49 research outputs found
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