Viscous Driving of Global Oscillations in Accretion Discs Around Black Holes

TL;DR

This study investigates how viscosity influences the excitation of global oscillation modes in accretion discs around black holes through hydrodynamic simulations, revealing mode types, excitation mechanisms, and effects of viscosity on mode stability.

Contribution

It provides new insights into the role of viscosity in exciting and suppressing oscillation modes in black hole accretion discs, including the effects of different boundary conditions and viscosity scaling.

Findings

Viscosity excites various global oscillation modes, including axisymmetric, non-axisymmetric, and hybrid modes.

Small viscosity favors non-axisymmetric modes, while large viscosity favors axisymmetric modes.

Viscosity can suppress or enhance trapped p-modes depending on the viscosity's dependence on surface density.

Abstract

We examine the role played by viscosity in the excitation of global oscillation modes (both axisymmetric and non-axisymmetric) in accretion discs around black holes using two-dimensional hydrodynamic simulations. The turbulent viscosity is modeled by the $\alpha$-ansatz, with different equations of state. We consider both discs with transonic radial inflows across the innermost stable circular orbit, and stationary discs truncated by a reflecting wall at their inner edge, representing a magnetosphere. In transonic discs, viscosity can excite several types of global oscillation modes. These modes are either axisymmetric with frequencies close to multiples of the maximum radial epicyclic frequency $\kappa_\mathrm{max}$, non-axisymmetric with frequencies close to multiples of of the innermost stable orbit frequency $\Omega_\mathrm{ISCO}$, or hybrid modes whose frequencies are linear combinations of these two frequencies. Small values of the viscosity parameter $\alpha$ primarily produce non-axisymmetric modes, while axisymmetric modes become dominant for large $\alpha$. The excitation of these modes may be related to an instability of the sonic point, at which the radial infall speed is equal to the sound speed of the gas. In discs with a reflective inner boundary, we explore the effect of viscosity on trapped $p$-modes which are intrinsically overstable due to the corotation resonance effect. The effect of viscosity is either to reduce the growth rates of these modes, or to completely suppress them and excite a new class of higher frequency modes. The latter requires that the dynamic viscosity scales positively with the disc surface density, indicating that it is a result of the classic viscous overstability effect.