Interface Modes and Their Instabilities in Accretion Disc Boundary Layers

TL;DR

This paper investigates the stability of interface modes at accretion disc boundaries, revealing conditions under which they become unstable and potentially explain observed high-frequency QPOs in X-ray binaries.

Contribution

It introduces a detailed analysis of interface mode instabilities at accretion disc boundaries, considering magnetic and density effects, and links these modes to observed QPO phenomena.

Findings

Interface modes are generally unstable due to Rayleigh-Taylor and Kelvin-Helmholtz instabilities.

High disc sound speed can suppress Rayleigh-Taylor instability.

Wave leakage and absorption can cause instabilities in star-disc boundary modes.

Abstract

We study global non-axisymmetric oscillation modes trapped near the inner boundary of an accretion disc. Observations indicate that some of the quasi-periodic oscillations (QPOs) observed in the luminosities of accreting compact objects (neutron stars, black holes and white dwarfs) are produced in the inner-most regions of accretion discs or boundary layers. Two simple models are considered in this paper: The magnetosphere-disc model consists of a thin Keplerian disc in contact with a uniformly rotating magnetosphere with and low plasma density, while the star-disc model involves a Keplerian disc terminated at the stellar atomosphere with high density and small density scale height. We find that the interface modes at the magnetosphere-disc boundary are generally unstable due to Rayleigh-Taylor and/or Kelvin-Helmholtz instabilities. However, differential rotation of the disc tends to suppress Rayleigh-Taylor instability and a sufficiently high disc sound speed (or temperature) is needed to overcome this suppression and to attain net mode growth. On the other hand, Kelvin-Helmholtz instability may be active at low disc sound speeds. We also find that the interface modes trapped at the boundary between a thin disc and an unmagnetized star do not suffer Rayleigh-Taylor or Kelvin-Helmholtz instability, but can become unstable due to wave leakage to large disc radii and, for sufficiently steep disc density distributions, due to wave absorption at the corotation resonance in the disc. The non-axisymmetric interface modes studied in this paper may be relevant to the high-frequency QPOs observed in some X-ray binaries and in cataclysmic variables.