arXiv subjects

Thierry Foglizzo

Publications and source records attributed to Thierry Foglizzo.

25 records · Page 2Linked to original sources

arXiv2008

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.

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arXiv2008

Effect of Rotation on the Stability of a Stalled Cylindrical Shock and its Consequences for Core-Collapse Supernovae

A perturbative analysis is used to investigate the effect of rotation on the instability of a steady accretion shock (SASI) in a simple toy-model, in view of better understanding supernova explosions in which the collapsing core contains angular momentum. A cylindrical geometry is chosen for the sake of simplicity. Even when the centrifugal force is very small, rotation can have a strong effect on the non axisymmetric modes of SASI by increasing the growth rate of the spiral modes rotating in the same direction as the steady flow. Counter-rotating spiral modes are significantly damped, while axisymmetric modes are hardly affected by rotation. The growth rates of spiral modes have a nearly linear dependence on the specific angular momentum of the flow. The fundamental one-armed spiral mode (m=1) is favoured for small rotation rates, whereas stronger rotation rates favour the mode m=2. A WKB analysis of higher harmonics indicates that the efficiency of the advective-acoustic cycles associated to spiral modes is strongly affected by rotation in the same manner as low frequency modes, whereas the purely acoustic cycles are stable. These results suggest that the linear phase of SASI in rotating core-collapse supernovae naturally selects a spiral mode rotating in the same direction of the flow, as observed in the 3D numerical simulations of Blondin & Mezzacappa (2007). This emphasizes the need for a 3D approach of rotating core-collapse, before conclusions on the explosion mechanisms and pulsar kicks can be drawn.

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arXiv2003

Non-radial instability of stalled accretion shocks: advective-acoustic cycle

The linear stability of stalled accretion shocks is investigated in the context of core collapse of type II supernovae. We focus on a particular instability mechanism based on the coupling of acoustic perturbations with advected ones (vorticity, entropy). This advective-acoustic cycle takes place between the shock and the nascent neutron star. Both adiabatic and non-adiabatic processes may contribute to this coupling, but only adiabatic ones are considered in this first approach. The growth time of the adiabatic instability scales like the advection time, and is dominated by low degree modes l=0,1,2. Non radial modes (l=1,2) found unstable by Blondin et al. (2003) can be related to this mechanism.

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arXiv2003

Non-axisymmetric instabilities in shocked accretion flows with differential rotation

The linear stability of a shocked isothermal accretion flow onto a black hole is investigated in the inviscid limit. The outer shock solution, which was previously found to be stable with respect to axisymmetric perturbations, is, however, generally unstable to non-axisymmetric ones. Eigenmodes and growth rates are obtained by numerical integration of the linearized equations. The mechanism of this instability is based on the cycle of acoustic waves between their corotation radius and the shock. It is a form of the Papaloizou-Pringle instability, modified by advection and the presence of the shock. As such it can be generalized to non isothermal shocked accretion flows. Blobs and vortices are generated by the shock as a by-product of the instability.

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arXiv1998

Are solar granules the only source of acoustic oscillations ?

The excitation mechanism of low degree acoustic modes is investigated through the analysis of the stochastic time variations of their energy. The correlation between the energies of two different modes is interpreted as the signature of the occurrence rate of their excitation source. The different correlations determined by Foglizzo et al. (1998) constrain the physical properties of an hypothetical source of excitation, which would act in addition to the classical excitation by the turbulent convection. Particular attention is drawn to the effect of coronal mass ejections. The variability of their occurrence rate with the solar cycle could account for the variation of the correlation between IPHIR and GOLF data. Such an interpretation would suggest that the mean correlation between low degree acoustic modes is at least 0.2 % at solar minimum.

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arXiv1996

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.

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arXiv1995

The Parker-Shearing instability in azimuthaly magnetized discs

We describe the effects of both magnetic buoyancy and differential rotation on a disc of isothermal gas embedded in a purely azimuthal magnetic field, in order to study the evolution and interplay of Parker and shearing instabilities. Both instabilities occur on the slow MHD branch of the dispersion relation, and can affect the same waves. We put a stress on the natural polarization properties of the slow MHD waves to get a better understanding of the physics involved. The mechanism of the shearing instability is described in details. Waves with a vertical wavelength shorter than the scale height of the disc are subject to both the Parker and the transient shearing instabilities. They occur in different ranges of radial wavenumbers, \ie at different times in the shearing evolution ; these ranges can overlap or, on the contrary, be separated by a phase of wave-like oscillations, depending on the strength of differential rotation. Our results can be applied to both galactic and accretion discs.

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