Stationary models of magnetized viscous tori around a Schwarzschild black hole

TL;DR

This paper develops stationary models of magnetized, viscous thick accretion disks around Schwarzschild black holes, highlighting how viscosity and curvature influence disk structure and stability near the black hole horizon.

Contribution

It introduces a relativistic hydrodynamics framework for modeling viscous, magnetized tori around black holes, emphasizing the effects of curvature and viscosity on disk morphology.

Findings

Viscosity and curvature effects are prominent near the disk cusp.

The cusp shifts inward with increased viscosity and curvature effects.

Magnetization reduces the inward shift of the cusp.

Abstract

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 second-order transport coefficients of the theory. Our results reveal that the effects of the shear viscosity and curvature are 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 isocontour - the cusp - moves to smaller radii (i.e. towards the black hole horizon) as the effects become more significant. For highly magnetized disks the shift in the cusp location is smaller. Our findings might have implications on the dynamical stability of constant angular momentum tori which, in the inviscid case, are affected by the runaway instability.