models of magnetized viscous tori around a Schwarzschild black hole

We present stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole. We assume that the tori are not self-gravitating, are endowed with a toroidal magnetic field and obey a constant angular momentum law. Our study focuses on the role of the black hole curvature in the shear viscosity tensor and in their potential combined effect on the stationary solutions. Those are built in the framework of a causality-preserving, second-order gradient expansion scheme of relativistic hydrodynamics in the Eckart frame description which gives rise to hyperbolic equations of motion. The stationary models are constructed by numerically solving the general relativistic momentum conservation equation using the method of characteristics. We place constraints in the range of validity of the secondorder transport coefficients of the theory. Our results reveal that the effects of the shear viscosity and curvature arc particularly noticeable only close to the cusp of the disks. The surfaces of constant pressure are affected by viscosity and curvature and the self-intersecting iscocontour-the cusp-moves to smaller radii (i.e., toward the black hole horizon) as the effects become more significant. For highly magnetized disks the shift in the cusp location is smaller. Our fmdings might have implications for the dynamical stability of constant angular momentum tori which, in the inviscid case, arc affected by the runaway instability.

Automated summary

This study explores stationary solutions of magnetized, viscous thick accretion disks around a Schwarzschild black hole, focusing on the role of black hole curvature in the shear viscosity tensor and their combined effect on the solutions. The effects of shear viscosity and curvature are particularly noticeable near the cusps of the disks, with less significant shifts in cusp locations for highly magnetized disks. This research may have implications for dynamical stability of constant angular momentum tori, especially in the context of runaway instability in inviscid cases.