1 07/10/2010 - séminaire du luth - jérôme guilet asymmetric explosions of core collapse...

107/10/2010 - Séminaire du LUTh - Jérôme Guilet

Asymmetric explosions of

Core collapse supernovae

Jérôme Guilet

En collaboration avec Thierry Foglizzo, Sébastien Fromang & Jun’ichi Sato


Outline

Introduction: Asymmetry in Core Collapse supernovae

The Standing Accretion Shock Instability The linear growth mechanism

The saturation of SASI

Effect of a magnetic field SASI in a magnetized flow

Dynamics of an Alfvén surface

Conclusions and perspectives


Supernova : death of a star

•Extremely powerful/bright explosion

•SN Ia : thermonuclear explosion

(not discussed here)

•SN II : Collapse of the core of a massive star

=> formation of a neutron star

•Electromagnetic waves detected days after the explosion : the central engine is difficult to detect

•Gravitational waves and neutrinos would give a view of the instant of explosion


Polarization Pulsar kicks

Indications of explosion asymmetry

Pulsars have high peculiar velocities : ~ 400 km.s-1, up to >1000 km.s-1

probably originated fromasymmetries in supernovaexplosion

guitar nebula


From core collapse to the stalled shock

Stalled shock

How to revive the shock and obtain an explosion ?

massive star

collapse of the iron core


heating

cooling

From the stalled shock to an explosion ???

•Classical delayed neutrino-driven mechanism :

•Many physical ingredients :– Nuclear physics– Neutrino transport– General relativity– Multi-Dimensional hydrodynamics– Magnetic field

-->Extremely challenging numerical task !

•No explosion in the most sophisticated 1D simulations... (Liebendorfer et al 2001)

Asymmetries are essential for the explosion mechanism !!

Neutrino heating below the shock

drives the explosion

Protoneutron

star

neutrinosphere(r~30-80km)

shock(r~200km) gain radius

collapsing core


Breaking the spherical symmetry

•Due to neutrino heating below the shock•small angular scale : l ~ 4-5

•Induces shock oscillations•large angular scale : l ~ 1-2

Neutrino driven convection Standing Accretion Shock Instability (SASI) Blondin et al 2003

induces a global asymmetry !

Foglizzo et al 2006 Foglizzo et al 2006


QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Neutrino driven explosion Acoustic explosion

- SASI and convection help neutrino heating by increasing the dwell time in the gain region

A marginal explosion in 2D ? (Marek & Janka 2009)

Robust explosion in 3D ?? (Nordhaus et al. 2010)

Marek & Janka 2009 Burrows et al. 2006

- SASI induces g-mode oscillations of the neutron star

- Acoustic power revives the shock


Important consequences of SASI

•Global asymmetry of the explosion :

– polarization observation

– profile of oxygen line

•Could explain neutron star kicks up to 1000 km/s (Scheck et al 2006, Wongwathanarat et al 2010)

•Affect the neutron star spin (Blondin & Mezzacappa 2007)

•Gravitational waves emission (e.g. Kotake et al 2009, Marek et al 2009)

Wongwathanarat et al 2010

Blondin & Mezzacappa 2007


Outline








Methods

•Perturbative analysis :– stationary flow

=>simplifying assumptions– add small perturbations– compute eigenmodes

• growth rates• frequencies• eigenfunctions: spatial distribution

•Numerical simulations :– No need for a stationnary flow– Can describe the non linear dynamics

growth rate

shock position

Foglizzo et al 2007


Two competing mechanisms

Purely acoustic mechanismAdvective-acoustic cycle

neutronstar

shock

entropy-vorticity wave

neutronstar

shock

acoustic wave acoustic wave

Foglizzo et al 2007 Blondin & Mezzacappa 2006

Advective-acoustic cycle favored by a WKB analysis

BUT : valid for high frequency modes only...


SASI mode frequencies

•Fundamental frequency (most unstable mode) is consistent with both mechanisms

(Foglizzo et al 2007, Scheck et al 2008)

•Higher harmonics inconsistent with the purely acoustic mechanism (Guilet & Foglizzo in prep)

frequencyrsh = 2.5rPNS

Advective-acoustic cycle wins !


Outline








Saturation by parasitic instabilities

advective-acoustic cycle

=> Saturation

entropy-vorticity wave


The parasitic instabilities

Entropy wave :

Rayleigh-Taylor instability

Vorticity wave :

Kelvin-Helmholtz instability

Stabilizing effects for the parasites :• Stratification (Stationary entropy caused by neutrino cooling) :

Efficient near the neutron star• Advection : efficient just below the shock


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sont requis pour visionner cette image.

QuickTime™ et undécompresseur


small amplitude entropy wave large amplitude entropy wave

potential step decelerating the flow


Efficiency of the acoustic feedback

Kelvin-Helmholtz(entropy-vorticity wave)

Rayleigh-Taylor(entropy wave)


Dissociation energy increases & neutrino cooling decreases

Fernandez &Thompson 2009



Scheck et al 2008






Estimate of the saturation amplitude

•Criterion :

•Result : Rayleigh-Taylor is responsible for the saturation

Stratification advectionSASI growth rate

This saturation mechanism seems to work well !

Guilet et al 2010


Outline








QuickTime™ et undécompresseur TIFF (LZW)




Neutrino driven explosion Magnetic explosion

- no magnetic field

- Magnetic field amplification: B ~1015 G

- Obtains for VERY rapid rotation

Marek & Janka 2009

Burrows et al. 2007

Moderate field effect ?


Outline








A toy model for SASI in a magnetized flow

neutronstar

shock

or

B

planar adiabatic toy model(Foglizzo 2009)

x

z v

« neutron star »

shock

deceleration byan external potential

Advective-acoustic cycle with a magnetic field : vorticity can propagate through Alfvén and slow waves !

decelerated flow

supersonic flow

neutrino cooling


Interference between vorticity cycles

Propagation of the vorticity

different cycles are out of phase

Entropy

Vorticity : Alfvén and slow waves

Wave - Wave +

choc

~vA~Bgrowth rate

magnetic field strength

The advective-acoustic cycle separates in up to 5 cycles !

Guilet & Foglizzo 2010


Coupling efficiency

-Vertical B : No effect

-Horizontal B : - Strong amplification of the

vorticity cycles when field lines are bent (k // B)

- Increase of the growth rate

- Significant effect if vA~v

magnetic field strength

growth rate

coupling efficiency

Conclusion : Ambiguous result...


Outline








Alfvén surface simulations

•The alfvén surface is defined by : v = vA

Alfvén speed : vA2 = B2/(

•An Alfvén wave propagates against the flow at the speed : v-vA

•Accumulation of Alfvén waves at the Alfvén surface !

•We performed 1D simulations with the code RAMSES


Alfvén wave amplification and pressure feedback

•The Alfvén wave amplifies while its wavelength decreases (Williams 1975) :

•When the wavelength is as small as the dissipative scale, the Alfvén wave is dissipated

•Creation of a pressure feedback that increases the upstream pressure

z

deceleration

Alfvén surface


Analytical estimate versus simulations

Small amplitude Alfvén wave Non linear saturation

frequency

incident amplitude

(Guilet et al submitted to ApJ)


How does this affect core collapse ?

•Fast enough amplification if the Alfvén surface is above the proto-neutron star surface

•Magnetic field required :

•SASI creates Alfvén waves with an amplitude :

•Amplitude of the pressure feedback (from the analytic estimate) :

Pressure increase pushes the shock :

-> might help the explosion

-> change the geometry

Important effect !!!


Outline








Conclusions

•Multidimensional dynamics is important in core collapse supernovae

•SASI can be attributed to the advective-acoustic cycle

•The saturation of SASI can be explained by the appearance of parasitic instabilities (Rayleigh-Taylor instability)

•The magnetic field could have an important effect when vA ~ v, even if the magnetic pressure is negligible

– SASI could be either stabilized or amplified

– Alfvén wave amplification at the Alfvén surface creates an important pressure feedback


Perspectives

•Dependence of the SASI amplitude on the physical ingredients ?

– Heating, cooling by neutrinos– Equation of state– Rotation...

•Analytical estimate of consequences of SASI :– amplitude of the kick, – spin of the NS, – gravitational wave signal...

•Effect of a more realistic magnetic field geometry ?

•Multidimensional dynamics at the Alfvén surface ? Effect of the turbulence of the flow ?

Merci de votre attention!

Dipolar magnetic field


Frequencies and associated timescales

•Fundamental mode (most unstable)

– advective-acoustic time

– azimuthal acoustic time

•Higher harmonics :

-> radial propagation time...

Acoustic modes of a box

Lz

Lx

Analogy

Lr=rsh-r*

Lx=r

frequency


Radial time in a simplified model of SASI

acoustic

advective-acoustic

timescale

Extracted from SASI eigenspectrum :

shock position


6 cycles (instead of 2)

Coupling at the shock

Cycle efficiencies :

∇Δz

2 cycles Alfvén

fast magnetosonic

1 cycle fast1 cycle entropy

2 cycles slow

« neutron star »

shock

coupling in the gradients

1 07/10/2010 - séminaire du luth - jérôme guilet asymmetric explosions of core collapse...

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