Open AccessThe runaway instability of thick discs around black holes – I. The constant angular momentum case
Author(s) -
Font José A.,
Daigne Frédéric
Publication year - 2002
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2002.05515.x
Subject(s) - physics , black hole (networking) , schwarzschild radius , instability , angular momentum , event horizon , rotating black hole , extremal black hole , spin flip , astrophysics , accretion (finance) , binary black hole , stellar black hole , white hole , classical mechanics , mechanics , gravitational collapse , event (particle physics) , gravitational wave , computer network , routing protocol , routing (electronic design automation) , galaxy , computer science , link state routing protocol
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.