The runaway instability of thick discs around black holes - II. Non-constant angular momentum discs

Abstract

We present results from a comprehensive number of relativistic, time‐dependent, axisymmetric simulations of the runaway instability of non‐constant angular momentum thick discs around black holes. This second paper in the series extends earlier results where only constant angular momentum discs were considered. All relevant aspects of the theory of stationary thick discs around rotating black holes, necessary to build the equilibrium initial data used in our simulations, are presented in great detail. The angular momentum of the evolved discs is assumed to increase outwards with the radial distance according to a power law, l=Krα, where K > 0 corresponds to prograde discs (with respect to the black hole rotation) and K < 0 to retrograde discs. The main simplifying assumptions of our approach are not to include magnetic fields or self‐gravity in the discs (test‐fluid approximation). Furthermore, the dynamics of the space–time is accounted for by computing the transfer of mass and angular momentum from the disc to the black hole through the event horizon. In this approximation the evolution of the central black hole, which initially is non‐rotating, is assumed to follow a sequence of Kerr black holes of increasing mass and spin. All discs we build slightly overflow the potential barrier at the cusp, departing from equilibrium, so that accretion is possible. In agreement with previous results based on stationary models we find that by allowing the mass and the spin of the black hole to grow, constant angular momentum discs rapidly become unstable on a dynamical time‐scale (a few orbital periods). The comparison with the results of our first paper shows that the effect of the angular momentum transfer from the tori to the black hole is to make constant angular momentum discs less unstable, increasing the time‐scale for the runaway instability to grow. However, we find that non‐constant angular momentum discs are dramatically stabilized for very small values of the angular momentum slope α, much smaller than the Keplerian value α= 1/2. Our fully relativistic and time‐dependent simulations thus confirm the predictions of stationary studies concerning the stabilizing effect of non‐constant angular momentum distributions. For the various disc‐to‐hole mass ratios considered, we systematically find that the critical values of α below which the runaway instability can exist are slightly smaller than those reported previously in the literature based on stationary studies.

Dynamical evolution of black hole-neutron star binaries in general relativity: Simulations of tidal disruption

“…The theory of accretion disk dynamics presents several interesting connections to that of merging binaries, since questions about the stability of mass transfer appear as well (see, e.g., [89] and references therein). One key difference between the models is the typical radial angular momentum distribution; parameterizing the tangential velocity profile as v t (r) ∝ r α , irrotational NS have a nearly flat velocity profile, α ∼ 0, and corotating NS a flat angular velocity profile, α = 1, both larger than the Keplerian value α K = −0.5.…”

Electromagnetic counterparts of recoiling black holes: general relativistic simulations of non-Keplerian discs

“…In these circumstances the vertical structure of the disc can be essentially neglected and twodimensional simulations are therefore indicative of the full threedimensional dynamics. It is worth mentioning that discs with a rotation law given by (13) have been the subject of a longstanding debate about whether they are subject to the so called "runaway instability" (Abramowicz et al 1983), which would lead to an exponentially rapid accretion onto the black hole (Font & Daigne 2002b,a;Zanotti et al 2003;Daigne & Font 2004;Zanotti et al 2005;Montero et al 2007). Because the onset and development of this instability depends on the response of the torus to the increased mass of the black hole, simulating this instability accurately requires also the evolution of the Einstein equations.…”

“…A detailed description of the equilibrium models for non-constant specific angular momentum discs can be found Daigne & Font (2004). In particular, we have chosen a value of S such that the resulting thick discs possess two well defined Keplerian points, namely the "cusp" (which is where matter can accrete onto the black hole) and the "centre" (which is where the pressure has zero gradient); cf.…”

Model for an optically thick torus in local thermodynamic equilibrium around a black hole

“…This equation was extensively studied in the context of geometrically thick disks around black holes, and depending on the specific 2 angular momentum = −u φ /u t , different classes of equilibrium tori can be obtained 3 whose structure and properties have been discussed in detail Kozlowski et al 1978;Font & Daigne 2002;Daigne & Font 2004). Here we investigate the possibility of adding an optically thick radiation field to those solutions without affecting their hydrodynamics.…”

“…One such relativistic system is represented by geometrically thick disks (tori) around black holes. Considered as inviscid purely fluid solutions, these objects have always attracted much interest, partly because they allow for relatively simple analytic or semi-analytic configurations (Fishbone & Moncrief 1976;Abramowicz et al 1978;Kozlowski et al 1978;Font & Daigne 2002;Daigne & Font 2004;Qian et al 2009;Penna et al 2013) and partly because they can be adopted to study various types of fluid instabilities and potentially observable physical effects in the vicinity of black holes (Abramowicz et al 1980(Abramowicz et al , 1983Papaloizou & Pringle 1984;Abramowicz et al 1998;Rezzolla et al 2003;Zanotti et al 2003;Blaes et al 2006;Montero et al 2010). Moreover, a renewed interest for them has been motivated by the outcome of recent numerical simulations in full general relativity, showing that high-density tori are indeed produced after the merger of unequal-mass neutron star binaries that form a black hole .…”