How to form a millisecond magnetar ? Magnetic field amplification in protoneutron stars Jérôme Guilet Max-Planck-Princeton Center (MPA, Garching) for plasma physics collaborators Ewald Müller, Thomas Janka, Oliver Just (MPA Garching) Andreas Bauswein (Heidelberg) Tomasz Rembiasz, Martin Obergaulinger, Pablo Cerda-Duran, Miguel Angel Alloy (Valencia) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 1/33 Plan of the talk 1. Introduction : Magnetic fields in core collapse supernovae 2. Can the magnetorotational instability grow ? Linear analysis → Effects of neutrino radiation 3. How strong is the final magnetic field ? Numerical simulations → Channel mode termination → Influence of buoyancy → Dependence on the magnetic Prandtl number → The dawn of global simulations 4. Conclusion & perspectives Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 2/33 Introduction Core collapse: formation of a neutron star Massive star Hydrogen NS Explosion Helium 600 millions km Oxygen Iron ? Iron -sphere Stalled accretion Iron 40 km 3000 km NS shock 1.4 Msol Collapse of the iron core Neutrino emission Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 3/33 Introduction A diversity of explosions Explosion kinetic energy : → Typical supernova 1051 ergs → Neutrino driven explosions ? e.g. Bruenn+14, Melson+15 52 → Rare hypernova (& GRB) 10 ergs → Millisecond magnetar ? e.g. Burrows+07, Takiwaki+09,11 Bucciantini+09, Metzger+11 Total luminosity : → Typical supernova 1049 ergs → Superluminous supernovae 1051 ergs → Millisecond magnetar ? e.g. Woosley+10, Dessart+12, Nicholl+13, Inserra+13 Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 4/33 Introduction Magnetic explosions ? Strong magnetic field: B ~ 1015 G + fast rotation (period of few milliseconds) => powerful jet-driven explosions ! e.g. Sibata+06, Burrows+07, Dessart+08, Takiwaki+09,11, Winteler+12 Burrows+07 But in 3D, jets can be unstable to kink instability Moesta+2014 Open question: Can magnetic explosions explain hypernovae ? Moesta+14 Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 5/33 Are millisecond magnetars powering Introduction superluminous supernovae ? Delayed energy injection by magnetar spin- down on timescale of weeks-months => very high luminosity Light curves can be fitted by: - strong dipole magnetic field: B ~ 1014-1015 G - fast rotation: P ~ 1-10 ms Talk by Ken Chen last week Inserra+2013 Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 6/33 Introduction Galactic magnetars Magnetars: Anomalous X-ray pulsars (AXP) Soft gamma repeater (SGR) Strong dipole magnetic field: B ~ 1014-1015 G Slow rotation: P ~ 1-10 s Typical age: 4 5 10 -10 years Talks by Michael Gabler & Pablo Cerda-Duran Rotation at birth unknown: were some or all of them born as millisecond magnetars ? Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 7/33 Missing theoretical piece: Introduction magnetic field origin Huge range of magnetic field strength : → Initially « weak » magnetic field : ( ? ) → After compression by the core-collapse: ( ? ) → Magnetar strength : Amplification mechanism ? Magnetorotational instability (MRI) ? Convective dynamo ? Similar to accretion disks Similar to solar & planetary dynamos → application to protoneutron stars → need of numerical simulations for neutron stars Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 8/33 Introduction The magnetorotational instability (MRI) B In ideal MHD (i.e. no resistivity or viscosity) : Condition for MRI growth Growth rate : with → Fast growth for fast rotation Wavelength : → Short wavelength for weak magnetic field Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 9/33 Introduction Rotation profile in the proto-neutron star Hydrostatic proto-neutron star Infalling matter Rotation frequency profile : → Differential rotation at radii > 10 km Rotation frequency decreases with radius : => MRI unstable ! Akiyama et al (2003) Obergaulinger et al (2009) Radius (km) Ott et al (2006) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 10/33 Introduction Proto-neutron stars vs disks conditions Main differences between proto-neutron stars and accretion disks: → Neutrinos: viscosity and drag → Prevent MRI growth ? → Buoyancy: radial entropy and composition gradients → Impact on magnetic field amplification by MRI ? → Geometry: spherical vs thin disk → Help global coherence ? neutrinos ! Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 11/33 2. Can the magnetorotational instability (MRI) grow ? Effects of neutrino radiation Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 12/33 MRI growth Effects of neutrino radiation : two regimes density scaleheight neutrino mean free path diffusive regime : neutrino viscosity optically thin regime : neutrino drag Neutron star structure from a simulation by Hanke et al (2013) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 13/33 MRI growth MRI with neutrino viscosity ideal MRI viscous MRI viscous ideal MRI MRI Too slow Dimensionless number : e.g. Pessah & Chan (2008) MRI growth requires a minimum initial magnetic field strength of > 1012 G... Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 14/33 MRI growth MRI with neutrino drag ideal MRI ideal « dragged » « dragged » MRI MRI MRI Neutrino drag : , with damping rate : The MRI can grow near the PNS surface from any weak field strength ! Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 15/33 MRI growth MRI growth: different regimes Guilet et al (2015) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 16/33 MRI growth Application to neutron star mergers massive neutron star torus Guilet+2016 Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 17/33 3. How strong is the final magnetic field ? → Channel mode termination → Influence of buoyancy → Dependence on the magnetic Prandtl number → The dawn of global simulations Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 18/33 magnetic field amplification Numerical simulations: local models - Small box : ~km size at a radius r ~ 20-40 km - Differential rotation => shearing periodic boundary conditions - Entropy/composition gradients + - Different numerical methods : spectral or finite volume - Fully compressible or quasi-incompressible approximation Obergaulinger+2009, Masada+2012, Guilet+2015, Rembiasz+2016a,b Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 19/33 magnetic field Channel mode termination by parasitic amplification instabilities Rembiasz et al. 2016a&b Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 20/33 3. How strong is the final magnetic field ? → Channel mode termination → Influence of buoyancy → Dependence on the magnetic Prandtl number → The dawn of global simulations Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 21/33 MRI & buoyancy Buoyancy from entropy and lepton fraction gradients Brünt-Väisälä frequency : Linear analysis of MRI with buoyancy : stable buoyancy can stabilise the MRI But : thermal diffusion allows the growth Balbus & Hawley (1994), Menou et al (2003), Masada et al (2007) radial displacement suppressedfavored Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 22/33 MRI & buoyancy Linear MRI growth with buoyancy High thermal diffusion Low thermal diffusion Confirms linear analysis : thermal diffusion by neutrinos allows fast MRI growth Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 23/33 MRI &MRI buoyancy Jérôme Guilet (MPA Garching) – Formation of millisecond of magnetars Formation – Garching) (MPA Guilet Jérôme Guilet & Müller(2015) unstable buoyancy unstable Magnetic energy Impact of stratification on the MRI units of (1015 G)2 buoyancy parameter color: azimuthal color: magnetic field magnetic high diffusion low diffusion stable stratification stratification stable 24 /33 3. How strong is the final magnetic field ? → Channel mode termination → Influence of buoyancy → Dependence on the magnetic Prandtl number → The dawn of global simulations Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 25/33 Magnetic Prandtl Dependence on the magnetic Prandtl number number Neutrino viscosity : Resistivity : Magnetic Prandtl number : Previous simulations used : Behaviour at very large magnetic Prandtl number ? Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 26/33 Magnetic Prandtl Dependence on the magnetic Prandtl number number Magnetic energy units of (1015 G)2 Behaviour at very large magnetic Prandtl number ? Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 27/33 3. How strong is the final magnetic field ? → Channel mode termination → Influence of buoyancy → Dependence on the magnetic Prandtl number → The dawn of global simulations Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 28/33 Global simulations Semi-global simulations Local in vertical direction global in horizontal direction Good vertical resolution but low horizontal resolution Masada+14 Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 29/33 Global simulations Global models Moesta+2015 : first simulation with large-scale magnetic field generation.. but started with magnetar strength dipolar field Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 30/33 Global simulations A simplified full-sphere MRI simulation Preliminary simulations of a simplified model