A global model of the magneto-rotational instability in ... · J. Guilet , R. Raynaud , M. Bugli 1...

ERC MagBURST

A global model of the magneto-rotational instability in proto-neutron stars

Alexis Reboul-Salze

J. Guilet , R. Raynaud , M. Bugli

1 : AIM, CEA Paris-Saclay

29th March 2019, Alexis Reboul-Salze�1

1

1 1 1

Motivation : Magnetars

• Radio Observations• Hard X-Ray and Soft Gamma

observations -> Anomalous X-Ray Pulsar

-> Soft Gamma Repeater

How to measure the B field -> Period + Spin down measurement

• Dipolar magnetic field strength of magnetars :

->


Bmagnetar ⇡ 1014 � 1015GCrédit : Rea et al. 2012

P � P diagram<latexit sha1_base64="TA5eYqWhT8Z7YCA0PJxZOQ2LQ+Y=">AAAB/XicdVDLSgMxFM3UV62v8bFzE2wFN5aZFtq6K7hxOYJthXYomTTThiaZIckIdSj+ihsXirj1P9z5N2baUlT0QOByzr0395wgZlRpx/m0ciura+sb+c3C1vbO7p69f9BWUSIxaeGIRfI2QIowKkhLU83IbSwJ4gEjnWB8memdOyIVjcSNnsTE52goaEgx0obq20cl77w3iHTqTUsQDigaSsT7dtEpX9QrVbcB3bIzAzRMza059SVTBAt4ffvD7MAJJ0JjhpTquk6s/RRJTTEj00IvUSRGeIyGpGtKgThRfjq7fgpPDTOAYSTNExrO2O8TKeJKTXhgOjnSI/Vby8i/tG6iw4afUhEnmgg8/yhMGNQRzKIwbiXBmk0y21hScyvEIyQR1iawgglh6f3/ol0pu9Wyc10pNhuLOPLgGJyAM+CCOmiCK+CBFsDgHjyCZ/BiPVhP1qv1Nm/NWYuZQ/AD1vsXOsuUag==</latexit>

Bdip = 1014( P5 s )

12 ( P

10�11 s s�1 )12 G

<latexit sha1_base64="mujz4ZTEKgtv/RRtJSW4LJ17cz0=">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</latexit>

Magnetars

See Marta Burgay’s talk and Diego Gotz’s talk

Neutron star formation

Elbereth Conference, Alexis Reboul-Salze�3

Core-Collapse Supernova

Hydrogène

Hélium

Oxygène

Fer

Hydrogen

Helium

Oxygene

Iron

600 millions km Iron

MFer ⇡ 1.4M�3000 km

Main sequence stars :

See Jacco Vink’s talk




Hydrogène

Hélium

Oxygène

Fer

Hydrogen

Helium

Oxygene

Iron


MFer ⇡ 1.4M�3000 km

NS

Iron

NS

1 s

Rebound and stalling shockMain sequence stars :





Hydrogène

Hélium

Oxygène

Fer

Hydrogen

Helium

Oxygene

Iron


MFer ⇡ 1.4M�3000 km

NS

Iron

NS

1 s

NSNS

Revived shock and explosion

Rebound and stalling shock

Proto-Neutron Star Neutrino emission

Main sequence stars :


Supernova observations

Extreme explosions


Kinetic energy of the explosion → Classic Supernova 1051 ergs → Hypernova (rare) (<1 %) 1052 ergs

Luminosity of the supernova : → Classic Supernova 1049 ergs → Super-Luminous Supernova (<0.1%) 1051 ergs

Outstanding explosions : millisecond magnetars ?


Extreme explosions




Neutrino-driven mechanismMagneto-rotational

e.g. Burrows+07, Takiwaki+09,11Bucciantini+09, Metzger+11, Obergaulinger+17


Luminosity curves fitted by a magnetar model with:

-> Strong dipole field : -> Fast Rotation : P ~ 1-10 ms

e.g. Kasen+10, Dessart+12, Nicholl+13, Inserra+13

B ⇡ 1014 � 1015G


Extreme explosions





Neutrino-driven mechanism

e.g. Burrows+07, Takiwaki+09,11Bucciantini+09, Metzger+11, Obergaulinger+17

Magneto-rotational

Open theoretical question : magnetic field origin


Compression of stellar field in core collapse supernovæ : <1012-1013 G (?)

Magnetic field of NS before merger : 108-1012 G

Magnetar dipolar strength : ~ 1014-1015 G

Amplification mechanism ?

Magnetorotational instability Convective dynamo

Both SN & mergers Both SN & mergers

Similar to accretion disks Similar to planetary & stellar dynamos

Outline

I- Presentation of the local models of the MRI

II- A global model of the MRI

III- Preliminary parameter study


Amplification mechanism : magneto-rotational instability (MRI)


Fromang et al. 2012

Instability criterion :

Growth rate:-> Fast growth for fast rotation Wavelength : -> Short wavelength for weak magnetic fields

d⌦

dr< 0

�MRI / B⇢⌦

MRI mechanism in a simple case :

� = q⌦2 with ⌦ / r�q

<latexit sha1_base64="P3/A4V5t4jbWCkjJhzfSew7ByHc=">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</latexit>

Local models in accretion disks


Turbulence MHD : toroidal field“Shearing box” models

Figure courtesy : G. Lesur Fromang et al. 2007

Guilet et al. 2015Guilet & Müller 2015

viscousMRI

idealMRI

Magnetic field amplification in local models


br field at different

Stable stratification

Buoyancy parameter

Mag

netic

ene

rgy

in u

nits

of (

1015

G)2

azimuthal magnetic field

Neutrino Impact Buoyancy impact

Crédit : Guilet and Müller. 2016

Guilet et al. (2015), Guilet et al. (2017)

Slow growth for weak initial magnetic field

Two regimes : Focus on the viscous regime

First attempt at a global model


Mösta et al 2015

• First time high enough resolution

• Initial strong dipolar field

• High computational costs

Outline

II- A global model of the MRI in a PNS


/ r�q<latexit sha1_base64="5Nbs/yvF5UQD6OHqfaPoYS7IlMg=">AAAB+XicbVBNSwMxEJ2tX7V+rXr0EiyCF8uuCnosevFYwX5Ady3ZNG1Ds9mYZAtl6T/x4kERr/4Tb/4b03YP2vpg4PHeDDPzIsmZNp737RRWVtfWN4qbpa3tnd09d/+goZNUEVonCU9UK8KaciZo3TDDaUsqiuOI02Y0vJ36zRFVmiXiwYwlDWPcF6zHCDZW6rhuIFUiTYICpB6zs6dJxy17FW8GtEz8nJQhR63jfgXdhKQxFYZwrHXb96QJM6wMI5xOSkGqqcRkiPu0banAMdVhNrt8gk6s0kW9RNkSBs3U3xMZjrUex5HtjLEZ6EVvKv7ntVPTuw4zJmRqqCDzRb2UI/vpNAbUZYoSw8eWYKKYvRWRAVaYGBtWyYbgL768TBrnFf+i4t1flqs3eRxFOIJjOAUfrqAKd1CDOhAYwTO8wpuTOS/Ou/Mxby04+cwh/IHz+QMctJNP</latexit>

Core in solid body rotation

Then :

Omega profile

Our setup

• Simplest model : Incompressible Nr = 256, Ntheta = 512, Nphi = 1024

• Initial velocity is fixed at the outer boundary

• Typical parameters values : B0 = 9x1014, Pm = 16 and Re = 5000


Magnetic field profile

⌦ = 103 s�1, ⌫ = 8 · 1011 cm2s�1, ⌘ = 5 · 1010 cm2s�1,r = 25 km, Bmean = 8.97 · 1014

Small scales ~ Local models

Amplitude of the magnetic field


�⌦

Results on the magnetic and dipole energies


Time Evolution of dipolar energy Dipolar tilt angle

Bdip ⇡ 1.25 1014 G<latexit sha1_base64="VL409jygMXACrkgy8s8TUDekEv0=">AAACC3icbVC7TsMwFHV4lvIKMLJYbZGYoqSAYKzKAGOR6ENqSuS4TmvVSSzbQVRRdhZ+hYUBhFj5ATb+BrfNAC1HutLROffq3nt8zqhUtv1tLC2vrK6tFzaKm1vbO7vm3n5LxonApIljFouOjyRhNCJNRRUjHS4ICn1G2v7ocuK374mQNI5u1ZiTXogGEQ0oRkpLnlmq1L20T3kGXcS5iB+gY1XPoAsd+y51TrMKvPLMsm3ZU8BF4uSkDHI0PPPL7cc4CUmkMENSdh2bq16KhKKYkazoJpJwhEdoQLqaRigkspdOf8ngkVb6MIiFrkjBqfp7IkWhlOPQ150hUkM5703E/7xuooKLXkojnigS4dmiIGFQxXASDOxTQbBiY00QFlTfCvEQCYSVjq+oQ3DmX14krarlnFj2TbVcq+dxFMAhKIFj4IBzUAPXoAGaAINH8AxewZvxZLwY78bHrHXJyGcOwB8Ynz+m2Zg4</latexit>

Axial dipole

Total dipole

Total magnetic energy

Btot ⇡ 2.5 1015 G<latexit sha1_base64="zLmFV0Mkp9WVVA/xMcR8NT1Ibm8=">AAACCnicbVA9TwJBEN3zE/Hr1NJmFUysyB2GaEmw0BIT+Ug4JHvLAhv2bi+7c0Zyobbxr9hYaIytv8DOf+MCVyj4kkle3pvJzDw/ElyD43xbS8srq2vrmY3s5tb2zq69t1/XMlaU1agUUjV9opngIasBB8GakWIk8AVr+MPLid+4Z0pzGd7CKGLtgPRD3uOUgJE69lG+0klAwhh7JIqUfMDFQgl72HXuErc0zuOrjp1zCs4UeJG4KcmhFNWO/eV1JY0DFgIVROuW60TQTogCTgUbZ71Ys4jQIemzlqEhCZhuJ9NXxvjEKF3ck8pUCHiq/p5ISKD1KPBNZ0BgoOe9ifif14qhd9FOeBjFwEI6W9SLBQaJJ7ngLleMghgZQqji5lZMB0QRCia9rAnBnX95kdSLBfes4NwUc+VKGkcGHaJjdIpcdI7K6BpVUQ1R9Iie0St6s56sF+vd+pi1LlnpzAH6A+vzB1nQmBg=</latexit>

Outline

III-Preliminary parameter study


Small impact of initial conditions and boundary conditions


Mode length

Tota

l mag

netic

am

plitu

de (i

n un

its o

f 101

5 G)

Maximum amplification (in units of 1015 G)

Mode length

Tota

l mag

netic

am

plitu

de (i

n un

its o

f 101

5 G)

Maximum amplification (in units of 1015 G)

Small impact of initial conditions and boundary conditions


Bavg = 1.8� 2.7⇥ 1015 G<latexit sha1_base64="txMueAoEQzcqRIU6dhN0E+IcC5I=">AAACDXicbVC7SgNBFJ31GeNr1dJmMBFsXHYikjRCiIWWEcwDknWZncwmQ2YfzMwGwrI/YOOv2FgoYmtv5984eRSaeODC4Zx7ufceL+ZMKtv+NlZW19Y3NnNb+e2d3b198+CwKaNEENogEY9E28OSchbShmKK03YsKA48Tlve8Hrit0ZUSBaF92ocUyfA/ZD5jGClJdcsFmtuikf9DF5BZFXOS1YZdhULqITIfkjRZVaEN65ZsC17CrhM0JwUwBx11/zq9iKSBDRUhGMpO8iOlZNioRjhNMt3E0ljTIa4Tzuahljvc9LpNxk81UoP+pHQFSo4VX9PpDiQchx4ujPAaiAXvYn4n9dJlF9xUhbGiaIhmS3yEw5VBCfRwB4TlCg+1gQTwfStkAywwETpAPM6BLT48jJplix0Ydl3pUK1No8jB47BCTgDCJRBFdyCOmgAAh7BM3gFb8aT8WK8Gx+z1hVjPnME/sD4/AHwn5hM</latexit>

Mode length

Dipole strength depends on total magnetic field


Dipolar magnetic strength

Dipo

lar m

agne

tic s

treng

th (i

n un

its o

f (10

15 G

)2 )

Total magnetic energy (in units of (1015 G)2)

Edip / Etot<latexit sha1_base64="bl3gXIa92T43oh65O4JqF6bKxu0=">AAACBHicbVDLSgMxFM3UV62vqstugkVwVWZU0GVRBJcV7AM6Q8mkmTY0MwnJHaEMs3Djr7hxoYhbP8Kdf2P6WGjrgcDhnHu5OSdUghtw3W+nsLK6tr5R3Cxtbe/s7pX3D1pGppqyJpVC6k5IDBM8YU3gIFhHaUbiULB2OLqe+O0Hpg2XyT2MFQtiMkh4xCkBK/XKlZte1ucqxz72lZYKpGVWAwl5r1x1a+4UeJl4c1JFczR65S+/L2kaswSoIMZ0PVdBkBENnAqWl/zUMEXoiAxY19KExMwE2TREjo+t0seR1PYlgKfq742MxMaM49BOxgSGZtGbiP953RSiyyDjiUqBJXR2KEoFtlEnjeA+14yCGFtCqOb2r5gOiSYUbG8lW4K3GHmZtE5r3lnNvTuv1q/mdRRRBR2hE+ShC1RHt6iBmoiiR/SMXtGb8+S8OO/Ox2y04Mx3DtEfOJ8/Go2Xvw==</latexit>

Bdip / Btot<latexit sha1_base64="qsVw4g3F3cVTVAmhaJUXS+4hhvU=">AAACBHicbVC7TsMwFHXKq5RXgLGLRYvEVCVlgLEqC2OR6ENqo8hx3daqE1v2DVIVdWDhV1gYQIiVj2Djb3AfA7QcydLROffq+pxICW7A876d3Mbm1vZOfrewt39weOQen7SMTDVlTSqF1J2IGCZ4wprAQbCO0ozEkWDtaHwz89sPTBsuk3uYKBbEZJjwAacErBS6xTKuh1mfqynGPaWlAjkTQMK0HLolr+LNgdeJvyQltEQjdL96fUnTmCVABTGm63sKgoxo4FSwaaGXGqYIHZMh61qakJiZIJuHmOJzq/TxQGr7EsBz9fdGRmJjJnFkJ2MCI7PqzcT/vG4Kg+sg44lKgSV0cWiQCmyTzhrBfa4ZBTGxhFDN7V8xHRFNKNjeCrYEfzXyOmlVK/5lpXpXLdXqyzryqIjO0AXy0RWqoVvUQE1E0SN6Rq/ozXlyXpx352MxmnOWO6foD5zPH12el0k=</latexit>

Mode length

Summary and perspectives


• Summary : Magnetar-like magnetic field strength

A dipole is robustly generated by the small scales

• Perspectives :

Influence of diffusion processes —> Towards more realistic values in models

Add the buoyancy force (stable stratification)

Implement a realistic EoS Interaction with a convective dynamo ?

Sub-grid modelling of the MRI for Magneto-rotational Explosions ?

Conclusions

THANK YOU


ERC Magburst

Soutenance de PFE, Alexis Reboul-Salze�25

~ 1-5 km ~ 10-50 km ~ 105-106 km

Step 1 : Local model of the MRI Step 2 : Global model Etape 3 : Hypernova

Jérôme Guilet Alexis Reboul-Salze & Raphaël Raynaud

(Convective dynamo)Matteo Bugli

Bucciantini+09

See Matteo Bugli’s talk

Conclusions

THANK YOU


A global model of the magneto-rotational instability in ... · J. Guilet , R. Raynaud , M. Bugli 1...

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