Simulations of Overstable Inertial-acoustic Modes in Black-Hole Accretion Discs

TL;DR

This paper uses hydrodynamic simulations to study overstable inertial-acoustic modes in black-hole accretion discs, confirming linear growth rates and exploring nonlinear saturation mechanisms.

Contribution

First simulation-based confirmation of linear growth rates and frequencies of overstable inertial-acoustic modes in black-hole accretion discs, including nonlinear saturation analysis.

Findings

Mode growth rates up to 10% of disc rotation frequency.

Saturation occurs when radial velocity perturbation approaches sound speed.

Nonlinear wave steepening and mode interactions likely cause saturation.

Abstract

We present two-dimensional inviscid hydrodynamic simulations of overstable inertial-acoustic oscillation modes (p-modes) in black-hole accretion discs. These global spiral waves are trapped in the inner-most region of the disc, and are driven overstable by wave absorption at the corotation resonance ($r_c$) when the gradient of the background disc vortensity (vorticity divided by surface density) at $r_c$ is positive and the disc inner boundary is sufficiently reflective. Previous linear calculations have shown that the growth rates of these modes can be as high as 10% of the rotation frequency at the disc inner edge. We confirm these linear growth rates and the primary disc oscillation frequencies in our simulations when the mode amplitude undergoes exponential growth. We show that the mode growth saturates when the radial velocity perturbation becomes comparable to the disc sound speed. During the saturation stage, the primary disc oscillation frequency differs only slightly (by less than a few percent) from the linear mode frequency. Sharp features in the fluid velocity profiles at this stage suggest that the saturation results from nonlinear wave steepening and mode-mode interactions.