3D GRMHD simulations of accretion
flows and relativistic jets
– for cosmic ray accelaration
Akira MIZUTA(RIKEN)
Toshikazu Ebisuzaki (RIKEN)
Toshiki Tajima (UCI)
Shigehiro Nagataki (RIKEN)DTA Symposium
＠NAOJ 16.11.25
Mizuta + in prep.

OUTLINE

Introduction
AGN jetGRMHD simulations of black hole andaccretion disksParticle acceleration by wakefield
acceleration for ultra high energy cosmicrays (<--> Fermi acceleration model)Summary

AGN and AGN Jets are laboratories for….
・ Supermassive black hole M~106-1010 M_sun・ Accretion disks– disk type & geometry (standard disk, ADAF, RIAF etc.)– angular momentum transport(B-filed amplification (Magnetorotational instability))・ jets– how to launch jets
– how to collimate outflows and how to keep collimation– how to accelerate to relativistic bulk velocity (Γ~10)
・ high energy astrophysics– gamma-ray blazars (on-axis view, multiwavelength
radio to high energy gamma-ray)– candidate object for particle accelerator of ultra-highenergy cosmic rays

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 analysis ofseveral bands of radioobservations.
 It is consistent that the shape ofthe jet near the core is notconical but parabola.
 Rim brightening @ 100Rs


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

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, B&P 1982)
Blandford-Znajek (general rela. + B filed effect, B&Z 1977)
or others ?
GRMHD simulations have been done in 2D & 3D (Koide+2002,McKinney, 2004,2006
Komissarov+2005 2009, Nagataki 2009, Takahashi (2016) etc...

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Initial ConditionzLog10 (Mass density)

Log10( Pgas/Pmag)z 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

βmin~100

Fisbone-Moncrief (1976) solution – hydrostatic solution of tori around=const =4.45, rin=6. > rISCO
rotating BH (a=0.9, rH~1.44),
With maximum 5% random perturbation in thermal pressure.

Units

L : Rg=GM/c2 (=Rs/2), T : Rg/c=GM/c3, mass : scale freea=0.9, 13cm(MBH/108Msun) ~500s (MBH/108Msun)~1.5x10

Magnetized jet launch

movie

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

Plasma beta(Pth /Pmag) & magnetic pressure

Plasma beta (right)
Magnetic pressure (left)
Highly non-axis symmetric mode is excited.
Filamentaly structure inside the disk with thickness ~0.5 Rg
Plasma beta @equator

Mizuta + in prep.

Electric-magnetic energy

B-filed is well amplified.

Mass accretion rate
shows short time
variability (~ a few tens)=> consistent with MRI
growth rate forλ~0.5Rg ~8 grids size
~filamentaly structure

Recurrence rate
~ a few hundreds=> consistent with highresolution local shearing
box simulations.
(high β state ⇔ low β state)

Mass accretion rate＠horizon

τ~ 10 ΩK ~ 100 Rg/c
(Stone et al. 1996, Suzuki & Inutsuka
2009, O'Neill et al. 2011)

Rising timescale~ a few 10s to a few 100.

Electric-magnetic energyB-filed is well amplified.

Mass accretion rate
shows short timevariability (~ a few tens)=> consistent with MRI
growth rate forλ~0.5Rg ~8 grids size
~filamentaly structure

Recurrence rate
~ a few hundreds=> consistent with highresolution local shearing
box simulations.
(high β state ⇔ low β state)

Mass accretion rate＠horizon

τ~ 10 ΩK ~ 100 Rg/c
(Stone et al. 1996, Suzuki & Inutsuka
2009, O'Neill et al. 2011)

・ BZ-effect & outflow properties
Electric-magnetic luminosity@ horizon is sometimes positive.
==> BZ effect works.
・But only ~1% in the jet

・ Short time variability on electricmagnetic luminosity in the jet.
This is similar with mass accretion rate.
・ About 1% of poloidal component of theAlfven flux (disk) goesto the jet.
・ Consistent with Ebisuzaki & TajimamodelCosmic-ray up to ~1020eV
Hillas plot : Emax~ZeBR

Cygnus A
jet(radioimage)

Systemsize
CygnusA > gyro radius

jet(radio1020eVimage)1021eV

Extra galactic origin?

GZK cutoff

LHC(14TeV Center-of-mass system)Cosmic-ray up to ~1020eV
Cosmic-ray- electron, positron,proton, neutron, charged nuclei etc.

Cygnus Ajet
(radioimage)

Hillas plot : Emax~ZeBR
Systemsize
CygnusA > gyro radiusjet(radio1020eVimage)1021eV

Extra galactic origin?

GZK cutoff

LHC(14TeV Center-of-mass system)Cosmic-ray up to ~1020eV
Hillas plot : Emax~ZeBR~1023cm
Cygnus A jet(radio image)CygnusA jet(radio image)

Active galactic nuclei (AGN) jets are
one of strong candidate objects forUHECR accelerator.

SystemCygnus size
A jet > gyro radius(radio image)1020eV1021eVWakefield acceleration (Tajima & Dawson PRL 1979)
Acceleration mechnism by interaction between wave and plasma.

Laser plasmainteraction
Osillation by Electrifield ⇒ v⇒ 8 shape motion. (ossilation up, down)
vxB force ⇒ ossilation forward
Short pulse laser and backward.
|v| ~ c => large amplification motion
2
grad E by vxB. (8 shape motion).
If there is gradient in E2, charged
particles feel the force towars lees E2side. = “Ponderamotive force”
Effective acceleration for
I~1018W/cm2 (relativistic intensity).
Experimentally observed.
Schwoere (2008)

Relativistic Alfven wave can be applied to wakefieldacceleration. (Takahashi+2000, Chen+2002,Lyubarusky 2006, Hoshino 2008)

AGN : UHECR accelarator ?
Wakefield acceleration model (excited by Alfven wave) (Ebisuzaki & Tajima 2014)
Relativistic Alfven wave in the jet => electric-magnetic wave>>1
nonlinear & relativistic Alfven mode for Standard-disk(Shakra & Sunyaev (1973) is assumed)

ωA>ωp
ωA<ωp

Ebisuzaki & Tajima 2014Strength parameter a0
In our numerical GRMHD simulation,– So many electric magnetic flares are observed in the jet.
– Disk activities show MRI growth and eruption of Alfven waves.
We can estimate the strength parameter a0 as,

Strength parameter highly exceeds unity.
The AGN jet can be good accelerator via wake-field acceleration.

Summary
3D GRMHD simulations of rotating
BH+accretion disk for the analysis of wakefield acc.
– B filefd amplification– Electromagnetic flux @ horizon (BZ effect)– Electric magnetic flares in the jet– consistent with Ebisuzaki & Tajima model– a0 ~1012 >>1 : good accelerator for UHECRs
via wakefiled acceleration
Future works– Higher resolution calculations are necessry toresolve fastest growing mode of MRI– Different initial B-field topology