The runaway instability of thick discs around black holes - I. The constant angular momentum case

Abstract

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma‐ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time‐dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux‐conservative system and solved using a suitable Godunov‐type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self‐gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc‐to‐hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical time‐scale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole (2.5 M⊙) and a large range of mass fluxes (m˙≳10‐3 M⊙ s‐1). The implications of our results in the context of gamma‐ray bursts are briefly discussed.

Relativistic outflows from remnants of compact object mergers and their viability for short gamma-ray bursts

“…We chose Schwarzschild BHs of 2.44 M or 3 M , being girded by a thick torus of 0.13 M or 0.17 M , respectively. The accretion torus was constructed either by relaxation of an initial toroidal cloud of matter or by creating a near-equilibrium configuration with the technique of Font & Daigne (2002). In the first case the BH-torus system is surrounded by a fairly dense (∼100 g cm −3 ) gas halo with a radius of about 10 9 cm (containing a mass of roughly 10 −4 M ), e.g., considered to be the consequence of a neutrino-driven wind from a transient, metastable NS which underwent collapse to a BH-torus system only after some time delay.…”

“…The production of type-B initial models uses a prescription very close to that of Font & Daigne (2002) in order to build an equilibrium torus around a Schwarzschild black hole. Differences with respect to Font & Daigne (2002) arise from the fact that we do not use a barotropic equation of state (EoS) and, therefore, it is not possible to obtain from the specific enthalpy distribution (which is the primary thermodynamical variable that is obtained from the Euler equation) unambiguously all other thermodynamic variables in the equilibrium torus.…”

ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics

“…This will be achieved through simulations in a 2D domain, assuming axisymmetry. For the analytical theory of equilibrium in the purely hydrodynamical case the reader is referred to Abramowicz et al (1978), Kozlowski et al (1978), and Font & Daigne (2002), while the GRMHD version with the addition of a purely toroidal magnetic field comes from Komissarov et al (2006). This test may also represent the basis for studying a class of relevant astrophysical problems, since the dynamics of accretion disks orbiting around black holes is believed to be strongly influenced by the presence of magnetic fields.…”

Hybrid approach to black hole perturbations from extended matter sources

“…where U w D; S r ; S ; S , F i and S are the statevector, the fluxes and the sources of the evolved quantities, respectively, (see [17] for the explicit expressions for F i and S in a Schwarzschild spacetime). The following set of equations The numerical code used in our computations is the same used in ref.…”

“…The case W 0 refers to that special equipotential surface which is closed at infinity (see Refs. [17,18] for details). local extrema on the equatorial plane of closed equipotential surfaces mark the radial positions of the cusp, r cusp , and of the '' center'' of the torus, r c .…”