On the linear growth mechanism driving the stationary accretion shock instability

During stellar core collapse, which eventually leads to a supernovae explosion, the stalled shock is unstable due to the standing accretion shock instability (SASI). This instability induces large-scale non spherical oscillations of the shock, which have crucial consequences on the dynamics and the geometry of the explosion. While the existence of this instability has been firmly established, its physical origin remains somewhat uncertain. Two mechanisms have indeed been proposed to explain its linear growth. The first is an advective-acoustic cycle, where the instability results from the interplay between advected perturbations (entropy and vorticity) and an acoustic wave. The second mechanism is purely acoustic and assumes that the shock is able to amplify trapped acoustic waves. Several arguments favouring the advective-acoustic cycle have already been proposed, however none was entirely conclusive for realistic flow parameters. In this article we give two new arguments which unambiguously show that the instability is not purely acoustic, and should be attributed to the advective-acoustic cycle. First, we extract a radial propagation timescale by comparing the frequencies of several unstable harmonics that differ only by their radial structure. The extracted time matches the advective-acoustic time but strongly disagrees with a purely acoustic interpretation. Second, we present a method to compute purely acoustic modes, by artificially removing advected perturbations below the shock. All these purely acoustic modes are found to be stable, showing that the advected wave is essential to the instability mechanism.Comment: 17 pages, 10 figures, accepted for publication in MNRA

The saturation of SASI by parasitic instabilities

The Standing Accretion Shock Instability (SASI) is commonly believed to be responsible for large amplitude dipolar oscillations of the stalled shock during core collapse, potentially leading to an asymmetric supernovae explosion. The degree of asymmetry depends on the amplitude of SASI, which nonlinear saturation mechanism has never been elucidated. We investigate the role of parasitic instabilities as a possible cause of nonlinear SASI saturation. As the shock oscillations create both vorticity and entropy gradients, we show that both Kelvin-Helmholtz and Rayleigh-Taylor types of instabilities are able to grow on a SASI mode if its amplitude is large enough. We obtain simple estimates of their growth rates, taking into account the effects of advection and entropy stratification. In the context of the advective-acoustic cycle, we use numerical simulations to demonstrate how the acoustic feedback can be decreased if a parasitic instability distorts the advected structure. The amplitude of the shock deformation is estimated analytically in this scenario. When applied to the set up of Fernandez & Thompson (2009a), this saturation mechanism is able to explain the dramatic decrease of the SASI power when both the nuclear dissociation energy and the cooling rate are varied. Our results open new perspectives for anticipating the effect, on the SASI amplitude, of the physical ingredients involved in the modeling of the collapsing star.Comment: 14 pages, 16 figures, accepted for publication in ApJ. Minor changes following the referee report

A simple toy model of the advective-acoustic instability. II. Numerical simulations

The physical processes involved in the advective-acoustic instability are investigated with 2D numerical simulations. Simple toy models, developped in a companion paper, are used to describe the coupling between acoustic and entropy/vorticity waves, produced either by a stationary shock or by the deceleration of the flow. Using two Eulerian codes based on different second order upwind schemes, we confirm the results of the perturbative analysis. The numerical convergence with respect to the computation mesh size is studied with 1D simulations. We demonstrate that the numerical accuracy of the quantities which depend on the physics of the shock is limited to a linear convergence. We argue that this property is likely to be true for most current numerical schemes dealing with SASI in the core-collapse problem, and could be solved by the use of advanced techniques for the numerical treatment of the shock. We propose a strategy to choose the mesh size for an accurate treatment of the advective-acoustic coupling in future numerical simulations.Comment: 9 pages, 10 figures, ApJ in press, new Sect. 5 and Fig.

A Shallow Water Analogue of the Standing Accretion Shock Instability: Experimental Demonstration and Two-Dimensional Model

Despite the sphericity of the collapsing stellar core, the birth conditions of neutron stars can be highly non spherical due to a hydrodynamical instability of the shocked accretion flow. Here we report the first laboratory experiment of a shallow water analogue, based on the physics of hydraulic jumps. Both the experiment and its shallow water modeling demonstrate a robust linear instability and nonlinear properties of symmetry breaking, in a system which is one million times smaller and about hundred times slower than its astrophysical analogue.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Letters. Supplementary Material (6 movies) available at http://irfu.cea.fr/Projets/SN2NS/outreach.htm

An analytical study of Bondi-Hoyle-Lyttleton accretion I. Stationary flows

We prove that the sonic surface of axisymmetric meridional stationary flows is always attached to the accretor, however small, if the adiabatic index of the gas is gamma=5/3. Using local expansions near a point-like accretor, we extend Bondi's classification of spherically symmetric flows to axisymmetric flows, introducing the possibility of angular sectors reached by no flow lines, and singular directions of infinite mass flux, in addition to the angular regions of subsonic and supersonic accretion. For gamma<5/3, we show the impossibility of subsonic accretion onto a point-like accretor when the entropy of the flow is not uniform. The special case gamma=5/3 is treated separately. We analyse the influence of the adiabatic index and Mach number of the flow at infinity on the mass accretion rate of shocked spherical flows. We propose an interpolation formula for the mass accretion rate of axisymmetric flows as a function of the Mach number and the adiabatic index, in the range 9/7<gamma<5/3.Comment: 22 pages, A&A LaTeX, submitted to A&

Characterizing SASI- and Convection-Dominated Core-Collapse Supernova Explosions in Two Dimensions

The success of the neutrino mechanism of core-collapse supernovae relies on the supporting action of two hydrodynamic instabilities: neutrino-driven convection and the Standing Accretion Shock Instability (SASI). Depending on the structure of the stellar progenitor, each of these instabilities can dominate the evolution of the gain region prior to the onset of explosion, with implications for the ensuing asymmetries. Here we examine the flow dynamics in the neighborhood of explosion by means of parametric two-dimensional, time-dependent hydrodynamic simulations for which the linear stability properties are well understood. We find that systems for which the convection parameter is sub-critical (SASI-dominated) develop explosions once large-scale, high-entropy bubbles are able to survive for several SASI oscillation cycles. These long-lived structures are seeded by the SASI during shock expansions. Finite-amplitude initial perturbations do not alter this outcome qualitatively, though they can lead to significant differences in explosion times. Supercritical systems (convection-dominated) also explode by developing large-scale bubbles, though the formation of these structures is due to buoyant activity. Non-exploding systems achieve a quasi-steady state in which the time-averaged flow adjusts itself to be convectively sub-critical. We characterize the turbulent flow using a spherical Fourier-Bessel decomposition, identifying the relevant scalings and connecting temporal and spatial components. Finally, we verify the applicability of these principles on the general relativistic, radiation-hydrodynamic simulations of Mueller, Janka, & Heger (2012), and discuss implications for the three-dimensional case.Comment: accepted by MNRAS with minor change