On the development of the Papaloizou-Pringle instability of the black hole-torus systems and quasi-periodic oscillations

TL;DR

This study numerically investigates the dynamical instability and oscillations of relativistic black hole-torus systems, revealing how perturbations trigger the Papaloizou-Pringle instability and produce quasi-periodic oscillations relevant to astrophysical observations.

Contribution

It provides a detailed numerical analysis of the Papaloizou-Pringle instability in black hole-torus systems, including the effects of black hole spin and torus parameters on instability growth and QPOs.

Findings

Perturbed tori develop instabilities causing gas accretion into the black hole.

Oscillating tori exhibit specific frequencies related to their parameters.

The $m=1$ mode of the instability grows across various conditions.

Abstract

We present the numerical study of dynamical instability of a pressure-supported relativistic torus, rotating around the black hole with a constant specific angular momentum on a fixed space-time background, in case of perturbation by a matter coming from the outer boundary. Two dimensional hydrodynamical equations are solved at equatorial plane using the HRSCS to study the effect of perturbation on the stable systems. We have found that the perturbed torus creates an instability which causes the gas falling into the black hole in a certain dynamical time. All the models indicate an oscillating torus with certain frequency around their instant equilibrium. The dynamic of the accreted torus varies with the size of initial stable torus, black hole spin and other variables, such as Mach number, sound speed, cusp location of the torus, etc. The mass accretion rate is slightly proportional to the torus-to-hole mass ratio in the black hole-torus system, but it strongly depends on the cusp location of the torus. The cusp located in the equipotential surfaces of the effective potential moves outwards into the torus. The dynamical change of the torus increases the mass accretion rate and triggers the Papaloizou-Pringle instability. It is also observed that the growth of the $m=1$ mode of the Papaloizou-Pringle instability occurs for a wide range of fluid and hydrodynamical parameters and a black hole spin. We have also computed the QPOs from the oscillating relativistic torus.