Quasi-periodic oscillations of perturbed tori

TL;DR

This study uses hydrodynamical simulations to analyze oscillating tori around black holes, identifying key oscillation modes and their frequency ratios, which could explain observed high-frequency QPOs.

Contribution

It introduces a method to simulate and analyze oscillation modes of perturbed tori in a pseudo-Newtonian potential, highlighting mode frequencies relevant to astrophysical observations.

Findings

Identified dominant oscillation modes: breathing, radial, and vertical epicyclic.

Found approximate 3:2 frequency ratio between certain modes.

Results relevant for understanding high-frequency QPOs in black hole systems.

Abstract

We performed axisymmetric hydrodynamical simulations of oscillating tori orbiting a non-rotating black hole. The tori in equilibrium were constructed with a constant distribution of angular momentum in a pseudo-Newtonian potential (Klu{\'z}niak-Lee). Motions of the torus were triggered by adding sub-sonic velocity fields: radial, vertical and diagonal to the tori in equilibrium. As the perturbed tori evolved in time, we measured $L_{2}$ norm of density and obtained the power spectrum of $L_{2}$ norm which manifested eigenfrequencies of tori modes. The most prominent modes of oscillation excited in the torus by a quasi-random perturbation are the breathing mode and the radial and vertical epicyclic modes. The radial and the plus modes, as well as the vertical and the breathing modes will have frequencies in an approximate 3:2 ratio if the torus is several Schwarzschild radii away from the innermost stable circular orbit. Results of our simulations may be of interest in the context of high-frequency quasi-periodic oscillations (HF QPOs) observed in stellar-mass black hole binaries, as well as in supermassive black holes.