Thierry Foglizzo

On the linear growth mechanism driving the standing 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.

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.

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, but the 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, 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.

Shallow water analogue of the standing accretion shock instability: experimental demonstration and a two-dimensional model.

Despite the sphericity of the collapsing stellar core, the birth conditions of neutron stars can be highly nonspherical 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 one hundred times slower than its astrophysical analogue.

The Explosion Mechanism of Core-Collapse Supernovae: Progress in Supernova Theory and Experiments

The explosion of core-collapse supernova depends on a sequence of events taking place in less than a second in a region of a few hundred kilometers at the center of a supergiant star, after the stellar core approaches the Chandrasekhar mass and collapses into a proto-neutron star, and before a shock wave is launched across the stellar envelope. Theoretical efforts to understand stellar death focus on the mechanism which transforms the collapse into an explosion. Progress in understanding this mechanism is reviewed with particular attention to its asymmetric character. We highlight a series of successful studies connecting observations of supernova remnants and pulsars properties to the theory of core-collapse using numerical simulations. The encouraging results from first principles models in axisymmetric simulations is tempered by new puzzles in 3D. The diversity of explosion paths and the dependence on the pre-collapse stellar structure is stressed, as well as the need to gain a better understanding of hydrodynamical and MHD instabilities such as SASI and neutrino-driven convection. The shallow water analogy of shock dynamics is presented as a comparative system where buoyancy effects are absent. This dynamical system can be studied numerically and also experimentally with a water fountain. The potential of this complementary research tool for supernova theory is analyzed. We also review its potential for public outreach in science museums.

DYNAMICS OF AN ALFVEN SURFACE IN CORE COLLAPSE SUPERNOVAE

We investigate the dynamics of an Alfven surface (where the Alfven speed equals the advection velocity) in the context of core collapse supernovae during the phase of accretion on the proto-neutron star. Such a surface should exist even for weak magnetic fields because the advection velocity decreases to zero at the center of the collapsing core. In this decelerated flow, Alfven waves created by the standing accretion shock instability or convection accumulate and amplify while approaching the Alfven surface. We study this amplification using one-dimensional MHD simulations with explicit physical dissipation (resistivity and viscosity). In the linear regime, the amplification continues until the Alfven wavelength becomes as small as the dissipative scale. A pressure feedback that increases the pressure in the upstream flow is created via a nonlinear coupling. We derive analytic formulae for the maximum amplification and the nonlinear coupling and check them with numerical simulations to very good accuracy. Interestingly, these quantities diverge if the dissipation is decreased to zero, scaling as the square root of the Reynolds number, suggesting large effects in weakly dissipative flows. We also characterize the nonlinear saturation of this amplification when compression effects become important, leading to either a change of the velocity gradient, or a steepening of the Alfven wave. Applying these results to core collapse supernovae shows that the amplification can be fast enough to affect the dynamics if the magnetic field is strong enough for the Alfven surface to lie in the region of strong velocity gradient just above the neutrinosphere. This requires the presence of a strong magnetic field in the progenitor star, which would correspond to the formation of a magnetar under the assumption of magnetic flux conservation. An extrapolation of our analytic formula (taking into account the nonlinear saturation) suggests that the Alfven wave could reach an amplitude of B ~ 1015 G, and that the pressure feedback could significantly contribute to the pressure below the shock.

New insights on the spin-up of a neutron star during core collapse

The spin of a neutron star at birth may be impacted by the asymmetric character of the explosion of its massive progenitor. During the first second after bounce, the spiral mode of the Standing Accretion Shock Instability (SASI) is able to redistribute angular momentum and spin-up a neutron star born from a non-rotating progenitor. Our aim is to assess the robustness of this process. We perform 2D numerical simulations of a simplified setup in cylindrical geometry to investigate the timescale over which the dynamics is dominated by a spiral or a sloshing mode. We observe that the spiral mode prevails only if the ratio of the initial shock radius to the neutron star radius exceeds a critical value. In that regime, both the degree of asymmetry and the average expansion of the shock induced by the spiral mode increase monotonously with this ratio, exceeding the values obtained when a sloshing mode is artificially imposed. With a timescale of 2-3 SASI oscillations, the dynamics of SASI takes place fast enough to affect the spin of the neutron star before the explosion. The spin periods deduced from the simulations are compared favorably to analytical estimates evaluated from the measured saturation amplitude of the SASI wave. Despite the simplicity of our setup, numerical simulations revealed unexpected stochastic variations, including a reversal of the direction of rotation of the shock. Our results show that the spin up of neutron stars by SASI spiral modes is a viable mechanism even though it is not systematic.

TOWARD A MAGNETOHYDRODYNAMIC THEORY OF THE STATIONARY ACCRETION SHOCK INSTABILITY: TOY MODEL OF THE ADVECTIVE-ACOUSTIC CYCLE IN A MAGNETIZED FLOW

The effect of a magnetic field on the linear phase of the advective-acoustic instability is investigated as a first step toward a magnetohydrodynamic (MHD) theory of the stationary accretion shock instability taking place during stellar core collapse. We study a toy model where the flow behind a planar stationary accretion shock is adiabatically decelerated by an external potential. Two magnetic field geometries are considered: parallel or perpendicular to the shock. The entropy-vorticity wave, which is simply advected in the unmagnetized limit, separates into five different waves: the entropy perturbations are advected, while the vorticity can propagate along the field lines through two Alfv?n waves and two slow magnetosonic waves. The two cycles existing in the unmagnetized limit, advective-acoustic and purely acoustic, are replaced by up to six distinct MHD cycles. The phase differences among the cycles play an important role in determining the total cycle efficiency and hence the growth rate. Oscillations in the growth rate as a function of the magnetic field strength are due to this varying phase shift. A vertical magnetic field hardly affects the cycle efficiency in the regime of super-Alfv?nic accretion that is considered. In contrast, we find that a horizontal magnetic field strongly increases the efficiencies of the vorticity cycles that bend the field lines, resulting in a significant increase of the growth rate if the different cycles are in phase. These magnetic effects are significant for large-scale modes if the Alfv?n velocity is a sizable fraction of the flow velocity.

Are pulsars spun up or down by SASI spiral modes

Pulsars may either be spun up or down by hydrodynamic instabilities during the supernova explosion of massive stars. Besides rapidly-rotating cases related to bipolar explosions, stellar rotation may affect the explosion of massive stars in the more common situations where the centrifugal force is minor. Using 2D simulations of a simplified setup in cylindrical geometry, we examine the impact of rotation on the Standing Accretion Shock Instability (SASI) and the corotation instability, also known as low-T/|W|. The influence of rotation on the saturation amplitude of these instabilities depends on the specific angular momentum in the accretion flow and the ratio of the shock to the neutron star radii. The spiral mode of SASI becomes more vigorous with faster rotation only if this ratio is large enough. A corotation instability develops at large rotation rates and impacts the dynamics more dramatically, leading to a strong one-armed spiral wave. Non-axisymmetric instabilities are able to redistribute angular momentum radially and affect the pulsar spin at birth. A systematic study of the relationship between the core rotation period of the progenitor and the initial pulsar spin is performed. Stellar rotation rates for which pulsars are spun up or down by SASI are estimated. Rapidly spinning progenitors are modestly spun down by spiral modes, less than

The non-linear onset of neutrino-driven convection in two- and three-dimensional core-collapse supernovae

\sim 30\%