Particle acceleration ina starved magnetosphereof a Kerr black hole
Shota Kisaka(FRIS, Tohoku Univ.)
Amir Levinson (Tel Aviv Univ.)
Kenji Toma (FRIS, Tohoku Univ.)Benoît Cerutti (Univ. Grenoble Alpes)

Plasma Injection Problem

・MeV Photon annihilation:
y
a
r
γ-

e- e+

n±
&1
nGJ

γ-r
ay

・Electromagnetic cascade:

y

e-

y
a
r
γ-

e+

M9

1/7

Levinson & Rieger 11
Hirotani & Pu 16(M87*, Sgr A*, isolated BHs, …)

E·B
Electric field Ek =6= 0
|B|・Large σ (>> 1)e- e+n± . nGJ
a
r
+
γ
ee

ṁ & 2 ⇥ 10

4

y
a
r
γ-

B-fielde+

Disk emission

E-field E||

・Non-ideal MHD condition
・Non-neutral charge
・Particle acceleration
・Pair creation
Difficult in MHD simulation

TeV Flare from Radio Galaxy
Aleksić+ 14

IC310

Flux doubling timescale < 4.8 min at 95% C.L.
corresponds to ~20% of the timescale rg/c.

→ Particle acceleration at sub-horizon scale?

Steady state?

Steady-state model(Assuming the gap position)

Beskin+ 92, Hirotani & Okamoto 98
Neronov & Aharonian 07, Rieger & Aharonian 08
Levinson & Rieger 11, Broderick & Tchekhovskoy 15
Hirotani & Pu 16, Hirotani+ 16, 17, 18a, 18b,
Levinson & Segev 17, Song+ 17, Lin+ 17,
Katsoulakos & Rieger 18

eDynamical model
Levinson & Cerutti 18
Chen, Yuan & Yang 18
Parfrey, Philippov & Cerutti 19
Chen & Yuan 19

Acceleration region
Acceleration region≠ Plasma injection region= Plasma injection regiondEke+e= 4⇡(⇢ ⇢GJ )+e e dxe- e++<latexit sha1_base64="gvaxSnCX5/ZX2eN0ZByvRD0S3MM=">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</latexit>

Accelregio erationne.g., pulsar outer gap

e-

e+

n
o
i
t
a
r
le
e
c
Ac ionrege.g., pulsar polar cap
black hole gap

1D PIC Model

Levinson & Cerutti 18
See also Chen & Yuan 19

・1-dimensional structure: the gap extends along a poloidal
magnetic surface as a function of θ.
→ Ignoring any MHD waves, considering only plasma oscillations.
・The gap constitutes a small disturbance.
→ The activity does not significantly affect the global structure(the B-field geometry and the angular velocity).
・Isotropic radiation field (from accretion disk) for seed photons.
Is (xµ , ✏s , ⌦s ) = I0 (✏s /✏s,min ) p , ✏s,min < ✏s < ✏s,max<latexit sha1_base64="lmetd4vlEqKOcwA986LF4HllJGU=">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</latexit>

JJ・No external plasma source.
・The global current is a free parameter.
・A split monopole geometry for the global B-field.
・The angular velocity of magnetic surface ⌦ = 0.5!H.
<latexit sha1_base64="FIoUPIjigMef9owCiuTmcOKdS1Y=">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</latexit>

Calculation
domainAccretion disk

Basic Equations
Gauss’s law

@µ (

p

tµ

gF ) = (<latexit sha1_base64="N1X74V0f0MWF/Az8RZpSqX3EkYM=">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</latexit>→
Contour of ρGJ
Null charge
surface

Levinson & Segev 17

p

t

gj )

Levinson & Cerutti 18

Basic Equations
Gauss’s law

@µ (

p

tµ

gF ) = (

p

t

gj )

<latexit sha1_base64="N1X74V0f0MWF/Az8RZpSqX3EkYM=">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</latexit>→
Ampère’s law(radial component)
p
p
rµ
@µ (
gF ) = (gj r )
J0<latexit sha1_base64="AgJ6bwpTR7oX5FG8RnxI1mj62zI=">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</latexit>→

J0

Calculation
domainLevinson & Cerutti 18

Particle-in-Cell Simulation
Solve EoM (e±, γ)

Photon production

Fp ! (xp , pp )(xe± , pe± ) ! (x , p )<latexit sha1_base64="OtdVPRm2YxEqv64sgiHU2DEFYAM=">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</latexit>

Pair production(x , p ) ! (xe± , pe± )t

Weighting<latexit sha1_base64="F5s/tPi5nugHMej8TkQTbkquS2k=">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</latexit>

Weighting(Ei , Bi ) ! Fp

(xe± , pe± ) ! (⇢i , ji )<latexit sha1_base64="f7gRImflvGYly0OVYuSb9PrESeA=">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</latexit>

Solve Maxwell eqs.
(⇢i , ji ) ! (Ei , Bi )

Parameters
Fiducial optical depth
Global current density
BH mass⌧0 = 4⇡rg T I0 /hc = 10<latexit sha1_base64="7es2BXSEM4+fZ6wCm0/3Lowwo0o=">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</latexit><latexit sha1_base64="dRplEZi2J+bB7UGygc7q7vc/h6g=">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</latexit>

j0 = 1.0(normalized by ρGJ,Hc)

MBH = 109 M<latexit sha1_base64="yj+x93+Bd2Pg9CN9GJXEW4upgOw=">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</latexit>

Dimensionless spin parameter
B-field on the horizona⇤ = 0.9<latexit sha1_base64="7pkSPR3yLhTFxxUbB34q9sx+hxs=">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</latexit>

BH = 2⇡ ⇥ 103 G<latexit sha1_base64="qGLvhoDG2L+K6+MvQYCL0xMn5Ik=">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</latexit>

Inclination angle of magnetic surface ✓ = 30
<latexit sha1_base64="xkSxiV2i8YKbWbqQnFcyl/mnZyc=">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</latexit>✏min = 10 9 (normalized by mec2)

Minimum energy of seed photon
Slope of seed photon spectrum<latexit sha1_base64="+TNu6rz/LEN/BrAEtzRtKSQ6R78=">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</latexit>

Curvature radius

p=2

Rcur = rg<latexit sha1_base64="oulvWjdZj07gxoLd4x9xfLyqing=">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</latexit>

Number of cells
N = 32768
rg
M9 BH,3
3
&
⇠ 10
lp
< 8>
<latexit sha1_base64="PVE3DMrfheXp/Tcmf3TVFWtudEQ=">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</latexit><latexit sha1_base64="xtV5sYzSMyTyvjBQaAvqesrfTcM=">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</latexit>

We neglect the scattering of particles with < 107 .
<latexit sha1_base64="VS0Uvahj7ogdlb8XOd3fI4JH7NU=">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</latexit>

Pair Multiplicity in Gap
Accelerated
e+ or eSeed photon✏1 (= ✏min )Scattered photon✏sc (⇠ min{ 2 ✏min , })Created e±

Seed photon✏2 (⇠ max{✏sc1 , ✏min })Required multiplicity in the gap ⇠ ⌧sc ⌧

&1

→

⌧0 &

r

⌧0 ⌧ 0⌧sc ⌧Pair Multiplicity
inGapr⌧0 ⌧ 0⌧sc ⌧⌧0 &⌧0 = 4⇡rg T I0 /hc = 10<latexit sha1_base64="7es2BXSEM4+fZ6wCm0/3Lowwo0o=">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</latexit>

e± quickly accelerate to the terminal Lorentz factor.
eEk = Prad /c⇠ max ⇠ 1010
<latexit sha1_base64="JnaEUpJFpgJS+fNaV/EJwx1ipa0=">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</latexit>✏min = 10 9✏min > 1 (Klein-Nishina regime)

Scattering optical depth⌧sc /⌧0 ⇠ ( ✏min ) 1

Pair creation optical depth⌧ /⌧0 ⇠ ( ✏min ) 1

Required optical depth
to screen E-field⌧0 & ✏minInsufficient Pair Creation

τ0 = 10, γmaxεmin ~ 100, different initial condition

Initial condition: e± beams

Initial condition: a photon beam

All photons and particles finally escapefrom the simulation box if τ0 < γmaxεmin.

Electric Currents
Polar region: j0 < 0Equatorial region : j0 > 0

j0 < 0j0 > 0j0 =Blandford & Znajek 77

1.0, 1.0 (normalized by ρGJ,Hc)

Parameters
Fiducial optical depth⌧0 = 30, 100, 300 >Global current densityj0 =BH mass

MBH = 109 M

max ✏min⇠ 10

1.0, 1.0 (normalized by ρGJ,Hc)<latexit sha1_base64="yj+x93+Bd2Pg9CN9GJXEW4upgOw=">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</latexit>

Dimensionless spin parameter
B-field on the horizona⇤ = 0.9<latexit sha1_base64="7pkSPR3yLhTFxxUbB34q9sx+hxs=">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</latexit>

BH = 2⇡ ⇥ 103 G<latexit sha1_base64="qGLvhoDG2L+K6+MvQYCL0xMn5Ik=">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</latexit>

Inclination angle of magnetic surface ✓ = 30
<latexit sha1_base64="xkSxiV2i8YKbWbqQnFcyl/mnZyc=">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</latexit>✏min = 10 9 (normalized by mec2)

Minimum energy of seed photon
Slope of seed photon spectrum<latexit sha1_base64="+TNu6rz/LEN/BrAEtzRtKSQ6R78=">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</latexit>

Curvature radius

p=2

Rcur = rg<latexit sha1_base64="oulvWjdZj07gxoLd4x9xfLyqing=">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</latexit>

Number of cells
N = 32768
rg
M9 BH,3
3
&
⇠ 10
lp
< 8>
<latexit sha1_base64="PVE3DMrfheXp/Tcmf3TVFWtudEQ=">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</latexit><latexit sha1_base64="xtV5sYzSMyTyvjBQaAvqesrfTcM=">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</latexit>

We neglect the scattering of particles with < 107 .
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Summary

We perform 1D GRPIC simulation for pair cascadein a starved magnetosphere of a Kerr black hole.