Resonant Excitation of Disk Oscillations in Deformed Disks IV: A New Formulation Studying Stability

TL;DR

This paper introduces a new formulation to analyze the stability of resonantly excited disk oscillations in deformed relativistic disks, focusing on mode interactions and their potential for amplitude growth.

Contribution

It presents a novel approach to studying wave excitation and stability in deformed disks by examining mode couplings and energy sign interactions.

Findings

Two prograde oscillations can grow through mutual coupling if their wave energies have opposite signs.

The study offers insights into the mechanisms behind high-frequency QPOs in low-mass X-ray binaries.

A simplified two-mode interaction model demonstrates conditions for amplitude amplification.

Abstract

The possibility has been suggested that high-frequency quasi-periodic oscillations observed in low-mass X-ray binaries are resonantly excited disk oscillations in deformed (warped or eccentric) relativistic disks (Kato 2004). In this paper we examine this wave excitation process from a viewpoint somewhat different from that of previous studies. We study how amplitudes of a set of normal mode oscillations change secularly with time by their mutual couplings through disk deformation. As a first step, we consider the case where the number of oscillation modes contributing to the resonance coupling is two. The results show that two prograde oscillations interacting through disk deformation can grow if their wave energies have opposite signs.