153 research outputs found
Instability of a stalled accretion shock: evidence for the advective-acoustic cycle
We analyze the linear stability of a stalled accretion shock in a perfect gas
with a parametrized cooling function L ~ rho^{beta-alpha} P^alpha. The
instability is dominated by the l=1 mode if the shock radius exceeds 2-3 times
the accretor radius, depending on the parameters of the cooling function. The
growth rate and oscillation period are comparable to those observed in the
numerical simulations of Blondin & Mezzacappa (2006). The instability mechanism
is analyzed by separately measuring the efficiencies of the purely acoustic
cycle and the advective-acoustic cycle. These efficiencies are estimated
directly from the eigenspectrum, and also through a WKB analysis in the high
frequency limit. Both methods prove that the advective-acoustic cycle is
unstable, and that the purely acoustic cycle is stable. Extrapolating these
results to low frequency leads us to interpret the dominant mode as an
advective-acoustic instability, different from the purely acoustic
interpretation of Blondin & Mezzacappa (2006). A simplified characterization of
the instability is proposed, based on an advective-acoustic cycle between the
shock and the radius r_nabla where the velocity gradients of the stationary
flow are strongest. The importance of the coupling region in this mechanism
calls for a better understanding of the conditions for an efficient
advective-acoustic coupling in a decelerated, nonadiabatic flow, in order to
extend these results to core-collapse supernovae.Comment: 29 pages, 18 figures, to appear in ApJ (1 new Section, 2 new Figures
A simple toy model of the advective-acoustic instability I. Perturbative approach
Some general properties of the advective-acoustic instability are described
and understood using a toy model which is simple enough to allow for analytical
estimates of the eigenfrequencies. The essential ingredients of this model, in
the unperturbed regime, are a stationary shock and a subsonic region of
deceleration. For the sake of analytical simplicity, the 2D unperturbed flow is
parallel and the deceleration is produced adiabatically by an external
potential. The instability mechanism is determined unambiguously as the
consequence of a cycle between advected and acoustic perturbations. The purely
acoustic cycle, considered alone, is proven to be stable in this flow. Its
contribution to the instability can be either constructive or destructive. A
frequency cut-off is associated to the advection time through the region of
deceleration. This cut-off frequency explains why the instability favours
eigenmodes with a low frequency and a large horizontal wavelength. The relation
between the instability occurring in this highly simplified toy model and the
properties of SASI observed in the numerical simulations of stellar
core-collapse is discussed. This simple set up is proposed as a benchmark test
to evaluate the accuracy, in the linear regime, of numerical simulations
involving this instability. We illustrate such benchmark simulations in a
companion paper.Comment: 14 pages, 10 figures, ApJ in pres
Entropic-acoustic instability of shocked Bondi accretion I. What does perturbed Bondi accretion sound like ?
In the radial flow of gas into a black hole (i.e. Bondi accretion), the
infall of any entropy or vorticity perturbation produces acoustic waves
propagating outward. The dependence of this acoustic flux on the shape of the
perturbation is investigated in detail. This is the key process in the
mechanism of the entropic-acoustic instability proposed by Foglizzo & Tagger
(2000) to explain the instability of Bondi-Hoyle-Lyttleton accretion. These
acoustic waves create new entropy and vorticity perturbations when they reach
the shock, thus closing the entropic-acoustic cycle. With an adiabatic index
1<gamma<=5/3, the linearized equations describing the perturbations of the
Bondi flow are studied analytically and solved numerically. The fundamental
frequency of this problem is the cut-off frequency of acoustic refraction,
below which ingoing acoustic waves are refracted out. This cut-off is
significantly smaller than the Keplerian frequency at the sonic radius and
depends on the latitudinal number l of the perturbations. When advected
adiabatically inward, entropy and vorticity perturbations trigger acoustic
waves propagating outward, with an efficiency which is highest for non radial
perturbations l=1. The outgoing acoustic flux produced by the advection of
vorticity perturbations is always moderate and peaks at rather low frequency.
By contrast, the acoustic flux produced by an entropy wave is highest close to
the refraction cut-off. It can be very large if gamma is close to 5/3. These
results suggest that the shocked Bondi flow with gamma=5/3 is strongly unstable
with respect to the entropic-acoustic mechanism.Comment: 14 pages, 11 figures, accepted for publication in A&
Criteria for Core-Collapse Supernova Explosions by the Neutrino Mechanism
We investigate the criteria for successful core-collapse supernova explosions
by the neutrino mechanism. We find that a
critical-luminosity/mass-accretion-rate condition distinguishes non-exploding
from exploding models in hydrodynamic one-dimensional (1D) and two-dimensional
(2D) simulations. We present 95 such simulations that parametrically explore
the dependence on neutrino luminosity, mass accretion rate, resolution, and
dimensionality. While radial oscillations mediate the transition between 1D
accretion (non-exploding) and exploding simulations, the non-radial standing
accretion shock instability characterizes 2D simulations. We find that it is
useful to compare the average dwell time of matter in the gain region with the
corresponding heating timescale, but that tracking the residence time
distribution function of tracer particles better describes the complex flows in
multi-dimensional simulations. Integral quantities such as the net heating
rate, heating efficiency, and mass in the gain region decrease with time in
non-exploding models, but for 2D exploding models, increase before, during, and
after explosion. At the onset of explosion in 2D, the heating efficiency is
2% to 5% and the mass in the gain region is 0.005 M_{\sun}
to 0.01 M_{\sun}. Importantly, we find that the critical luminosity for
explosions in 2D is 70% of the critical luminosity required in 1D. This
result is not sensitive to resolution or whether the 2D computational domain is
a quadrant or the full 180. We suggest that the relaxation of the
explosion condition in going from 1D to 2D (and to, perhaps, 3D) is of a
general character and is not limited by the parametric nature of this study.Comment: 32 pages in emulateapj, including 17 figures, accepted for
publication in ApJ, included changes suggested by the refere
Multidimensional supernova simulations with approximative neutrino transport. II. Convection and the advective-acoustic cycle in the supernova core
By 2D hydrodynamic simulations including a detailed equation of state and
neutrino transport, we investigate the interplay between different non-radial
hydrodynamic instabilities that play a role during the postbounce accretion
phase of collapsing stellar cores. The convective mode of instability, which is
driven by negative entropy gradients caused by neutrino heating or by time
variations of the shock strength, can be identified clearly by the development
of typical Rayleigh-Taylor mushrooms. However, in cases where the gas in the
postshock region is rapidly advected towards the gain radius, the growth of
such a buoyancy instability can be suppressed. In such a situation the shocked
flow nevertheless can develop non-radial asymmetry with an oscillatory growth
of the amplitude. This phenomenon has been termed ``standing accretion shock
instability'' (SASI). It is shown here that the SASI oscillations can trigger
convective instability and like the latter they lead to an increase of the
average shock radius and of the mass in the gain layer. Both hydrodynamic
instabilities in combination stretch the advection time of matter through the
neutrino-heating layer and thus enhance the neutrino energy deposition in
support of the neutrino-driven explosion mechanism. A rapidly contracting and
more compact nascent NS turns out to be favorable for explosions, because the
accretion luminosity and neutrino heating are larger and the growth rate of the
SASI is higher. Moreover, we show that the oscillation period of the SASI and a
variety of other features in our simulations agree with estimates for the
advective-acoustic cycle (AAC), in which perturbations are carried by the
accretion flow from the shock to the neutron star and pressure waves close an
amplifying global feedback loop. (abridged)Comment: 23 pages, 20 figures; revised version with extended Sect.5, accepted
by Astronomy & Astrophysics; high-resolution images can be obtained upon
reques
Stability of the Accretion Flows with Stalled Shocks in Core-Collapse Supernovae
Bearing in mind the application to the theory of core-collapse supernovae, we
performed a global linear analysis on the stability of spherically symmetric
accretion flows through a standing shock wave onto a proto neutron star. As
unperturbed flows, we adopted the spherically symmetric steady solutions to the
Euler equations obtained with realistic equation of state and formulae for
neutrino reaction rates taken into account. Then we solved the equations for
linear perturbations numerically, and obtained the eigen frequencies and eigen
functions. We found (1) the flows are stable for all modes if the neutrino
luminosity is lower than ergs/s for
. (2) For larger luminosities, the non-radial
instabilities are induced, probably via the advection-acoustic cycles.
Interestingly, the modes with and 3 become unstable at first for
relatively low neutrino luminosities, e.g. ergs/s
for the same accretion rate, whereas the mode is the most unstable for
higher luminosities, ergs/s. These are all oscillatory
modes. (3) For still larger luminosities, ergs/s for
, non-oscillatory modes, both radial and
non-radial, become unstable. These non-radial modes were identified as
convection. We confirmed the results obtained by numerical simulations that the
instabilities induced by the advection-acoustic cycles are more important than
the convection for lower neutrino luminosities.Comment: 46 pages, 19 figures, Accepted by Ap
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