1 07/10/ Séminaire du LUTh - Jérôme Guilet Asymmetric explosions of Core collapse supernovae Jérôme Guilet En collaboration avec Thierry Foglizzo, Sébastien Fromang & Jun’ichi Sato

2 07/10/ Séminaire du LUTh - Jérôme Guilet 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

3 07/10/ Séminaire du LUTh - Jérôme Guilet 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

4 07/10/ Séminaire du LUTh - Jérôme Guilet Polarization Pulsar kicks Indications of explosion asymmetry Pulsars have high peculiar velocities : ~ 400 km.s -1, up to >1000 km.s -1 probably originated from asymmetries in supernova explosion guitar nebula

5 07/10/ Séminaire du LUTh - Jérôme Guilet 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

6 07/10/ Séminaire du LUTh - Jérôme Guilet 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 Proto neutron star neutrinosphere (r~30-80km) shock (r~200km) gain radius collapsing core

7 07/10/ Séminaire du LUTh - Jérôme Guilet 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

8 07/10/ Séminaire du LUTh - Jérôme Guilet 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 SASI induces g-mode oscillations of the neutron star - Acoustic power revives the shock

9 07/10/ Séminaire du LUTh - Jérôme Guilet 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

10 07/10/ Séminaire du LUTh - Jérôme Guilet 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

11 07/10/ Séminaire du LUTh - Jérôme Guilet 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

12 07/10/ Séminaire du LUTh - Jérôme Guilet Two competing mechanisms Purely acoustic mechanism Advective-acoustic cycle neutron star shock entropy-vorticity wave neutron star shock acoustic wave Foglizzo et al 2007 Blondin & Mezzacappa 2006 Advective-acoustic cycle favored by a WKB analysis BUT :valid for high frequency modes only...

13 07/10/ Séminaire du LUTh - Jérôme Guilet 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) frequency r sh = 2.5r PNS Advective-acoustic cycle wins !

14 07/10/ Séminaire du LUTh - Jérôme Guilet 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

15 07/10/ Séminaire du LUTh - Jérôme Guilet Saturation by parasitic instabilities advective-acoustic cycle => Saturation entropy-vorticity wave

16 07/10/ Séminaire du LUTh - Jérôme Guilet 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

17 07/10/ Séminaire du LUTh - Jérôme Guilet small amplitude entropy wave large amplitude entropy wave potential step decelerating the flow

18 07/10/ Séminaire du LUTh - Jérôme Guilet Efficiency of the acoustic feedback Kelvin-Helmholtz (entropy-vorticity wave) Rayleigh-Taylor (entropy wave)

19 07/10/ Séminaire du LUTh - Jérôme Guilet Dissociation energy increases & neutrino cooling decreases Fernandez &Thompson 2009 Scheck et al 2008

20 07/10/ Séminaire du LUTh - Jérôme Guilet Estimate of the saturation amplitude Criterion : Result : Rayleigh-Taylor is responsible for the saturation Stratification advection SASI growth rate This saturation mechanism seems to work well ! Guilet et al 2010

21 07/10/ Séminaire du LUTh - Jérôme Guilet 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

22 07/10/ Séminaire du LUTh - Jérôme Guilet Neutrino driven explosion Magnetic explosion - no magnetic field - Magnetic field amplification: B ~10 15 G - Obtains for VERY rapid rotation Marek & Janka 2009 Burrows et al Moderate field effect ?

23 07/10/ Séminaire du LUTh - Jérôme Guilet 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

24 07/10/ Séminaire du LUTh - Jérôme Guilet A toy model for SASI in a magnetized flow neutron star shock or B planar adiabatic toy model (Foglizzo 2009) v « neutron star » shock deceleration by an external potential Advective-acoustic cycle with a magnetic field : vorticity can propagate through Alfvén and slow waves ! decelerated flow supersonic flow neutrino cooling

25 07/10/ Séminaire du LUTh - Jérôme Guilet Interference between vorticity cycles Propagation of the vorticity different cycles are out of phase Entropy Vorticity : Alfvén and slow waves Wave -Wave + choc  ~v A ~B growth rate magnetic field strength The advective-acoustic cycle separates in up to 5 cycles ! Guilet & Foglizzo 2010

26 07/10/ Séminaire du LUTh - Jérôme Guilet 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 v A ~v magnetic field strength growth rate coupling efficiency Conclusion : Ambiguous result...

27 07/10/ Séminaire du LUTh - Jérôme Guilet 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

28 07/10/ Séminaire du LUTh - Jérôme Guilet Alfvén surface simulations The alfvén surface is defined by : v = v A Alfvén speed : v A 2 = B 2 /(    An Alfvén wave propagates against the flow at the speed : v-v A Accumulation of Alfvén waves at the Alfvén surface ! We performed 1D simulations with the code RAMSES

29 07/10/ Séminaire du LUTh - Jérôme Guilet 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

30 07/10/ Séminaire du LUTh - Jérôme Guilet Analytical estimate versus simulations Small amplitude Alfvén wave Non linear saturation frequency incident amplitude (Guilet et al submitted to ApJ)

31 07/10/ Séminaire du LUTh - Jérôme Guilet 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 !!!

32 07/10/ Séminaire du LUTh - Jérôme Guilet 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

33 07/10/ Séminaire du LUTh - Jérôme Guilet 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 v A ~ 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

34 07/10/ Séminaire du LUTh - Jérôme Guilet 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

35 07/10/ Séminaire du LUTh - Jérôme Guilet Frequencies and associated timescales Fundamental mode (most unstable) –advective-acoustic time –azimuthal acoustic time Higher harmonics : -> radial propagation time... Acoustic modes of a box LzLz LxLx Analogy L r =r sh -r * Lx=rLx=r frequency

36 07/10/ Séminaire du LUTh - Jérôme Guilet Radial time in a simplified model of SASI acoustic advective-acoustic timescale Extracted from SASI eigenspectrum : shock position

37 07/10/ Séminaire du LUTh - Jérôme Guilet 6 cycles (instead of 2) Coupling at the shock Cycle efficiencies : 2 cycles Alfvén fast magnetosonic 1 cycle fast 1 cycle entropy 2 cycles slow « neutron star » shock coupling in the gradients