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高橋 真聡（愛教大）、高橋 労太（東京大）Black Hole Aurora★ BH (black hole) Magnetosphere★ MHD Accretion & MHD Shock★ Energy extraction from rotating★ MHD Shock & High-energy radiation

December 25–27, 2006

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■ BH Magnetosphere (1)：AGNs—“central engine”• Black Hole ( mass, spin ? )• Accretion Disk (Standard Disk, ADAF, Slim Disk, CDAF, MDAF, ... )

HB

M
Fi ag
el ned ti
L cinesA

cc

retionDisk• Relativistic Jet ( Magnetic ? or Thermal driven ?)Black Hole — Accretion Disk — Jet Active Region

3■ BH Magnetosphere (2)：GRBs• Energy generation (1049–1052 erg/sec :—“central engine”

initial size 107 cm)• Duration ( 1 msec ∼ 103 sec )• Jet formation ( Γ ∼ 100 )Black Hole?
torusbag?

Black Hole (1 ∼ 10M ) – Accretion Disk – Jet
MGRB (Magnetic GRB) ?

4■2■Black Hole Magnetosphere model
Tomimatsu & Takahashi et al.(2001), Uzdensky(2004,2005)“ BH Magnetosphere ” =Loop (bag) +Disk–BH (inflow) +outflow

BH – r∞ (outflow)

Hard X-ray

inflowSHOCKMHD Accretion

subsuperHot Plasma

Magnetosonic Point

sublightsurface

Shock Front

SHOCKBlackHoleergospheresuperbagrin

thin disk

MagnetosonicPoint

Hard X-ray

B.H.

★ Ingoing MHD flows along Disk-BH magnetic field lines★ Fast/Slow MHD Shocks can be generated near the BH. ⇒Hot plasma region !

★ Magnetically dominated outgoing winds⇒ (Energy conversion from Magnetic Energy to plasma’s Kinetic Energy )⇒ Relativistic Jets

5Disk-BH magnetic field line (vacuum solution)
30

Tomimatsu & Takahashi et al.(2001)

100

2580
2060
1540102050005101520253002005406080100+ Uniform (Wald) magnetic field lines-0.3303025252020151510105500.20051015202530

1015202530

6Accretion & Jet ( GR-MHD simularion )McKinney & Gammie (2004)[TOP]Initial (left) and Final (right) density distribution[BOTTOM] Final Magnetic field lines○ Jet region (around Rotational Axis):
Magnetically-Dominated ; Blandford-Znajek process
Well-ordered poloidal magnetic fields (radial)○ Corona region :Magnetic turbulence○ Equatorial Torus ：MHD Fluid (MRI)■ 3-A ■7GR-MHD ( Magnetohydrodynamics )Basic Equations＊ The ideal MHD condition

uβ Fαβ = 0＊ The particle conservation law(nuα );α = 0＊ Maxwell equations

F;νµν = −4πj µ ,＊ Polytropic relation(Tooper 1965)

P = KρΓ0T;βαβ = 0＊ The equation of motion
whereF[µν;σ] = 011F αλ F λβ + g αβ F 2T αβ = nµuα uβ − P g αβ +4π41Pρ = ρ0 +
Γ−1
ρ0 = nmpΓ Pρ+P= mp +µ =nΓ−1 nfield-aligned “five conserved quantities”

uα : the fluid 4-velocity,: the energy-momentum tensor

Γ : the adiabatic index,: the total energy density

n : the number density,: the rest mass density

P : the gas pressure,: the relativistic entalpy

F 2 ≡ Fµν F µν ,mp : the particle’s mass

Stationary & Axisymmetric flowsp＊ Number flux per unit magnetic flux

η(Ψ) = nu
Bp＊ Angular velocity of the field linesΩF (Ψ) = −Ftr /Fφr = −Ftθ /Fφθ

＊ Total energy of the magnetized flowΩFE(Ψ) = µut − 4πηBφ＊ Total angular momentum

1L(Ψ) = −µuφ − 4πηBφ＊ EntropyS(Ψ)( ⇒ entropy related accretion rate Ṁ )

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■ 3-B ■

General Relativistic MHD Shock

Shock conditions
GR Rankine-Hugoniot shock conditions (Lichnerowicz 1967)＊ The particle number conservation[nuα ]`α = 0＊ The energy momentum conservation[T αβ ]`α = 0＊ The magnetic flux conservation[∗F αβ ]`α = 0★ The Entropy S ( or Ṁ) increasemagnetic field lines

across the shock front.

plasma flowupstream★ The parameters E, L, ΩF , η are
Shock front

conserved across the shock front.
downstream★ Lab-frame (BL-coordinate) :Bα ≡∗αFαβ k ,Eα ≡ Fαβ kat the Shock front[B⊥] = 0(B⊥ ≡ B α `α)αFast MHD Shock■ 3-C ■9MHD Accretion with Fast MHD Shock
Fukumura, Takahashi & Tsuruta (2006)★ (1) 90 ° ★

Large Angular momentum: LΩF /E = 0.57

★ (2) 40 ° ★

Small Angular momentum: LΩF /E = 0.23(b)(a)
304(2)
25r|u |F out203u15φ(1)

(1)

(2)

0

2.2 2.4 2.6 2.83

2.2 2.4 2.6 2.8(d)

^B
φ

σ2
110 F
in

2.50-2.5-5-7.5-10-12.5-15(c)
1.2
1
0.8
0.6
0.4
0.2
0-0.2

(1)

(2)

2.2 2.4 2.6 2.8

33(f)

(e)
0.5
0.5
0.3(2)n(1)2.2 2.4 2.6 2.8 3

(1)

0.4

Θ 0.3

0.2
0.15

(1)

0.2

(2)

0.1

2.2 2.4 2.6 2.8 300.1(2)

2.2 2.4 2.6 2.83

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Parameters for MHD shock formationFukumura et al. (2006)★ LEFT ★

Shock surface distribution★ RIGHT ★ Compression ratio λ( λ ≡ ndown /nup )◎ Angular velocity of field lines：(a) ΩF = 0.10m(b) ΩF = 0.14m(c) ΩF = 0.20m◎ total Angular Momentum

LΩF /E = constant ＜ solid curves ＞◎ total Energy

E = constant ＜ dotted curves ＞

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11Energy Extraction from BH— 『 BZ process 』 Blandford & Znajek (1977)

Force-free Magnetosphere

Outgoing Enerfy Flux at the event horizon ⇐= Boundary Condition at the horizon:ΩFΩF > ωHBHωHΩF < ωHBH★ Rotational Energy of BH ＝ Energy source of AGN / GRB !?
＊ Magneticall Dominated=⇒Poynting Jets ?

★ What is the Energy conversion mechanism for observations :Emagnetic ⇒ Eradiation / Efluid ?

— The problem of BZ process !

＊ Another processes by GR-Plasma Physics should be introduced.

=⇒ Magnetic Penrose Process / BH Dynamo / MHD Shock . . . etc

12MHD Magnetosphere— 『 Negative Energy Inflow 』

Takahashi et al.(1990), Takahashi (2002)[Total Energy] = [Fluid Energy] + [Magnetic Energy] < 0Ingoing MHD flow solution :★ Slow P. ⇒ Alfvén P. ⇒ Fast P. ⇒ BH
★ MHD flow’s “Energy E ” and “Angular Mo-mentum L ” are specified by the location of theAlfvén point.
★ The Alfvén point for the E < 0 flow locatesinside the Ergosphere.

The rotational energy can be extracted by MHD inflows with E < 0 and L < 0.
=⇒

High-Energy Plasma phenomena !

High-energy Radiation by MHD Shocks !?

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High energy radiation from MHD Shock[ BH-Rotation Power ] ＋ [ Accretion Power ] =⇒ [ Radiation Power ]RadiationRadiation
Energy flux

Energy flux

Inflow

Inflow

F A
BH

BHFFAF

Possitive Energy Inflow
Negative Energy Inflow● Energy :Negative Energy Inflow∆E = Epre − Epost● Angular momentum : ∆L = Lpre − Lpost

What is the restriction on ∆E and ∆L for making high energy radiation ?

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Radiative MHD Shocks

Takahashi & Takahashi (2006)(1) Shock conditions : [T rt] = 0 and [T rφ] = 0nurrtrtrt
T = Tfluid + TEM + Trad = ρ2 [gφφ (Efluid + EEM + Erad) + gtφ (Lfluid + LEM + Lrad)] T rφ =w
rrφrφrφTfluid+ TEM+ Trad= nuρ2w [−gtφ (Efluid + EEM + Erad ) − gtt (Lfluid + LEM + Lrad )]rtµν
Trad= uµ q ν + uν q µ ,q µ : flux four vector
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Erad =(uq+qu),
L=−(ur qφ + qr uφ )
rt
rt
rad
nurnur(2) Shock condition : [T rr ] = 0 and [T rθ ] = 0
Connect Upstream and Downstream solutions.
(3) Given : upstream conserved quantities, emitting mechanism( q µ ⇐ synchrotron radiation, etc) . . .

(local) Spectrum is obtained.

(4) Frame transformations of q µ value :Fluid Rest Frame ⇒ ZAMO ⇒ Boyer-Lindquist Frame(5) Calculate expected Observed Images and Energy Spectrum :Doppler boosting, gravitational red-shift, frame-dragging, light bending, . . .

■7■15Summary■ GR-MHD is applied to a “Black Hole Magnetosphere”.

Trans-magnetosonic ingoing winds are discussed.
■ “Very Hot Plasma region” is generated by the MHD Shock.

Fluid kinetic energy of upflows can be released there.
(It converts to the magnetic and thermal energies.)
This is a High-Energy Radiation source located close to the event horizon.
■ “Negative Energy Postshock-inflows” are possibleby the MHD Shock formation near the event horizon.
Rotational energy of BH can be converted to Radiative Energy(γ-rays/X-rays) at the Shock front (the hot plasma region).
■ Expected Images of shocked region and Energy spectrum :We may observe direct informations of BH spacetime.