The adiabatic shock produced by a compact object moving supersonically
relative to a gas with uniform entropy and no vorticity is a source of entropy
gradients and vorticity. We investigate these ...analytically. The
non-axisymmetric Rayleigh-Taylor and axisymmetric Kelvin-Helmholtz linear
instabilities are potential sources of destabilization of the subsonic
accretion flow after the shock. A local Lagrangian approach is used in order to
evaluate the efficiency of these linear instabilities. However, the conditions
required for such a WKB type approximation are fulfilled only marginally: a
quantitative estimate of their local growth rate integrated along a flow line
shows that their growth time is at best comparable to the time needed for
advection onto the accretor, even at high Mach number and for a small accretor
size. Despite this apparently low efficiency, several features of these
mechanisms qualitatively match those observed in numerical simulations: in a
gas with uniform entropy, the instability occurs only for supersonic accretors.
It is nonaxisymmetric, and begins close to the accretor in the equatorial
region perpendicular to the symmetry axis. The mechanism is more efficient for
a small, highly supersonic accretor, and also if the shock is detached. We also
show by a 3-D numerical simulation an example of unstable accretion of a
subsonic flow with non-uniform entropy at infinity. This instability is
qualitatively similar to the one observed in 3-D simulations of the
Bondi-Hoyle-Lyttleton flow, although it involves neither a bow shock nor an
accretion line.
Astrophys.J.652:1436-1450,2006 A toy model is analyzed in order to evaluate the linear stability of the gain
region immediately behind a stalled accretion shock, after core bounce. This
model ...demonstrates that a negative entropy gradient is not sufficient to
warrant linear instability. The stability criterion is governed by the ratio
\chi of the advection time through the gain region divided by the local
timescale of buoyancy. The gain region is linearly stable if \chi< 3. The
classical convective instability is recovered in the limit \chi\gg 3. For
\chi>3, perturbations are unstable in a limited range of horizontal wavelengths
centered around twice the vertical size H of the gain region. The threshold
horizontal wavenumbers k_{min} and k_{max} follow simple scaling laws such that
Hk_{min}\propto 1/{\chi} and Hk_{max}\propto \chi. The convective stability of
the l=1 mode in spherical accretion is discussed, in relation with the
asymmetric explosion of core collapse supernovae. The advective stabilization
of long wavelength perturbations weakens the possible influence of convection
alone on a global l=1 mode.
The instability of Bondi-Hoyle-Lyttleton accretion, observed in numerical
simulations, is analyzed through known physical mechanisms and possible
numerical artefacts. The mechanisms of the ...longitudinal and transverse
instabilities, established within the accretion line model, are clarified. They
cannot account for the instability of BHL accretion at moderate Mach number
when the pressure forces within the shock cone are taken into account. The
advective-acoustic instability is considered in the context of BHL accretion
when the shock is detached from the accretor. This mechanism naturally explains
the stability of the flow when the shock is weak, and the instability when the
accretor is small. In particular, it is a robust proof of the instability of 3D
accretion when gamma=5/3 if the accretor is small enough, even for moderate
shock strength (M sim 3). The numerical artefacts that may be present in
existing numerical simulations are reviewed, with particular attention paid to
the advection of entropy/vorticity perturbations and the artificial acoustic
feedback from the accretor boundary condition. Several numerical tests are
proposed to test these mechanisms.
Astrophys.J.654:1006-1021,2007 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.
A new instability mechanism is described in accretion flows where the gas is accelerated from a stationary shock to a sonic surface. The instability is based on a cycle of acoustic and entropic waves ...in this subsonic region of the flow. When advected adiabatically inward, entropy perturbations trigger acoustic waves propagating outward. If a shock is present at the outer boundary, acoustic waves reaching the shock produce new entropy perturbations, thus creating an entropic-acoustic cycle between the shock and the sonic surface. The interplay of acoustic and entropy perturbations is estimated analytically using a simplified model based on the compact nozzle approximation. According to this model, the entropic-acoustic cycle is unstable if the sound speed at the sonic surface significantly exceeds the sound speed immediately after the shock. The growth rate scales like the inverse of the advection time from the outer shock to the sonic point. The frequency of the most unstable perturbations is comparable to the refraction cutoff, defined as the frequency below which acoustic waves propagating inward are significantly refracted outward. This generic mechanism should occur in Bondi-Hoyle-Lyttleton accretion, and also in shocked accretion discs.
The adiabatic shock produced by a compact object moving supersonically relative to a gas with uniform entropy and no vorticity is a source of entropy gradients and vorticity. We investigate these ...analytically. The non-axisymmetric Rayleigh-Taylor and axisymmetric Kelvin-Helmholtz linear instabilities are potential sources of destabilization of the subsonic accretion flow after the shock. A local Lagrangian approach is used in order to evaluate the efficiency of these linear instabilities. However, the conditions required for such a WKB type approximation are fulfilled only marginally: a quantitative estimate of their local growth rate integrated along a flow line shows that their growth time is at best comparable to the time needed for advection onto the accretor, even at high Mach number and for a small accretor size. Despite this apparently low efficiency, several features of these mechanisms qualitatively match those observed in numerical simulations: in a gas with uniform entropy, the instability occurs only for supersonic accretors. It is nonaxisymmetric, and begins close to the accretor in the equatorial region perpendicular to the symmetry axis. The mechanism is more efficient for a small, highly supersonic accretor, and also if the shock is detached. We also show by a 3-D numerical simulation an example of unstable accretion of a subsonic flow with non-uniform entropy at infinity. This instability is qualitatively similar to the one observed in 3-D simulations of the Bondi-Hoyle-Lyttleton flow, although it involves neither a bow shock nor an accretion line.
A toy model is analyzed in order to evaluate the linear stability of the gain region immediately behind a stalled accretion shock, after core bounce. This model demonstrates that a negative entropy ...gradient is not sufficient to warrant linear instability. The stability criterion is governed by the ratio \chi of the advection time through the gain region divided by the local timescale of buoyancy. The gain region is linearly stable if \chi< 3. The classical convective instability is recovered in the limit \chi\gg 3. For \chi>3, perturbations are unstable in a limited range of horizontal wavelengths centered around twice the vertical size H of the gain region. The threshold horizontal wavenumbers k_{min} and k_{max} follow simple scaling laws such that Hk_{min}\propto 1/{\chi} and Hk_{max}\propto \chi. The convective stability of the l=1 mode in spherical accretion is discussed, in relation with the asymmetric explosion of core collapse supernovae. The advective stabilization of long wavelength perturbations weakens the possible influence of convection alone on a global l=1 mode.
We present a detailed study of the growth of the Parker instability in a
differentially rotating disk embedded in an azimuthal equilibrium magnetic
field, such as the interstellar gas or an accretion ...disk. Basic properties of
the instability without shear are first recalled. Differential rotation is
modeled in the shearing sheet approximation, classical in the theory of spiral
density waves. The action of differential rotation is reduced to two different
effects, (i) a linear time-dependence of the radial wavenumber, and (ii) a
radial differential force. We present both exact numerical solutions, and
approximate analytical ones based on the WKB approximation in the limit of weak
differential rotation. Most important are (i) a transient natural stabilization
of the Parker mode due to the radial differential force (ii) the generation of
magnetosonic and Alfvenic waves, and (iii) in a certain parameter range a
possible ``turn-over'' of the perturbation whereby, quite surprisingly, matter
which had started being elevated by the instability may end up dropping towards
the disk midplane. A simplified model shows the possible observable effects of
this turn-over.
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)
The instability of Bondi-Hoyle-Lyttleton accretion, observed in numerical simulations, is analyzed through known physical mechanisms and possible numerical artefacts. The mechanisms of the ...longitudinal and transverse instabilities, established within the accretion line model, are clarified. They cannot account for the instability of BHL accretion at moderate Mach number when the pressure forces within the shock cone are taken into account. The advective-acoustic instability is considered in the context of BHL accretion when the shock is detached from the accretor. This mechanism naturally explains the stability of the flow when the shock is weak, and the instability when the accretor is small. In particular, it is a robust proof of the instability of 3D accretion when gamma=5/3 if the accretor is small enough, even for moderate shock strength (M sim 3). The numerical artefacts that may be present in existing numerical simulations are reviewed, with particular attention paid to the advection of entropy/vorticity perturbations and the artificial acoustic feedback from the accretor boundary condition. Several numerical tests are proposed to test these mechanisms.
