GRMHD simulations of black hole and accretion disk

Akira MIZUTA(RIKEN)
Toshikazu Ebisuzaki (RIKEN)
Toshiki Tajima (UCI)
Shigehiro Nagataki (RIKEN)

The extreme Universe viewed invery-high-energy
gamma-rays 2015
＠ICRR, U. Tokyo 16.01.14

OUTLINE
Introduction: observations of AGN jets
 GRMHD simulations of black hole andaccretion disks− Blandford-Znajek process− bulk acceleration outflows Particle acceleration by wakefield
acceleration
SummaryIntroduction
observations of AGN jets

M87 radio observations
M87 D=16.7Mpc9 M
BH~3.2-6.6x 10 M_sun
 Location of the central BH isnear the radio core by analysisof several bands of radioobservations.
 The shape of the jet near thecore is not conical butparaboric.
 Rim brightening @ 100Rs


BH ?
No !
M87 radio observation Hada +(2011)

Where is acceleration site ?
・Bulk velocities are measured
by using a series of radio
observations of M87 up to105-6 Rs.
・Acceleration to relativistic
velocities occurs at ~104Rs.
Rs ・ Similar results for Cygnus A

jets. (Boccardi + A&A (2016))

HST-1

Asada +2014

Relativistic jet launched from BH+accretion disk
JET
M87 opitical・Central Engine-Black Hole(BH)＋accretion disk
-B filed amplification
・relativistic jet (Γ~10 for AGN jet)-How to launch the jet is also a big problem for astrophyics.
Blandford-Payne (magnetic centrifugal force)
Blandford-Znajek (general relativistic + B filed effect)
or others ?
B filed plays an important role !

GRMHD simulationsof Black hole andaccretion disks

Basic Equations : GRMHD Eqs.
GM=c=1, a: dimensionless Kerr spin parameter
Mass conservation Eq.

Energy-momentum conservation Eq.
Induction Eq.

EOS (γ=4/3)

Constraint equations.
No-monopoles
constraintIdeal MHD condition
Normalization of 4-velocity

Energy-momentum tensor

GRMHD code (Nagataki 2009,2011)
Kerr-Schild metric (no singular at event horizon)
HLL flux, 2nd order in space (van Leer), 2nd or 3rd order in time
See also, Gammie +03, Noble + 2006
Flux-interpolated CT method for divergence freeComputational domain, grids
Spherical coordinate (r, θ, φ) R[1.4:3e4] θ[0:π] φ[0:2π][Nr=124,Nθ=124, Nφ=28]
r=exp(nr), dθ~1.5o, dφ~13o: uniform– not enough high resolution to resolve fastest MRI growth modeUnits

L : Rg=GM/c2 (=Rs/2), T : Rg/c=GM/c3, Mass : scale free~1.5x1013cm(MBH/108Msun) ~500s (MBH/108Msun)

Initial condition
Fisbone-Moncrief (1976) solution – hydrostatic solution of tori around=const =4.45, rin=6. > rISCO
rotating (a=0.9, rH~1.44),– equilibrium state : gravitational potential, pressure gradient, andcentrifugal force, geometrical thick disk
– impose weak poloidal B-field (Minimum plasma beta =100)

case1. maximum 5% random perturbation in thermal pressure (3D)
case2. w/o perturbation in thermal pressure (2D)

Magnetized jet launch

movie

Low mass density and electromagnetic flux
along the polar axis. Intermittent

Magnetized jet launch~60Rg

Mass accretion rate＠horizon

Electric-magnetic energy

In transition phase(t<18000 for 3D)
accretion late is relativelyhigh.
After that a new phasestarts.
Short time availability(Δt ~a few tens to a few
hundreds.)
Accretion rate for 2D is
1/10-1/100 lower thanthat of 3D.
Outflow luminosity for 3Dcase ( 0<θ<10°)
θ0=0
θ1=10

Short time variavilitry (Δt~a few tensGM/c3) in electromagneticcomponents (green and pink) :=> possible origine for flares in blazars (on axis observer),Blandford-Znajek processElectricmagnetic power at the horizon
Electromagnetic components in Tμνθ0=0,θ1=π

BZ powered ?
Efficiency (Ele-mag power/M_dot) is goodfor 2D case.

BZ flux v.s. EM flux @ horizon (1)BZ1977, McKinney & Gammie2004Radial electric-magnetic flux is described as@ event horizon

Rotation frequencyof BH

Rotation frequency of EM
field0<ω＜ΩH ⇒ outgoing flux

incomingoutgoing

From Takahashi's(AUE) slideBZ flux v.s. EM flux @ horizon (2)2D axi-symmeric

Triple peak profile.

Time averaged [20000:30000]

McKinney+2004
a=0.938 2D axi-symmetric
See also Barkov +(2008)

For 2D axi-symmetric case, time-averaged BZ flux is good
agreement with electromagnetic flux at horizon.

BZ flux v.s. EM flux @ horizon (3)3D caseAveraged in Φ [0:2π]
Time averaged [20000:30000]

Electromagnetic flux is roughly good agreement with BZ flux.
Outgoing flux is concentrated around equator.

B-Filed line @equator
2D Axis-symmetric case

Axisymmeric

Small Br

3D caseLarge Br

Tilt angle of B-field line to black hole Tilt angle of B-filed line to blacksurface normal is large.
hole surface normal is large.
Small BrBr large in Local

Bulk Acceleration

How to convert magnetic energy
to kinetic energy ?

MHD instability(current driven instability)

Z-pinchB∝1/r
Sausage instability
m=0 mode

Kink instability
m=1 modeSausage instability (m=0 mode)
ρΓ∞

104Rg

・2D GRMHD simulation
・ Sausage (pinch) instability
grows up.
・ It enhances oscillation andgenerates waves, converting
magnetic energy into lateralkinetic energy
・Finally shock dissipation
Γ(EM)∞

Γ(Thermal)∞ΓMcKinney 2006 MNRAS 368 (2006)

Kink instability (m=1 mode)
・Magnetized jet propagationin large scale.
・ Kink instability (m=1 mode)
grows up.
・ Dissipation (recconection)
happens. Then magnetic
energy is convertedto thermal and kinetic energy.

Kink instability riggers smallangle recconection(Drenkhahn 2002,Drenkhahn & Spruit 2002)
3D RMHD simulationof magnetized jets propagationin massive star.
(Bromberg & Tchekhovskoy 2015)

Left: log10 [rot(∇xB)] (conduction current)
Right: log10 [ σ ]Bulk acceleration Γ~2

Γ∞

Γ∞

Γ

Structures are resolved by only 1-2 grids.
Higher resolution calculation necessary to see MHD instability
and bulk acceleration.
Mizuta+ in prep.

AGN : UHECR accelarator ?
Wakefield acceleration model (excited by Alfven wave)
Intense laser pulse => strong Alfven wave (vA~c, transverse wave)
Alfven waves excited in the accretion disk propagates into theoutflows.If magnetic field is enough high, relativistic Alfven waves ispossible.
>>1
nonlinear & relativistic Alfven mode Standard-disk(Shakra & Sunyaev (1973) is assumed)

ωA>ωp
ωA<ωp

Ebisuzaki & Tajima 2014

Wakefield acceleration (Tajima & Dawson PRL 1979)
Acceleration mechnism by interaction between wave and plasma.
Short pulse laser
Osillation of Electrifield ⇒ v (ossilationup, down)
vxB force ⇒ ossilation forward
and backward.
|v| ~ c => large amplification motion byvxB. (8 shape motion).

Laser plasma
Interaction⇒ 8 shape motion.

grad E2
If there is gradient in E2, charged
particles feel the force towars lees E2
side. = Ponderamotive force

Schwoere (2008)

Effective acceleration for I~1018W/cm2(relativistic intensity).
– acceleration efficiency 10GeV/m(100-1000 higher than normal
accelarators.,
Electrons: ~GeV, Ions : a few tens MeV

Relativistic Alfven wave can be applied to Wakefield acceleration.
Takahashi+2000, Chen+2002 (for short GRBs : NS-NS merger)
Lyubarusky 2006, Hoshino 2008 (wakefield acc. @ relativistic shock)Summary
2D & 3D GRMHD simulations of rotating
BH+accretion disk
– B filefd amplification, saturation, dissipation– Higher mass accretion rate for 3D than thatin 2D case
– Electromagnetic flux @ horizon is consistent with
BZ flux– Higher resolution calculations are necessry todiscuss bulk acceleration