Stability of general-relativistic accretion disks

TL;DR

This study investigates the stability of self-gravitating relativistic accretion disks around black holes using 3D general relativistic hydrodynamics simulations, revealing the development of non-axisymmetric instabilities similar to Newtonian predictions.

Contribution

First detailed simulation of relativistic accretion disk stability showing non-axisymmetric modes and their effects in full general relativity.

Findings

Disks do not develop runaway instability within several orbital periods.

All models develop non-axisymmetric instabilities, including Papaloizou-Pringle and intermediate types.

The m=1 mode causes black hole outspiraling, amplifying instability growth.

Abstract

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core-collapse of massive stars. We explore the stability of such disks against runaway and non-axisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the THOR code. We model the disk matter using the ideal fluid approximation with a $\Gamma$-law equation of state with $\Gamma=4/3$. We explore three disk models around non-rotating black holes with disk-to-black hole mass ratios of 0.24, 0.17 and 0.11. Due to metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m = 1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m = 1 mode in some cases. Overall, our simulations show that the properties of the unstable non-axisymmetric modes in our disk models are qualitatively similar to those in Newtonian theory.