mizuno meudon080430

8/18/2019 Mizuno Meudon080430

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Context

1. Introduction

2. Development of 3D GRMHD code

3. 2D GRMHD simulations of Jet Formation

4. Stability of relativistic jets5. MHD boost mechanism of relativistic jets

6. Summary and Future Research Plan



Astrophysical Jets• Astrophysical jets: outflow of highlycollimated plasma

– Microquasars, Active Galactic Nuclei,

Gamma-Ray Bursts, Jet velocity ～c,

Relativistic Jets.

– Generic systems: Compact object

（White Dwarf, Neutron Star, Black

Hole）+ Accretion Disk

• Key Problems of Astrophysical Jets

– Acceleration mechanism and

radiation processes – Collimation

– Long term stability

M87



Relativistic Jets in Universe

Mirabel & Rodoriguez 1998



Energy conversion from accreting matter is the most efficientmechanism

• Gas pressure model – Jet velocity ~ sound speed (maximum is ~0.58c)

– Difficult to keep collimated structure

• Radiation pressure model

– Can collimate by the geometrical structure of accretion disk (torus) – Difficult to make relativistic speed with keeping collimated structure

• Magnetohydrodynamic (MHD) model – Magneto-centrifugal force and/or magnetic pressure

• Jet velocity ~ Keplerian velocity of accretion disk – Can keep collimated structure by magnetic hoop-stress

• Direct extract of energy from a rotating black hole (Blandford &Znajek 1977, force-free model)

Modeling of Astrophysical Jets



Magnetic

field line

Centrifugal

force

Outflow (jet)

Magnetic

field line

outflow (jet)

accretion

• Acceleration – Magneto-centrifugal force (Blandford-Payne

1982)

• Like a force worked a bead when swing awire with a bead

– Magnetic pressure force

• Like a force when stretch a spring

– Direct extract a energy from a rotating black hole

• Collimation

– Magnetic pinch (hoop stress)• Like a force when the shrink a rubber

band

Magneticfield line

MHD model



Requirment of Relativistic MHD• Astrophysical jets seen AGNs show the relativistic

speed (~0.99c)

• The central object of AGNs is suppermassive blackhole (~105-1010 solar mass)

• The jet is formed near black hole

Require relativistic treatment (special or general)

• In order to understand the time evolution of jetformation, propagation and other time dependent phenomena, we need to perform relativisticmagnetohydrodynamic (MHD) simulations



Applicability of MHD Approximation

• MHD describe macroscopic behavior of plasmas

if – Spatial scale >> ion Larmor radius

– Time scale >> ion Larmor period

• But MHD can not treat

– Particle acceleration

– Origin of resistivity

– Electromagnetic waves



Recent Work for Relativistic Jets

• Investigate the role of magnetic fields in relativistic jets againstthree key problems

– Jet formation

– Jet acceleration and radiation process

• Acceleration of particles to very high energy

– Jet stability

• Recent research topics – Development of 3D general relativistic MHD (GRMHD) code “RAISHIN”

– GRMHD simulations of jet formation and radiation from Black Hole

magnetosphere

– A relativistic MHD boost mechanism for relativistic jets

– Stability analysis of magnetized spine-sheath relativistic jets

– Particle-In-Cell (PIC) simulations of relativistic jets



1. Development of 3D GRMHD

Code “RAISHIN”

Mizuno et al. 2006a, Astro-ph/0609004

Mizuno et al. 2006, PoS, MQW6, 45



Numerical Approach to Relativistic MHD

• RHD: reviews Marti & Muller (2003) and Fonts (2003)

• SRMHD: many authors• Application: relativistic Riemann problems, relativistic jet propagation, jet

stability, pulsar wind nebule, etc.

• GRMHD

– Fixed spacetime (Koide, Shibata & Kudoh 1998; De Villiers &

Hawley 2003; Gammie, McKinney & Toth 2003; Komissarov 2004;

Anton et al. 2005; Annios, Fragile & Salmonson 2005; Del Zanna et al.

2007, Tchekhovskoy et al. 2008)

• Application: The structure of accretion flows onto black hole and/or formationof jets, BZ process near rotating black hole, the formation of GRB jets in

collapsars etc.

– Dynamical spacetime (Duez et al. 2005; Shibata & Sekiguchi 2005;

Anderson et al. 2006; Giacomazzo & Rezzolla 2007, Cedra-Duran et al.2008)



Propose to Make a New GRMHD Code• The Koide’s GRMHD Code (Koide, Shibata & Kudoh 1999;

Koide 2003) has been applied to many high-energyastrophysical phenomena and showed pioneering results.

• However, the code can not perform calculation in highly

relativistic (γ>5) or highly magnetized regimes.

• The critical problem of the Koide’s GRMHD code is the

schemes can not guarantee to maintain divergence free

magnetic field.

• In order to improve these numerical difficulties, we havedeveloped a new 3D GRMHD code RAISHIN (R elAtIviStic

magnetoHydrodynamc sImulatio N, RAISHIN is the Japanese

ancient god of lightning).



4D General Relativistic MHD Equation

• General relativistic equation of conservation laws and Maxwell equations:

∇ν ( ρ U ν

) = 0 (conservation law of particle-number)

∇ν T µν

= 0 (conservation law of energy-momentum)

∂µ F νλ +

∂ν F λµ+

∂λ F µν = 0

∇µ F µν

= - J ν

• Ideal MHD condition: F νµU ν

= 0

• metric： ds2=g µν dxµ dxν

• Equation of state : p=( Γ -1) u

ρ : rest-mass density. p : proper gas pressure. u: internal energy. c: speed of light.

h : specific enthalpy, h =1 + u + p / ρ .

Γ : specific heat ratio.

U µυ

: velocity four vector. J µυ : current density four vector.

∇µν

: covariant derivative. gµν : 4-metric,

T µν

: energy momentum tensor, T µν

= ρ h U µ

U ν+ pg

µν+ F

µσ F

νσ -gµν F

λκ F λκ/4.

F µν : field-strength tensor,

(Maxwell equations)



Conservative Form of GRMHD

Equations ( 3+1 Form )

(Particle number conservation)

(Momentum conservation)

(Energy

conservation)

(Induction equation)

U (conserved variables) Fi

(numerical flux) S (source term)√ -g : determinant of 4-metric

√ γ : determinant of 3-metric

Detail of derivation of

GRMHD equations Anton et al. (2005) etc.

Metric:α: lapse function,

βi: shift vector,

γij: 3-metric



New 3D GRMHD Code “RAISHIN”

• RAISHIN utilizes conservative, high-resolution shockcapturing schemes (Godunov-type scheme) to solve the3D general relativistic MHD equations (metric is static)

• Ability of RAISHIN code

– Multi-dimension (1D, 2D, 3D)

– Special (Minkowski spcetime) and General relativity (static metric;Schwarzschild or Kerr spacetime)

– Different coordinates (RMHD: Cartesian, Cylindrical,Spherical and GRMHD: Boyer-Lindquist of non-rotating or

rotating BH) – Use several numerical methods to solving each problem

– Maintain divergence-free magnetic field by numerically

– Use constant Gamma-law or variable equation of states

– Parallelized by Open MP

Mizuno et al. (2006)



Detailed Features of the Numerical

Schemes• RAISHIN utilizes conservative, high-resolution shock

capturing schemes (Godunov-type scheme) to solve the

3D GRMHD equations (metric is static)

* Reconstruction: PLM (Minmod & MC slope-limiter function),

convex ENO, PPM

* Riemann solver: HLL, HLLC approximate Riemann solver

* Constrained Transport: Flux interpolated constrained transport

scheme

* Time evolution: Multi-step Runge-Kutta method (2nd & 3rd-order)

* Recovery step: Koide 2 variable method, Noble 2 variable method,

Mignore-McKinney 1 variable method

Mizuno et al. 2006a, astro-ph/0609004



Relativistic MHD Shock-Tube TestsExact solution: Giacomazzo & Rezzolla (2006)



Relativistic MHD Shock-Tube Tests Balsara Test1 (Balsara 2001 )

Black: exact solution, Blue: MC-limiter ,

Light blue: minmod-limiter , Orange: CENO,

red: PPM

• The results show good

agreement of the exact solution

calculated by Giacommazo &

Rezzolla (2006).

• Minmod slope-limiter and

CENO reconstructions are more

diffusive than the MC slope-limiter and PPM reconstructions.

• Although MC slope limiter and

PPM reconstructions can resolve

the discontinuities sharply, somesmall oscillations are seen at the

discontinuities.

400 computational zones

FR

FR

SR

CD

SS



Relativistic MHD Shock-Tube Tests

• Komissarov: Shock Tube Test1 △ ○ ○ ○ ○ (large P)

• Komissarov: Collision Test × ○ ○ ○ ○ (large γ)

• Balsara Test1(Brio & Wu) ○ ○ ○ ○ ○

• Balsara Test2 × ○ ○ ○ ○

(large P & B)

• Balsara Test3 × ○ ○ ○ ○ (large γ)

• Balsara Test4 × ○ ○ ○ ○ (large P & B)

• Balsara Test5 ○ ○ ○ ○ ○

• Generic Alfven Test ○ ○ ○ ○ ○

KO MC Min CENO PPM



2. 2D GRMHD Simulation of Jet

Formation

Mizuno et al. 2006b, Astro-ph/0609344

Hardee, Mizuno, & Nishikawa 2007, ApSS, 311, 281

Wu et al. 2008, CJAA, submitted



2D GRMHD Simulation of Jet Formation

Initial condition

– Geometrically thin Keplerian

disk ( ρ d / ρ c=100) rotates

around a black hole (a=0.0,0.95)

– The back ground corona is

free-falling to a black hole

(Bondi solution) – The global vertical magnetic

field (Wald solution)

Numerical Region and Mesh

points – 1.1（ 0.75) r S < r < 20 r S , 0.03<

θ < π /2, with 128*128 mesh

points

Schematic picture of the jet formation near

a black hole



Time evolution (Density)

non-rotating BH case ( B0=0.05,a=0.0 )

Parameter

B0=0.05a=0.0

Color: density

White lines: magnetic

field lines (contour of

poloidal vector

potential)Arrows: poloidal

velocity



Time evolution (Density)

rotating BH case ( B0=0.05,a=0.95 )

Parameter

B0=0.05a=0.95

Color: density

White lines: magnetic

field lines (contour of

poloidal vector

potential)Arrows: poloidal

velocity



Results• The matter in the disk loses its angular

momentum by magnetic field and falls to a black

hole.

• A centrifugal barrier decelerates the falling

matter and make a shock around r=2rS.• The matter near the shock region is accelerated

by the J×B force and the gas pressure gradient

and forms jets.

• These results are similar to previous work

(Koide et al. 2000, Nishikawa et al. 2005).

• In the rotating black hole case, additional inner

jets form by the magnetic field twisted resulting

from frame-dragging effect.

White curves: magnetic field lines (density), toroidal

magnetic field (plasma beta)vector: poloidal velocity

Non-rotating BH Fast-rotating BH

ρ ρρ ρ

β ββ β

vtot

Bφ



Results (Jet Properties)WEM: Lorentz force

Wgp: gas pressure gradient

• Outer jet: toroidal velocity

is dominant. The magnetic

field is twisted by rotation of

Keplerian disk. It isaccelerated mainly by the

gas pressure gradient (inner

part of it may be accelerated

by the Lorentz force).• Inner jet: toroidal velocity

is dominant (larger than

outer jet). The magnetic field

is twisted by the frame-

dragging effect. It is

accelerated mainly by the

Lorentz force

Non-rotating BH

Fast-rotating BH



Relativistic Radiation Transfer

Distribution of Absorbing Clouds

Accretion Disk

Black HoleObserver

Photon

αuem

uclα

uabα

upα

Image of Emission, absorption &

scattering

Wu et al., 2008, CJAA, submitted

• We have calculated the thermal free-free

emission and thermal synchrotron emission

from a relativistic flows in black holesystems based on the results of our 2D

GRMHD simulations (rotating BH cases).

• We consider a general relativistic radiation

transfer formulation (Fuerst & Wu 2004,

A&A, 424, 733) and solve the transfer

equation using a ray-tracing algorithm.

• In this algorithm, we treat general

relativistic effect (light bending, gravitational

lensing, gravitational redshift, frame-dragging effect etc.).



Radiation images of black hole-disk system• We have calculated the thermal free-

free emission and thermal synchrotron

emission from a relativistic flows in

black hole systems (2D GRMHD

simulation, rotating BH cases).

• We consider a GR radiation transferformulation and solve the transfer

equation using a ray-tracing algorithm.

• The radiation image shows the front

side of the accretion disk and the otherside of the disk at the top and bottom

regions because the GR effects.

• We can see the formation of two-

component jet based on synchrotron

emission and the strong thermal

radiation from hot dense gas near the

BHs.

Radiation image seen from

θ=85 (optically thin)


θ=85 (optically thick )


θ=45 (optically thick )



Instability of Relativistic Jets

• Interaction of jets with external

medium caused by suchinstabilities leads to the formation

of shocks, turbulence, acceleration

of charged particles etc.

• Used to interpret many jet

phenomena

– quasi-periodic wiggles and knots,

filaments, limb brightening, jetdisruption etc

•When jets propagate outward, there are possibility to grow of twomajor instabilities

• Kelvin-Helmholtz (KH) instability

• Important at the shearing boundary flowing jet and external medium

• Current-Driven (CD) instability

• Important in twisted magnetic field

Limb brightening of M87 jets (observation)



Spine-Sheath Relativistic Jets

(observations)M87 Jet: Spine-Sheath (two-component) Configuration?

VLA Radio Image (Biretta, Zhou, & Owen 1995)HST Optical Image (Biretta, Sparks, & Macchetto 1999)

Typical ProperMotions < c

Radio ~ outside

optical emission

Sheath wind ?

Typical ProperMotions > c

Optical ~ inside

radio emission

Jet Spine ?

• Observations of QSOs show the evidence of high speed wind （~0.1-0.4c）(Pounds et

al. 2003):

•Related to Sheath wind• Spine-sheath configuration proposed to explain

•limb brightening in M87, Mrk501jets （Perlman et al. 2001; Giroletti et al. 2004）

•TeV emission in M87 (Taveccio & Ghisellini 2008)

•broadband emission in PKS 1127-145 jet (Siemiginowska et al. 2007)



Spine-Sheath Relativistic Jets

(GRMHD Simulations)

• In many GRMHD simulation

of jet formation (e.g., Hawley &Krolik 2006, McKinney 2006, Hardee

et al. 2007), suggest that

• a jet spine driven by the

magnetic fields threadingthe ergosphere

• may be surrounded by a

broad sheath wind driven

by the magnetic fieldsanchored in the accretion

disk.

Non-rotating BH Fast-rotating BH

BH Jet Disk Jet/WindDisk Jet/Wind

Total velocity distribution of 2D GRMHD

Simulation of jet formation

(Hardee, Mizuno & Nishikawa 2007)



Key Questions of Jet Stability

• When jets propagate outward, there are possibility togrow of two instabilities

– Kelvin-Helmholtz (KH) instability

– Current-Driven (CD) instability

• How do jets remain sufficiently stable?

• What are the Effects & Structure of KH / CDInstability in particular jet configuration (such asspine-sheath configuration)?

• We investigate these topics by using 3D relativisticMHD simulations



3D Simulations of Spine-Sheath Jet Stability

• Solving 3D RMHD equations in Cartesian coordinates

(using Minkowski spacetime)

• Jet (spine): u jet = 0.916 c ( γ j=2.5), ρ jet = 2 ρ ext (dense, cold jet)

• External medium (sheath): uext = 0 (static), 0.5c ( sheath wind )

• Jet spine precessed to break the symmetry (frequency, ω=0.93)

• RHD: weakly magnetized (sound velocity > Alfven velocity)

• RMHD: strongly magnetized (sound velocity < Alfven velocity)• Numerical box and computational zones

• -3 r j< x,y< 3r j, 0 r j< z < 60 r j (Cartesian coordinates) with 60*60*600 zones,

(1r j=10 zones)

Mizuno, Hardee & Nishikawa, 2007

• Cylindrical super-Alfvenic

jet established across the

computational domain with a

parallel magnetic field (stableagainst CD instabilities)

Initial condition

Previous works: jet propagation simulation of Spine-Sheath jet model(e.g., Sol et al. 1989; Hardee & Rosen 2002)



Simulation results: global structure

(nowind, weakly magnetized case)

3D isovolume of density with B-field lines show the jet is

disrupted by the growing KH instability

Transverse cross section show the strong

interaction between jet and external medium

Longitudinal cross section

y

zx

y

Eff t f ti fi ld d h th i d



Effect of magnetic field and sheath wind

• Previous works: Study the effect of sheath wind on KH modes for non-rel HD

RMHD and RHD simulations (Hanasaz & Sol 1996, 1998; Hardee & Rosen 2002)

•The sheath flow reduces the growth rate of KH modes and slightly increases the

wave speed and wavelength as predicted from linear stability analysis.

•The magnetized sheath reduces growth rate relative to the weakly magnetized case

•The magnetized sheath flow damped growth of KH modes.

Criterion for damped KH modes:(linear stability analysis)

vw=0.0 vw=0.0vw=0.5c vw=0.5c

1D radial velocity profile along jet



4. MHD Boost mechanism of

Relativistic Jets

Mizuno, Hardee, Hartmann, Nishikawa & Zhang, 2008,ApJ, 672, 72

A MHD b t f l ti i ti j t



A MHD boost for relativistic jets

• The acceleration mechanism boostingrelativistic jets to highly-relativisticspeed is not fully known.

• Recently Aloy & Rezzolla (2006) have

proposed a powerful hydrodynamicalacceleration mechanism of relativistic jets by the motion of two fluid between jets and external

– If the jet is hotter and at much higher

pressure than a denser, colder externalmedium, and moves with a large velocitytangent to the interface, the relative motionof the two fluids produces a hydrodynamicalstructure in the direction perpendicular to the

flow. – The rarefaction wave propagates into the jet

and the low pressure wave leads to strongacceleration of the jet fluid into theultrarelativistic regime in a narrow region

near the contact discontinuity.

Schematic picture of simulations



Motivation• This hydrodynamical boosting mechanism is

very simple and powerful.• But it is likely to be modified by the effects ofmagnetic fields present in the initial flow, orgenerated within the shocked outflow.

• We investigate the effect of magnetic fields onthe boost mechanism by using RelativisticMHD simulations.

Initial Condition (1D RMHD)



Initial Condition (1D RMHD)• Consider a Riemann problem consisting of two uniform initial states

• Right (external medium): colder fluid with larger rest-mass density andessentially at rest.

• Left (jet): lower density, higher temperature and pressure, relativistic velocitytangent to the discontinuity surface

• To investigate the effect of magnetic fields, put the poloidal (Bz: MHDA) ortoroidal (By: MHDB) components of magnetic field in the jet region (left state).

• For comparison, HDB case is a high gas pressure, pure-hydro case (gas pressure = total pressure of MHD case)

Schematic picture of simulations

Simulation region

-0.2 < x < 0.2 with 6400 grid

d C



Hydro Case

Solid line (exact solution), Dashed line (simulation)

In the left going rarefaction region,

the tangential velocity increases

due to the hydrodynamic boostmechanism.

jet is accelerated to γ ~12 from an

initial Lorentz factor of γ ~7.

MHD C



MHD Case

HDA case (pure hydro) :

dotted line

MHDA case (poloidal)

MHDB case (toroidal)

HDB case (hydro, high-p)

• When gas pressure becomes large, the normal velocity

increases and the jet is more efficiently accelerated.

• When a poloidal magnetic field is present, strongersideways expansion is produced, and the jet can achieve

higher speed due to the contribution from the normal

velocity.

• When a toroidal magnetic field is present, although the

shock profile is only changed slightly, the jet is more

strongly accelerated in the tangential direction due to the

Lorentz force.

• The geometry of the magnetic field is a very important

geometric parameter.

Dependence on Magnetic Field Strength



Dependence on Magnetic Field Strength

Solid line: exact solution, Crosses: simulationMagnetic field strength is measured in fluid flame

• When the poloidal magnetic field

increases, the normal velocityincreases and the tangential velocity

decreases.

• When the toroidal magnetic field

increases, the normal velocity

decreases and the tangential velocity

increases.

• In both of cases, when the magnetic

field strength increases, maximum

Lorentz factor also increases.• Toroidal magnetic field provides the

most efficient acceleration.

toroidalpoloidal



M lti di i l Si l ti



Multi-dimensional Simulation

(Results)• A thin surface is accelerated by

the MHD boost mechanism to

reach a maximum Lorentz factor g~15 from an initial Lorentz factor

g~7 .

• The jet in cylindrical coordinates

is slightly more accelerated than

the jet in Cartesian coordinates,which suggests that different

coordinate systems can affect

sideways expansion, shock profile,

and acceleration (slightly).

• The field geometry is animportant factor.



Summary

• We have developed a new 3D GRMHD code``RAISHIN’’by using a conservative, high-resolutionshock-capturing scheme.

• We have performed simulations of jet formation from ageometrically thin accretion disk near both non-rotatingand rotating black holes. Similar to previous results (Koide

et al. 2000, Nishikawa et al. 2005a) we find magneticallydriven jets.

• It appears that the rotating black hole creates a second,faster, and more collimated inner outflow. Thus, kinematic

jet structure could be a sensitive function of the black holespin parameter.



Summary (cont.)•We have investigated stability properties of magnetized

spine-sheath relativistic jets by the theoretical work and

3D RMHD simulations.

• The most important result is that destructive KH modes

can be stabilized even when the jet Lorentz factorexceeds the Alfven Lorentz factor. Even in the absence of

stabilization, spatial growth of destructive KH modes can

be reduced by the presence of magnetically sheath flow

(~0.5c) around a relativistic jet spine (>0.9c)



Summary (cont.)• We performed relativistic magnetohydrodynamicsimulations of the hydrodynamic boosting mechanismfor relativistic jets explored by Aloy & Rezzolla (2006)using the RAISHIN code.•We find that magnetic fields can lead to more efficient

acceleration of the jet, in comparison to the pure-hydrodynamic case.• The presence and relative orientation of a magneticfield in relativistic jets can significant modify thehydrodynamic boost mechanism studied by Aloy &Rezzolla (2006).

Future Work



Future Work

• Code Development – Kerr-Schild Coordinates: long-term simulation in GRMHD

– Resistivity: extension to non-ideal MHD; (e.g., Watanabe &

Yokoyama 2007; Komissarov 2007)

– Couple with radiation transfer: link to observation

• Research of Jet Formation and Propagation – Dependence on Magnetic field structure, BH spin parameter,

disk structure and perturbation etc.• Research of Jet Stability – Dependence on EoS

– Current-Driven instability

• Apply to astrophysical phenomena in which relativisticoutflows and/or GR essential (AGNs, microquasars,

neutron stars, and GRBs etc.)

mizuno meudon080430

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