mizuno meudon080430
TRANSCRIPT
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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
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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
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Relativistic Jets in Universe
Mirabel & Rodoriguez 1998
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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
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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
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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
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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
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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
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1. Development of 3D GRMHD
Code “RAISHIN”
Mizuno et al. 2006a, Astro-ph/0609004
Mizuno et al. 2006, PoS, MQW6, 45
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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)
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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).
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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)
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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
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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)
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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
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Relativistic MHD Shock-Tube TestsExact solution: Giacomazzo & Rezzolla (2006)
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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
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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
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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
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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
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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
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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
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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
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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
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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.).
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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)
Radiation image seen from
θ=85 (optically thick )
Radiation image seen from
θ=45 (optically thick )
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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)
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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)
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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)
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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
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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)
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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M lti di i l Si l ti
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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.
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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.
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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)
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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
8/18/2019 Mizuno Meudon080430
http://slidepdf.com/reader/full/mizuno-meudon080430 48/48
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.)