On BZ power in M87
磁場 (回転角速度ΩF) に絡まって噴出するプラズマ?

Motoki Kino (Kogakuin Univ/NAOJ)
with M. Takahashi, M. Nakamura, K. Toma, T. Kawashima,JH Park, K. Hada, HW Ro, Y Cui et al.
2020/01/21

AGN jet workshop 2020 @ Tohoku U

How to extract energy from black hole?

(c) EAVN Collaboration

The M87 jet is one of the best cases toinvestigate energy extraction from BH.
(c) EHT Collaboration

Park, Hada, MK +2019

A new question
How to explain the discrepancy between obs. and model?!

poloidal velocity

Main observation was donewith KaVA arrayby KaVA/EAVN AGN
Science Working Group.

How to solve General Relativistic MHD?
Basic equations
The ideal MHD condition
The particle conservation law
Maxwell equations
Polytropic relation (Tooper 1965)
The equation of motion

steady ( t=0) &axi-symmetric ( φ=0)
Bernoulli equation
Grad-Shafranov (GS) eq.
Here, we choose this way.
Easy comparison w/ VLBI data!

u F =0(nu ); = 0
F;µ = 4 j µ , F[µ ; ] = 0
P =K 0T; = 0non-steady & 3D
GRMHD simulation

Steady and axisymmetric flow
magnetic-surface

Conserved quantities along themagnetic surface (Ψ=const.).
1.
2.
3.
4.
5.

Number flux per unit magnetic flux
Angular velocity of the field lines
Total energy of the magnetized flow
Total angular momentum
Entropyp( ) = nu
Bp
Ft
Ftr
F( ) =F r =F
E( ) = µut 4 F B
1
L( ) = µu
B
4S( )Motion along Ψ=const surface<=> Bernoulli eq.
Balance between Ψ= const surface <=> GS eq.
(a.k.a. trans-field eq.)
A well known approximated form of Ψ isTomimatsu & Takahashi (2003) modell Assumptions
ü Steady, axisymmetricü Special Relativistic (not GR)
ü A jet has relativistic speed andhas a narrow opening-angle.

l Boundary condition
ü confined by outer boundary-wallü Inner-boundary = light-cylinderü At inlet-boundary, ΩF(Ψ)= constl Advantages of TT03 modelü Solving GS equation
ü Trans fast magnetosonic solutionΨ-dependence can naturally explainsa stratified velocity field.
htaehsts
FaKino+ in prep

inpsslow

poloidal velocity (up) along
a given Ψ=const. surface
TT03erKino+ in prepu_pE-dependenceKino+ in prep!
w
Ne

ΩF dependence

slower-ΩF-> thicker-Rlc-> Jet acceleration starts
from more distant point.

Kino+ in prep

Slower rotation of B-field ΩF ~ c/100rg(= larger light-cylinder radius ~100rg) can explain up profile!

!
w
NeA difference between our result and GRMHD simulations.
Our result suggests~10 times thicker
light cylinder.
Light Cylinder
in McKinney 06

by McKinney 06
10102rg

Discussions(1) How to realize slower Ω̲F? (comments welcome)(2) estimate of B-field on the horizon via BZ-powerHow to realize slower ΩF？
(1) Random ang-momentum accretion could makemore slowly rotating magnetosphere.
Chatterjee+19

Accreting plasma with random angularmomentum rather than Fishbone-torus
could realize smaller Ω̲F.

トーラス

How to realize slower ΩF?
(2) and (3)(2) Floor conditions in GRMHD simulations may be different
from the real case.
ü Need microscopic physics on particle creation and/or injection
ü Need GRMHD simulations w/ different floor condition(3) The jet base is anchored to the accretion flow, rather thanthe black hole.
ü It easily realizes slower Ω̲F. However, it seems unlikely since anaccretion flow is low σ, in which the flow does not acceleratesufficiently fast.

ΩF (magnetoshare) vs ΩH (Black Hole)BZ process works when

Assuming reasonably high BH-spin i.e., 0.5 < a< 1in order to produce powerful jets, then we haveOK, then let us assume BZ process in action in M87.

BZ power as the origin of jet power
The power of the M87 jet can be estimated as

The BH power is given by

The condition here

Allowed range of BH on the horizon
Ruled out(too large LBZ)

Ruled out(too slowΩH)

Allowed

Ruled out(too small LBZ)

PrelimRuled out(too fast ΩF)

in arySummaryl From the comparison of KaVA measured M87 jet velocity profile
with steady-axisymmetric SRMHD model (TT03), we find thatü velocity stratification (fast-sheath-slow-spine) is naturally expectedü slower Ω̲F ~ c/100 r̲g (thicker light cylinder) can explain the datal Possible reasons of slower Ω̲F are discussed.
ü Outer boundary (torus) condition?
ü Inner boundary (floor) condition?

l An estimate of BHorizon is done based on required BZ-power (LBZ).
ü Although smaller Ω̲F makes L̲BZ smaller, the estimated B-fieldstrength BHorizon~103-4 G. The value looks to support MAD.