How to form a millisecond magnetar ? Magnetic field amplification - PowerPoint PPT Presentation

How to form a millisecond magnetar ? Magnetic field amplification in protoneutron stars Jérôme Guilet Max-Planck-Princeton Center for plasma physics (MPA, Garching) 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

Core collapse: formation of a neutron star Introduction Massive star Hydrogen Explosion NS NS Helium 600 millions km Oxygen Iron ? Iron  -sphere Stalled accretion Iron 40 km 3000 km NS shock 1.4 M sol Neutrino emission Collapse of the iron core Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 3/33

A diversity of explosions Introduction Explosion kinetic energy : → Typical supernova 10 51 ergs → Neutrino driven explosions ? e.g. Bruenn+14, Melson+15 → Rare hypernova (& GRB) 10 52 ergs → Millisecond magnetar ? e.g. Burrows+07, Takiwaki+09,11 Bucciantini+09, Metzger+11 Total luminosity : → Typical supernova 10 49 ergs → Superluminous supernovae 10 51 ergs → Millisecond magnetar ? e.g. Woosley+10, Dessart+12, Nicholl+13, Inserra+13 Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 4/33

Magnetic explosions ? Introduction Strong magnetic field: B ~ 10 15 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 ~ 10 14 -10 15 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

Galactic magnetars Introduction Magnetars: Anomalous X-ray pulsars (AXP) Soft gamma repeater (SGR) Strong dipole magnetic field: B ~ 10 14 -10 15 G Slow rotation: P ~ 1-10 s Typical age: 10 4 -10 5 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

The magnetorotational instability (MRI) Introduction 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

Rotation profile in the proto-neutron star Introduction Hydrostatic Infalling matter proto-neutron star 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

Proto-neutron stars vs disks conditions Introduction 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

Effects of neutrino radiation : two regimes MRI growth 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 with neutrino viscosity MRI growth 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 > 10 12 G... Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 14/33

MRI with neutrino drag MRI growth 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: different regimes MRI growth Guilet et al (2015) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 16/33

Application to neutron star mergers MRI growth massive torus neutron star 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 Numerical simulations: local models amplification - 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

Channel mode termination by parasitic magnetic field 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

Buoyancy from entropy and lepton MRI & buoyancy 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), radial displacement suppressed radial displacement favored Masada et al (2007) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 22/33

Linear MRI growth with buoyancy MRI & buoyancy Low thermal diffusion High thermal diffusion Confirms linear analysis : thermal diffusion by neutrinos allows fast MRI growth Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 23/33

Impact of stratification on the MRI MRI & buoyancy unstable buoyancy stable stratification color: azimuthal magnetic field units of (10 15 G) 2 Magnetic energy low diffusion high diffusion buoyancy parameter Guilet & Müller (2015) Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 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 (10 15 G) 2 Behaviour at very large magnetic Prandtl number ? Jérôme Guilet (MPA Garching) – Formation of millisecond magnetars 27/33