Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

Abstract

We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind the application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch & Ott (2013) demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without the fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 ${\mathrm{M}}_{\odot }$ progenitor model by Woosley & Heger (2007), which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically showed that the growth rate is proportional to $l$, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

11 pages, 9 figures, accepted for publication in The Astrophysical Journal

References in corpus (4)

• Instability of a stalled accretion shock: evidence for the advective-acoustic cycle
• Effect of Rotation on the Stability of a Stalled Cylindrical Shock and its Consequences for Core-Collapse Supernovae
• Stability of the Accretion Flows with Stalled Shocks in Core-Collapse Supernovae
• Standing Accretion Shocks in the Supernova Core: Effects of Convection and Realistic EOS

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• 3D Simulations of Strongly Magnetised Non-Rotating Supernovae: Explosion Dynamics and Remnant Properties
• Three-dimensional Hydrodynamics Simulations of Precollapse Shell Burning in the Si- and O-rich Layers
• Impact of rotation on the evolution of convective vortices in collapsing stars