General Relativistic Hydrodynamic Simulations and Linear Analysis of the Standing Accretion Shock Instability around a Black Hole

Abstract

We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole using two-dimensional general relativistic hydrodynamic simulations, as well as linear analysis, in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to nonaxisymmetric perturbations. The results of the dynamical simulations show good agreement with the linear analysis on the stability and the oscillation and growth timescales. A comparison of different wave-travel times with the growth timescales of the instability suggests that it is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of the perturbations are too long to allow a clear definition of the reflection point. By analyzing the nonlinear phase in the dynamical simulations, we show that quadratic mode couplings precede the nonlinear saturation. It is also found that not only short-term random fluctuations due to turbulent motion, but also quasi-periodic oscillations on longer timescales, take place in the nonlinear phase. We give some possible implications of the instability for black hole quasi-periodic oscillations and the central engine in gamma-ray bursts.

Dynamical Structure of Viscous Accretion Disks With Shocks

“…This establishes for the first time that highly viscous ADAF disks can contain standing shock waves. The stability of such a shock is an open question, but Nagakura & Yamada (2008) and Okuda et al (2007) recently found that shocks in inviscid disks are persistent, although the shock radius may oscillate. These results at least suggest the possibility that shocks in viscous disks may be stable as well, although this needs to be investigated in future work.…”

Standing Shock Instability in Advection-Dominated Accretion Flows

“…Furthermore, shock stability analysis for thin disks has been studied using both analytical(e.g., Chakrabarti & Molteni 1993;Nakayama 1992Nakayama , 1994Nobuta & Hanawa 1994;Molteni et al 1996;Gu & Lu 2006;Nagakura & Yamada 2009) and numerical simulation approaches(e.g., Chakrabarti & Molteni 1993;Nobuta & Hanawa 1994;Molteni et al 1996;Gu & Lu 2006;Nagakura & Yamada 2008). However, several of these studies mainly focused on the assumption of a constant disk height(e.g., Chakrabarti & Molteni 1993;Nobuta & Hanawa 1994) or did not fully examine the multiple modes of oscillation(e.g., Chakrabarti & Molteni 1993;Nobuta & Hanawa 1994;Molteni et al 1996;Gu & Lu 2006;Nagakura & Yamada 2008), which are known to exist in the WD accretion shock case studied by, e.g., Chevalier & Imamura (1982) and Imamura et al (1984).…”

Studies of accretion flows around rotating black holes - III. Shock oscillations and an estimation of the spin parameter from QPO frequencies

“…Indeed, the same mechanism of resonance oscillations can be used for all the black holes, from super‐massive to stellar mass. The oscillations mentioned here could be radial, vertical or even azimuthal (Molteni et al 1999, 2006; Okuda et al 2007; Nagakura & Yamada 2008, 2009). It has also been shown that the shocks oscillate when the Rankine–Hugoniot conditions are not satisfied, especially when the entropy at the inner sonic point is higher than that at the outer sonic point (Ryu, Chakrabarti & Molteni 1997).…”

“…The theoretical investigation of Chakrabarti (1989) was later fully generalized in the Kerr geometry (Chakrabarti 1996a). Using non‐axisymmetric perturbations, Molteni, Toth & Kuznetsov (1999), Okuda et al (2005), Molteni, Gerardi & Teresi (2006), Gu & Lu (2006), Okuda, Teresi & Molteni (2007) and, more recently, Nagakura & Yamada (2008, 2009) showed that the standing axisymmetric shocks are extremely stable, though non‐axisymmetric blobs may anchor them and cause variations in X‐ray emissions.…”