BH-NS MAGNETOSPHERE collaborator Masaru Shibata (YITP, AEI) - - PowerPoint PPT Presentation

BH-NS MAGNETOSPHERE

YITP

和田知己

collaborator Masaru Shibata 
 (YITP, AEI)

(Tomoki Wada)

高エネルギー宇宙物理学研究会 2018

Binary Black Hole → GW150916, .. 5 detection Binary Neutron Star → GW170817 & GRB170817A, macronova, afterglow

γ-ray Radio

Electromagnetic Counterpart was detected !!!

GW ASTRONOMY

∼

Binary Black Hole → GW150916, …5.5 detection Binary Neutron Star → GW170817 & GRB170817A, macronova, afterglow

γ-ray Radio

Electromagnetic Counterpart was detected !!!

GW ASTRONOMY

∼

What can we detect with GW from BH-NS merger ???

What happens with BH-NS merger？ Typically ・light BH → tidal disruption … destroyed NS will light ・heavy BH → NO tidal disruption

COUNTERPART WITH BH-NS MERGER

Nothing will light ??

MBH/MNS ≲ 5, a ≳ 0.5

（Else） （ ）

What happens with BH-NS merger？ Typically ・light BH → tidal disruption … destroyed NS will light ・heavy BH → NO tidal disruption

COUNTERPART WITH BH-NS MERGER

Nothing will light ??

MBH/MNS ≲ 5, a ≳ 0.5

（Else） （ ）

NS … STRONG MAGNETIC FIELD → LIGHT EMISSION？

・assume pulsar is dipole ・NS is conductor →. in coronation frame ・Poisson equation ・Electric field parallel to Magnetic field will accelerate charged particles

PULSAR MAGNETOSPHERE

⃗ E NS = − ( ⃗ Ω × ⃗ r) c × ⃗ B NS

⃗ B NS ⃗ B out Eout

∥

∼ ΩR c B

R

Eout

∥

⃗ B out

⃗ B NS

⃗ E out

e−

Eout ∼ ΩBNSR5 cr4

パ

LIGHT EMISSION

⃗ E = ⃗

・assume pulsar is dipole ・NS is conductor →. in coronation frame ・Poisson equation ・Electric field parallel to Magnetic field will accelerate charged particles

PULSAR MAGNETOSPHERE

⃗ E NS = − ( ⃗ Ω × ⃗ r) c × ⃗ B NS

⃗ B NS ⃗ B out Eout

∥

∼ ΩR c B

R

Eout

∥

⃗ B out

⃗ B NS

⃗ E out

e−

Eout ∼ ΩBNSR5 cr4

パ

LIGHT EMISSION

⃗ E = ⃗

IF THIS HAPPENS IN BH-NS BINARY, CHARGED PARTICLE WILL EMIT LIGHT →THIS CAN BE COUNTERPART OF GW FROM BH-NS MERGER

PROBLEM

Pulsar … accelerates particles Does exist in binary ?? Setting Consider magnetic dipole rotating BH Is there which accelerate particles from NS ??

Eout

∥

Calculate induced electric field

パ

Eout

∥

Eout

∥

AIM

Pulsar magnetosphere Binary magnetosphere Assume NS is dipole which is spinning → Calculate induced electric field → will accelerate particles

パ

Eout

∥

Assume NS is dipole which is rotating BH → Calculate induced electric field → is there ? Eout

∥

BASIC EQUATIONS

Maxwell equations （ in flat spacetime ） Current is rotating dipole

∂t ⃗ B + ⃗ ∇ × ⃗ E = 0

⃗ ∇ ⋅ ⃗ B = 0

∂t ⃗ E − ⃗ ∇ × ⃗ B = − 4π ⃗ J

⃗ ∇ ⋅ ⃗ E = 4πρ

mλμ ：magnetic moment

xμ

NS(τ) ：orbit of NS

：angular direction party even

VECTOR HARMONICS EXPANSION

Expand vector fields using vector harmonics Maxwell equations Time evolution equation

Blm

3

Blm

2

Blm

1 ：radial direction

：angular direction party odd

Bi

Blm

1

Blm

3

Blm

2

GREEN FUNCTION METHOD

・Fourier transformation

ωr jl(ωr) ωr h(1)

l (ωr)

BH NS

r

r = 0

Regular at

• utgoing wave at infinity

・give boundary condition Construct Green function & Solve equation

MAGNETIC FIELD

times vector harmonics & sum up l, m

ELECTRIC FIELD

times vector harmonics sum up l, m

ELECTRIC FIELD

times vector harmonics sum up l, m

WHAT IS HAPPENING ????

NUMERICAL ELECTRIC(Z=0)

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rEz0

/M

/M

2π Ω ∼ 60

R = 5

Mtot = 10M⊙

separation total mass

@ constant time surface

r ⋅ E

NUMERICAL ELECTRIC（ ）

rE

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rEz30

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rEz60

z=30 z=90

NUMERICAL MAGNETIC ( )

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rBz10

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rBz30

z=10 z=30

almost dipole dipole + spiral arm (radiation)

r ⋅ B

NUMERICAL MAGNETIC ( )

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rBz10

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rBz30

z=10 z=30

almost dipole dipole + spiral arm (radiation)

r ⋅ B

dipole radiative dipole

NUMERICAL MAGNETIC

z=60 z=100

almost spiral arm (radiation)

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rBz60

∼ 2π Ω

• 200
• 150
• 100
• 50

50 100 150 200

• 200 -150 -100 -50

50 100 150 200 y x 1000rBz100

spiral arm (radiation) radiative radiative

• 10
• 5

5 10 5 10 15 20 z x 50rE 5rB

IS THERE ??

There is and Particle acceleration will happen

PARTICLE ACCELERATION

Eout

∥

Eout

∥

z10cos

• 200
• 150
• 100-50 0 50 100

150 200 x

• 200
• 150
• 100
• 50

50 100 150 200 y

• 1
• 0.5

0.5 1 cos z60cos

• 200
• 150
• 100-50 0 50 100

150 200

• 200
• 150
• 100
• 50

50 100 150 200 y

• 1
• 0.5

0.5 1 cos

BINARY MAGNETOSPHERE

magnetosphere can’t be vacuum and may filled with plasma.. There are gaps in co-rotating magnetosphere particle acceleration & charged particle emits light

パ

Eout

∥

There is In binary, electromagnetic field changes dynamically → there must be many gaps

PARTICLE ACCELERATION

Order estimate of particle acceleration BH NS

r

R

Plasma

ρ ∼ E R ∼ v B(R) R ∼ mzΩ R3

Er ∼ mzΩ2R r2

Considering only mode

l = 1

PARTICLE ACCELERATION

BH NS

r

R

ρ ∼ E R ∼ v B(R) R ∼ mzΩ R3

Er(r) ∼ mzΩ2R r2

S ∼ R2

Emitting area Accelerating region

Racc ∼ Ω−1

L ∼ IV ∼ (ρcR2) ⋅ (Er(Racc) Racc)

∼ (mz)2Ω3R−1

acc

∝ R−6

PARTICLE ACCELERATION

BH NS

r

R

S ∼ R2

Emitting area

L ∼ (mz)2Ω3R−1

acc

∼ 1042 erg/s

• cf. rotating dipole

Accelerating region

Racc ∼ Ω−1

L ∼ IV ∼ (ρcR2) ⋅ (Er(Racc) Racc)

∼ (mz)2Ω3R−1

acc

∝ R−6

L ∼ ∝ R−7

SUMMARY

・BH-NS binary … there is especially near binary → magnetosphere must filled with plasma ・charged particle may be accelerated → luminosity → it can be electromagnetic counterpart as precursor

・frequency ・evaluate acceleration ・effect of plasma ・effect of GR

FUTURE WORK

L ∼ 1042 erg/s

Eout

∥