Corotation resonance and overstable oscillations in black-hole accretion discs: general-relativistic calculations

TL;DR

This paper investigates how relativistic effects influence wave dynamics in black-hole accretion discs, revealing conditions under which certain oscillation modes become overstable, potentially explaining observed high-frequency QPOs.

Contribution

It generalizes Newtonian wave theory to general relativity, deriving new expressions for disc vortensity and demonstrating how relativistic effects can induce overstability in p-modes.

Findings

Relativistic wave absorption at corotation can amplify or damp spiral waves.

Black hole spin and disc parameters affect p-mode frequencies and growth rates.

Overstable p-modes may explain high-frequency QPOs in black hole X-ray binaries.

Abstract

We study the dynamics of spiral waves and oscillation modes in relativistic rotating discs around black holes. Generalizing the Newtonian theory, we show that wave absorption can take place at the corotation resonance, where the pattern frequency of the wave matches the background disc rotation rate. We derive the general relativistic expression for the disc vortensity (vorticity divided by surface density), which governs the behaviour of density perturbation near corotation. Depending on the gradient of the generalized disc vortensity, corotational wave absorption can lead to the amplification or damping of the spiral wave. We apply our general theory of relativistic wave dynamics to calculate the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the inner-most region of a black hole accretion disc. Because general relativity changes the profiles of the radial epicyclic frequency and disc vortensity near the inner disc edge close to the black hole, these p-modes can become overstable under appropriate conditions. We present the numerical results of the frequencies and growth rates of p-modes for various black hole spin and model disc parameters (the surface density profile and sound speed), and discuss their implications for understanding the enigmatic high-frequency quasi-periodic oscillations observed in black hole X-ray binaries.