Magnetized binary neutron star merger
Kiuchi Kenta

Collaboration Shibata Masaru, Kyutoku Koutarou,
Hotokezaka Kenta, Sekiguchi Yuichirou

Y TPYUKAW A INSTITUTE FOR
THEORETICAL PHYSICS
1Introduction
High energy astrophysical phenomenae.g., binary black hole (BH), neutron star (NS) merger,
Supernovae, gravitational stellar collapse✓Density ∼ 1015 g/cm3 ⇒ Gravity, Strong interaction✓Temperature ∼ 1011K ⇒ Weak interaction✓Magnetic field ∼ 1011-15G ⇒ Electromagnetic interaction✓Asymmetric and dynamical feature ⇒ Numerical Modeling
Numerical Relativity = Solving Einstein eqs. +(magneto) hydrodynamics + (radiation field) to explore extreme
physics✓ Experiments of high energy
phenomena on computers✓ Theoretical prediction ofgravitational waves
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Introduction
Magnetic Fields of NS

Observed binary NS (BNS)（Manchester 04）

Clustering around 1.35-1.4 M

Period derivative(Lattimer & Paraksh 06)

Magnetic field ∼ 1011-15 G

Spin period✓Canonical total mass of BNS ⇒ 2.7-2.8 M
✓Canonical magnetic field strength ⇒ 1011-13 G✓Maximum mass of NS ⇒ Mmax= 1.97∓0.04 M(PSR J1614-2230)(Demorest+ 10)

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Introduction
Overview of BNS merger
InspiralAnimation by AEI & Koyamada lab.

Merger(B) Post merger (BH)

Mtotal < Mcritical(A) Post merger(Rapidly rotating NS)✓ Mcritical ≃ 1.3-1.7 Mmax (Hotokezaka+ 11)✓ Mtotal ∼2.7-2.8 M
✓Mmax= 1.97∓0.04 M ⇒ “Realistic” path is (A)Mtotal > Mcritical

BH formation ?

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Introduction
Magnetic field amplification mechanism✓ Magnetic winding
Differential rotation (Angular velocity Ω≠ const.) ⇒ B ∝ t α
Magnetic field line
Rotation✓ Magneto rotational instability (Balbus & Hawley 91)
Differential rotation (∇Ω < 0) ⇒ B ∝ e α t
deceleration
Center×
Fluid element
Magnetic field line×acceleration
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Motivation
Points✓Case for Mtotal<Mcritical : Rapid rotating NS formation✓Case for Mtotal>Mcritical : BH formation✓ Initial magnetic field configuration （Previous works : Confinedmagnetic fields (see below)）
Confined field line (Liu+08)

Dipole field line

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Set up✓Total mass : 1.35-1.35 M (NS formation)or 1.45-1.45 M(BH formation)✓EOS (P ∝ ρΓ(ρ)) ⇒ Mmax > 1.97∓0.04 M✓Dipole field (1013G) or Confined field (1013G)
Density on the orbital plane

NS formation case
Vector = velocity

Magnetic field amplification inside NS7

Numerical Results
Density on the merdional plane
BH formation case

Magnetic field amplification inside the accretion disk around BH

8Numerical Results
Magnetic filed on the meridional plane
NS formation case
Initial confined field
Initial dipole field

Initial fields are completely destroyed and amplified

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Numerical Results
Central density

Maximum magnetic fieldMerger
Secular evolution

NS oscillation✓Dynamics does not depend on the magnetic field configuration✓ Until ∼70ms、 power law amplification (B∝ t1.3)✓For 70-90 ms, exponential growth (B ∝e0.09t)✓After 90ms、saturation
10✓ Qualitatively same feature for the confined modelNumerical Results✓Power law amplification (B∝ t1.3) ⇒ Magnetic winding✓Exponential growth (B ∝e0.09t) ⇒ Magneto Rotational Instability✓Recall that the condition for winding and MRI is ∇Ω < 0Angular velocity profileon the orbital plane

Wave length

Strong differential rotation
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Numerical ResultsBH formation case

Magnetic field amplification inside the accretion disk
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Numerical Results
Maximum magnetic field

Accretion disk massB ≠0

B =0

Angular momentum transport bymagnetic field✓Dominant toroidal field amplified by winding✓Saturation at 1016G✓More massive disk for B ≠0 model ⇒ favored model for
Gamma Ray Burst central engine

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Summary✓Numerical Relativity simulation for magnetized binary neutronstar merger✓ Long-lived massive NS (favored evolution path for observational
constraint with PSR J1614-2230)

Magnetic winding ⇒ Magneto Rotational Instability ⇒ Saturation
But, need a careful resolution study because of λMRI ∝ B✓BH formation (disfavored evolution path ?)Winding amplification up to 1016G and massive disk

✓Utilizing the technique developed here, we’ll explore the origin of
NS magnetic fields in HPCI Strategic program field 5 (SupernovaExplosion)
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Numerical Results
Magnetic field energy vs rotational energy
MRIwinding∼1051 erg

Emag ∼0.01 Erotでsaturation
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