1. Current-Driven Kink Instability in Magnetically Dominated Relativistic Jets
Yosuke Mizuno
Institute for Theoretical Physics
Goethe University Frankfurt am Main
Mizuno, Lyubarsky, Nishikawa, & Hardee 2012, ApJ, 757, 16
DESY, Germany, November 27, 2014

2. Contents Introduction: Relativistic Jets
Introduction: Current-Driven Kink Instability
3D (G)RMHD Simulation Code RAISHIN
3D RMHD Simulations of CD Kink Instability (static plasma column case), effect of radial density and magnetic pitch profile
3D RMHD Simulations of CD Kink Instability (rotating relativistic jet case), jet flow & rotation effect
Summary

3. Plasma in the Universe
A plasma is a quasi-neutral gas consisting of positive and negative charged particles
Liquid is heated, atoms vaporize => gas
Gas is heated, atoms collide each other and knock their electrons => decompose into ions & electrons (plasma)
Plasma state: fourth state of matter
Most of (visible) universe is in form of plasma
Plasma form wherever temperatures are high enough or radiation is strong enough to ionize atoms
Magnetohydrodynamics (MHD) is the most simplest description of plasma which approximates to consider as a single fluid and is captured macroscopic behavior

4. Relativistic Regime Kinetic energy >> rest-mass energy
Fluid velocity ~ light speed (Lorentz factor gamma >> 1)
Relativistic jets/ejecta/wind/blast waves (shocks) in AGNs, GRBs, Pulsars
Thermal energy >> rest-mass energy
Plasma temperature >> ion rest mass energy
GRBs, magnetar flare?, Pulsar wind nebulae
Magnetic energy >> rest-mass energy
Magnetization parameter sigma (Poynting to kinetic energy ratio) >> 1
Pulsars magnetosphere, Magnetars
Gravitational energy >> rest-mass energy
GMm/rmc2 = rg/r > 1
Black hole, Neutron star
Radiation energy >> rest-mass energy
Supercritical accretion flow 4

5. Applicability of Hydrodynamic Approximation
To apply hydrodynamic approximation, we need the condition:
Spatial scale >> mean free path
Time scale >> collision time
These are not necessarily satisfied in many astrophysical plasmas
E.g., solar corona, galactic halo, cluster of galaxies etc.
But in plasmas with magnetic field, the effective mean free path is given by the ion Larmor radius.
Hence if the size of phenomenon is much larger than the ion Larmor radius, hydrodynamic approximation can be used. 5

6. Applicability of MHD Approximation
Magnetohydrodynamics (MHD) describe macroscopic behavior of plasmas if
Spatial scale >> ion Larmor radius
Time scale >> ion Larmor period
But MHD can not treat
Kinetic properties of plasma
Particle acceleration
Origin of resistivity 6

7. Relativistic Jets Radio observation of M87 jet
Relativistic jets: outflow of highly collimated plasma
Microquasars, Active Galactic Nuclei, Gamma-Ray Bursts, Jet velocity ～c
Generic systems: Compact object（White Dwarf, Neutron Star, Black Hole）+ Accretion Disk
Key Issues of Relativistic Jets
Acceleration & Collimation
Propagation & Stability
Modeling for Jet Production
Magnetohydrodynamics (MHD)
Relativity (SR or GR)
Modeling of Jet Emission
Particle Acceleration
Radiation mechanism

8. Relativistic Jets
M87 jets (AGNs)
A tremendous, elongated and collimated outflows of plasma with relativistic speed (~ light speed)
Many sources for relativistic jets (from stellar size to galaxy size)
Jets (Outflows) are common in the universe
Lunching from accreting compact objects (Black Holes)
Observed relativistic jet (at large scale) is kinetic energy is dominated = magnetic field is weak

9. Jet Speeds Sub-relativistic: protostars, v/c ~ 10-3
Mildly-relativistic: SS433, XRBs (v/c = 0.26)
Doppler-shifted emission lines
Highly-relativistic: X-ray binaries (microquasars), ~10% of AGNs (~ 2-30)
Doppler beaming (One-sideness)
Illusion of superluminal motion
Gamma-ray flares (to avoid -pair production)
Hyper-relativistic: Gamma-Ray Bursts ( ~ )
Gamma-ray variability
Ultra-relativistic: Pulsar jets/winds ( ~ 106)
Modeling of radiation and pulsar nebulae

10. Fundamental Problems in Relativistic jets
How are the jets formed near the compact objects (BHs)? (formation mechanism)
How are the jets accelerated up to relativistic speed? (acceleration mechanism)
How the collimated jet structure make? (collimation mechanism)
How the jets remain stable over large distance? (Jet stability mechanism)
How to emit the radiation in the relativistic jets? (Radiation mechanism and particle acceleration mechanism) 10

11. Simulation and Theory of Jet Formation & Acceleration
Magnetic field lines
Relativistic jet is formed and accelerated by macroscopic plasma (MHD) process
Collimated jet is formed near the central BH and accelerates g >> 1
But, it has problems
Most of energy remains in Poynting energy (magnetic energy)
Acceleration needs take long time (slow acceleration efficiency)
Inconsistent with current observation
=> Rapid energy conversion (dissipation)
Jets
MHD process (schematic picture)
GRMHD simulations
(McKinney 06) 11

12. Relativistic Jets Formation from GRMHD Simulations
Many GRMHD simulations of jet formation (e.g., Hawley & Krolik 2006, McKinney 2006, Hardee et al. 2007) suggest that
a jet spine (Poynting-flux jet) driven by the magnetic fields threading the ergosphere via MHD process or Blandford-Znajek process
may be surrounded by a broad sheath wind driven by the magnetic fields anchored in the accretion disk.
High magnetized flow accelerates G >>1, but most of energy remains in B field.
Non-rotating BH Fast-rotating BH
Spine
Sheath
Total velocity
Disk
Density distribution
(McKinney 2006)
Disk Jet/Wind
BH Jet Disk Jet/Wind
(Hardee, Mizuno & Nishikawa 2007)

13. Jet Energetics Gravity, Rotational energy (BH or accretion disk)
Poynting flux (magnetic energy)
Jet kinetic energy
Efficient conversion to EM energy
Easy to get ~ equipartition, hard to get full conversion
Magnetic field is a medium for a transmission not a source

14. Dissipation in the Relativistic Jet
Shocks
Time-dependent energy injection (internal shock)
Change of external medium spatial structure (recollimation shock)
Magnetic Reconnections
Magnetic field reversal or deformation of ordered magnetic field
Turbulences
Leads from MHD instabilities in jets
MHD Instabilities
Kelvin-Helmholtz instability at jet shear boundary
Current-Driven Kink instability at jet interior
=> Turbulence in the jets and/or magnetic reconnection?

15. Ultra-Fast TeV Flare in Blazars
PKS (Aharonian et al. 2007)
See also Mrk501, PKS
Ultra-Fast TeV flares are observed in some Blazars (AGN jets).
Variation timescale:
tv~3min << Rs/c ~ 3M9 hour
For the TeV emission to escape pair creation Γem>50 is required (Begelman, Fabian & Rees 2008)
But bulk jet speed is not so high (g ~ 5-10)
Emitter: compact & extremely fast
Proposed Model:
Magnetic Reconnection inside jet (Giannios et al. 2009)
Giannios et al.(2009)

16. Jet Wobbling
15 GHz VLBI image of 4C+12.50
High resolution VLBI observations of some AGN jets show regular or irregular swings of innermost jet structural position angle (jet wobbling).
Parsec scale AGN jet curvatures and helical-like structures (inner parsec or large scale) are believed to be triggered by changes in direction at the jet nozzle.
Physical origin of jet wobbling (Agudo 2009)
Accretion disk precession
Orbital motion of accretion system (binary BH?)
Jet instabilities
Position angle oscillation of 3C273
P.A.
year

17. Key Questions of Jet Stability
When jets propagate outward, there are possibility to grow of two major instabilities
Kelvin-Helmholtz (KH) instability
Important at the shearing boundary flowing jet and external medium
In kinetic-flux dominated jet (>103 rs)
Current-Driven (CD) instability
Important in existence of twisted magnetic field
Twisted magnetic field is expected jet formation simulation & MHD theory
Kink mode (m=1) is most dangerous in such system
In Poynting-flux dominated jet (<103 rs)
Questions:
How do jets remain sufficiently stable?
What are the Effects & Structure of instabilities in particular jet configuration?
We try to answer the questions through 3D RMHD simulations

18. The Five Regions of AGN Jet Propagation
Hot Spot/Lobe: ~109 rS (~100 kpc; or 20’)
 Outer jet is not Poynting-Flux Dominated
Kinetic-Flux-Dominated (KFD) Jet: ~103 – 109 rS
(0.1 – 105 pc; 1 mas – 20’)
Transition Region: ~102.50.5 rS (< 0.1 pc; < 1 mas)
Poynting-Flux Dominated (PFD)  KFD
MHD Acceleration/Collimation Region: ~10 – 102.50.5 rS
(1 – < 100 mpc; 10 as – < 1 mas)
The Jet “Nozzle”
Jet Launching Region: The Accretion Flow; ~5 – 50 rS
(0.5 – 5 mpc; 5 – 50 as)
Probably unresolved or slightly resolved

19. CD Kink Instability
Well-known instability in laboratory plasma (TOKAMAK), astrophysical plasma (Sun, jet, pulsar etc).
In configurations with strong toroidal magnetic fields, current- driven (CD) kink mode (m=1) is unstable.
This instability excites large-scale helical motions that can be strongly distort or even disrupt the system
Distorted magnetic field structure may trigger of magnetic reconnection.
Schematic picture of CD kink instability
Kink instability in experimental plasma lab (Moser & Bellan 2012) 19

20. CD Kink Instability
Well-known instability in laboratory plasma (TOKAMAK), astrophysical plasma (Sun, jet, pulsar etc).
In configurations with strong toroidal magnetic fields, current-driven (CD) kink mode (m=1) is unstable.
This instability excites large-scale helical motions that can be strongly distort or even disrupt the system
For static cylindrical force-free equilibria, well known Kruskal-Shafranov (KS) criterion
Unstable wavelengths:
l > |Bp/Bf |2pR
However, rotation and shear motion could significant affect the instability criterion
Distorted magnetic field structure may trigger of magnetic reconnection. (short-time variability)
Schematic picture of CD kink instability
3D RMHD simulation of CD kink instability in PWNe (Mizuno et al. 2011)

21. CD Kink Instability in Jets (Newtonian)
Appl et al. (2000)
Consider force-free field with different radial pitch profile in the rest frame of jet
maximum growth rate: Gmax=0.133 vA/P0,
unstable wave length: lmax=8.43P0
Wave number
Growth rate for m=-1~-4 in constant pitch case.
(P0=a in our notation:
Magnetic pitch =RBz/Bf )
Growth rate for m=-1 mode as a function of wavenumber with different pitch profile
Maximum growth rate and unstable wave number for m=-1 kink as a function of magnetic Pitch

22. Previous Work for CD Kink Instability
For relativistic force-free configuration
Linear mode analysis provides conditions for the instability but say little about the impact instability has on the system (Istomin & Pariev (1994, 1996), Begelman(1998), Lyubarskii(1999), Tomimatsu et al.(2001), Narayan et al. (2009))
Instability of potentially disruptive kink mode must be followed into the non-linear regime
Helical structures have been found in Newtonian /relativistic simulations of magnetized jets formation and propagation (e.g., Nakamura & Meier 2004; Moll et al. 2008; McKinney & Blandford 2009; Mignone et al. 2010)

23. Purpose
We investigate detail of non-linear behavior of relativistic CD kink instability in relativistic jets
Relativistic: not only moving systems with relativistic speed but any with magnetic energy density comparable to or greater than the plasma energy density.
First task: static configuration
In generally, rigidly moving flows considered in the proper frame
The simplest ones for studying the basic properties of the kink instability
Second task: rotating relativistic jets
Consider differentially rotating relativistic jets motivated from analytical work of Poynting-flux dominated jets (Lyubarsky 2009)

24. 4D General Relativistic MHD Equation
General relativistic equation of conservation laws and Maxwell equations:　　　
　　　　　　　∇n ( r U n ) = 0　　　 (conservation law of particle-number)
　　　　　　　∇n T mn = (conservation law of energy-momentum)
　　　　　　　∂mFnl + ∂nFlm + ∂lF mn = 0
　　　　　　　∇mF mn = - J n
Ideal MHD condition: FnmUn = 0
metric：　ds2=-a2 dt2+gij (dxi+b i dt)(dx j+b j dt)
Equation of state : p=(G-1) u
(Maxwell equations)
r : rest-mass density. p : proper gas pressure. u: internal energy. c: speed of light.
h : specific enthalpy, h =1 + u + p / r.
G: specific heat ratio.
Umu : velocity four vector. Jmu : current density four vector.
∇mn : covariant derivative. gmn : 4-metric. a : lapse function, bi : shift vector, gij : 3-metric
Tmn : energy momentum tensor, Tmn = pgmn + r h Um Un+FmsFns -gmnFlkFlk/4.
Fmn : field-strength tensor,

25. 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
√g : determinant of 3-metric
Relativistic density
momentum density
Total energy density

26. RAISHIN Code (3DGRMHD)
Mizuno et al. 2006a, 2011c, & progress
RAISHIN utilizes conservative, high-resolution shock capturing schemes (Godunov-type scheme) to solve the 3D ideal GRMHD equations (metric is static)
Ability of RAISHIN code
Multi-dimension (1D, 2D, 3D)
Special & General relativity (static metric)
Different coordinates (RMHD: Cartesian, Cylindrical, Spherical and GRMHD: Boyer-Lindquist coord. of non-rotating or rotating BH, Kerr-Schild coord. is underdeveloped)
Different schemes of numerical accuracy for numerical model (spatial reconstruction, approximate Riemann solver, constrained transport schemes, time advance, & inversion)
Using constant G-law and approximate Equation of State (Synge-type)
Parallel computing (based on OpenMP, MPI)
Free to download from my HP (

27. Initial Condition for Static Plasma Column of CDI
Mizuno et al. (2009)
Solving ideal RMHD equations using RAISHIN in Cartesian coordinates
Static Cylindrical Plasma column with force-free equilibrium helical magnetic field
Magnetic pitch (P=RBz/Bf): constant, increase, decrease
Density profile: constant or decrease (r=r0 B2)
Numerical box: -2L < x, y < 2L, 0 < z < 2L (Cartesian coordinates:160 x 160 x 80 zones)
Boundary: periodic in axial (z) direction
Small velocity perturbation with m=1(-1) and n=1(-1) modes

28. Force-Free Helical Magnetic Field
Measured in Laboratory frame
Force-free equilibrium:
B0: magnetic amplitude
a: characteristic radius
a=1/8L in this work
a: pitch profile parameter
Choose poloidal magnetic field:
Find toroidal magnetic field:
Magnetic pitch (P= RBz/Bf) :
a < 1 ⇒ pitch increase
a=1 ⇒ constant helical pitch (same as previous non-relativistic work)
a >1 ⇒ helical pitch decrease

29. Initial Radial Profile
Magnetic pitch
(P= RBz/Bf)
Black: constant density
Red: decreasing density
Solid: constant pitch
dotted: increase pitch
Dashed: decrease pitch
density
Sound velocity
Alfven velocity

30. 3D Structure (Decrease density with Constant pitch )
Displacement of the initial force-free helical magnetic field leads to a helically twisted magnetic filament around the density isosurface by CD kink instability
Slowly continuing outwards radial motion is confined to a lower density sheath around the high density core
Color: density
White line: magnetic field lines

31. Dependence on pitch profile
tA: Alfven crossing time
Increase pitch
Constant pitch
Decrease pitch
Constant pitch: Amplitude growth slows at later time.
Increase pitch: 3D density structure looks similar to constant pitch case. However, amplitude growth ceases at later time.
Decrease pitch: slender helical density wrapped by B-field developed. Amplitude growth continues throughout simulation.

32. Time evolution Volume-averaged kinetic energy transverse to the z-axis
Constant density
Decrease density
tA: Alfven crossing time
Solid: constant pitch
Dotted: increase pitch
Dashed: decrease pitch
Initial exponential linear growth phase and subsequent non-linear evolution
Density Decline: more rapid initial growth and decline (by more gradual radial decline in the Alfven velocity) .
Pitch increase: slower growth
Pitch decrease: more rapid growth
Consistent with non relativistic linear analysis in Appl et al. (2000)

33. CD Kink Instability in Rotating Relativistic Jets
Here: we investigate the influence of jet rotation and bulk motion on the stability and nonlinear behavior of CD kink instability.
We consider differentially rotating relativistic jets motivated from analytical work of Poynting-flux dominated jets (Lyubarsky 2009).
The jet structure relaxes to a locally equilibrium configuration if the jet is narrow enough (the Alfven crossing time is less than the proper propagation time). So cylindrical equilibrium configuration is acceptable.

34. Initial Condition
Mizuno et al. (2012)
Consider: Differential rotation relativistic jet with force-free helical magnetic field
Solving RMHD equations in 3D Cartesian coordinates
Magnetic pitch (P=RBz/Bf): constant (in no-rotation case)
Angular velocity (W0=0,1,2,4,6)
Density profile: decrease (r=r0 B2)
Numerical box: -3L < x, y < 3L, 0 < z < 3L (Cartesian coordinates: 240 x 240 x 120 zones)
Boundary: periodic in axial (z) direction
Small velocity perturbation with m=1 and n=0.5 ~ 4 modes

35. Force-Free Helical Magnetic Field and Velocity
Measured in comoving frame
Force-free equilibrium:
Choose poloidal magnetic field:
B0: magnetic amplitude
R0: characteristic radius
R0=1/4L in this work
a: pitch profile parameter
b: differential rotation parameter
a=1, b=1 in this work
Choose Angular velocity:
Find toroidal magnetic field:
Magnetic pitch (P= RBz/Bf) :
Jet Velocity
(Drift velocity):

36. Initial Radial Profile
solid: W0=0
dotted: W0=1
dashed: W0=2
dash-dotted: W0=4
dash-two-dotted: W0=6
Initial Radial Profile
Angular velocity
Toroidal field
Poloidal filed
Jet rotation velocity
Axial jet velocity
Magnetic pitch
Sound velocity
Density
Alfven velocity

37. Time Evolution of 3D Structure
W0=1
Color density contour with magnetic field lines
Displacement of the initial force-free helical field leads to a helically twisted magnetic filament around the density isosurface with n=1 mode by CD kink instability
From transition to non-linear stage, helical twisted structure is propagates in flow direction with continuous increase of kink amplitude.
The propagation speed of kink ~0.1c (similar to initial maximum axial drift velocity)

38. Dependence on Jet Rotation Velocity: growth rate
solid: W0=0
dotted: W0=1
dashed: W0=2
dash-dotted: W0=4
dash-two-dotted: W0=6
Volume-averaged Kinetic energy of jet radial motion
Volume-averaged magnetic energy
Alfven crossing time
First bump at t < 20 in Ekin is initial relaxation of system
Initial exponential linear growth phase from t ~ 40 to t ~120 (dozen of Alfven crossing time) in all cases
Agree with general estimate of growth rate, Gmax~ 0.1vA/R0
Growth rate of kink instability does not depend on jet rotation velocity

39. Dependence on Jet Rotation Velocity: 3D Structure
W0=2 case: very similar to W0=1 case, excited n=1 mode
W0=4 & 6 cases: n=1 & n=2 modes start to grow near the axis region
Because pitch decrease with increasing W0
In nonlinear phase, n=1 mode wavelength only excited in far from the axis
Propagation speed of kink is increase with increase of angular velocity

40. Multiple Mode Interaction
In order to investigate the multiple mode interaction, perform longer simulation box cases with W0=2 & 4
n=1 & n=2 modes grow near the axis region, in nonlinear phase, growth of the CD kink instability produces a complicated radially expanding structure as a result of the coupling of multiple wavelengths
Cylindrical jet structure is almost disrupted in long-term evolution.
The coupling of multiple unstable wavelength is crucial to determining whether the jet is eventually disrupted.

41. Influence of magnetic field structure (magnetic pitch)
The radial distribution of magnetic field in the relativistic jet is unknown.
From the theoretical and simulation work of jet formation, we expected that the magnetic pitch is increase with increasing radius from the jet axis (poloidal field is dominated).
Therefore, we investigate the influence of radial distribution of helical magnetic field.
Initial condition
W0=4
a=1, 0.75, 0.5, 0.35 <= determine how magnetic pitch is increase.

42. Initial Radial Profile
solid: s=1
dotted: a=0.75
dashed: a=0.5
dash-dotted: a=0.35
Angular velocity
Toroidal field
Poloidal field
Magnetic pitch
Axial velocity
Jet rotation velocity
Sound speed
Density
Alfven speed

43. Dependence on B-field structure: growth rate
solid: s=1
dotted: a=0.75
dashed: a=0.5
dash-dotted: a=0.35
Volume-averaged kinetic and magnetic energies
When a is increasing, growth rate of CD kink instability becomes small (slow growth)
When a becomes small, the kinetic and magnetic energies do not decrease in non-linear phase
This indicates nonlinear stabilization and structure developed initially is maintained in the nonlinear stage (see 3D structure in next).

44. Dependence on B-field structure: 3D structure
a=0.75 case: growth of n=1 & n=2 axial modes around the jet axis. Nonlinear evolution is similar to a=1 case.
a=0.5 case: growth of n=2 axial mode near the jet axis. Helical structure is slowly evolving radially.
a=0.35 case: growth of n=2 axial mode near the axis. In nonlinear phase, helical structure does not evolve radially and maintain the structure = nonlinear evolution is saturated
The growth of instability saturates when the magnetic pitch increases with radius = jet is stabilized.

45. CD Kink Instability in Sub-Alfvenic Jets: Spatial Properties
Mizuno et al. 2014, ApJ, 784, 167
Purpose
In previous study, we follow temporal properties (a few axial wavelengths) of CD kink instability in relativistic jets using periodic box.
In this study, we investigate spatial properties of CD kink instability in relativistic jets using non-periodic box.
Initial Condition
Cylindrical (top-hat) non-rotating jet established across the computational domain with a helical force-free magnetic field (mostly sub-Alfvenic speed)
Vj=0.2c, Rj=1.0
Radial profile: Decreasing density with constant magnetic pitch (a=1/4L)
Jet spine precessed to break the symmetry (l~3L) to excite instability

46. 3D Helical Structure
jet
Density
+ B-field
Density
+ B-field
Velocity
+B-field
Precession perturbation from jet inlet produces the growth of CD kink instability with helical density distortion.
Helical kink structure is advected with the flow with continuous growth of kink amplitude in non-linear phase.
Helical density and magnetic field structure appear disrupted far from the jet inlet.

47. Summery
In CD kink instability of static plasma column, the initial configuration is strongly distorted but not disrupted.
In rotating relativistic jet case, developed helical kink structure propagates along jet axis with continuous growth of kink amplitude.
The growth rate of CD kink instability depends on magnetic pitch & radial density profiles and does not depend on the jet rotation.
The coupling of multiple unstable wavelength is crucial to determining whether the jet is eventually disrupted in nonlinear stage.
The strongly deformed magnetic field via CD kink instability may trigger of magnetic reconnection in the jet (need Resistive Relativistic MHD simulation).

48. Relativistic Magnetic Reconnection using RRMHD Code
Mizuno 2013, ApJS
Assumption
Consider Pestchek-type magnetic reconnection
Initial condition
Harris-type model（anti-parallel magnetic field）
Anomalous resistivity for triggering magnetic reconnection （r<0.8）
Results
B-filed：typical X-type topology
Density：Plasmoid
Reconnection outflow: ~0.8c

49. Regions of AGN Jet Propagation
Modified from Graphic
courtesy David Meier
Jet Launching Region
Jet Collimation Region (10 –100  Launching Region)
Alfven Point
Sheath
Modified Fast Point
Kinetic Energy Flux Dominated
with Tangled (?) Field
Fast MS Point
Collimation Shock
Slow
MS Point
High speed spine
Poynting Flux Dominated
CD Unstable Magnetic Helicity Driven Region
Combined CD/KH
Unstable Region
KH Unstable Velocity Shear Driven Region 49

50. Frontier of research Numerical simulations:
Supercomputer becomes larger (Peta-scale computing), new technique (GPU parallel computing)
GRMHD simulations are possible
Additional physics: Resistivity, radiation, microphysics, …
Effects of time-dependence, non-asymmetry (3D)
GR radiation transfer calculation is a key tool to connect MHD simulations and observations (Need correct radiation process including particle acceleration)
Observations: mm & submm-VLBI trying to observe BH shadow & jet launching region (EHT, BH Cam projects)

51. High resolution VLBI observations
Source
SgrA*
M87
Cen A
BH Mass (Msun)
0.045 x 108
66 x 108
0.45 x 108
Distance
0.008 pc
16.7 Mpc
3.4 Mpc rS
11 mas
8 mas
0.3 mas
Size of shadow
52 mas
40 mas
1.5 mas
Submm-VLBI (Hawaii-ALMA-Gleenland)
GLT
In radio VLBI observation, angular resolution ∝l/D, l: wavelength, D: baseline
Resolution ~ 50 mas atl ~1mm (300GHz) & D=4000 km
In EHT project (with other sub-mm array), D > km => 20 mas at 345 GHz
BH Cam project (ERC Synergy grant) supports EHT project from EU side (theoretical research and development of sub-mm array)
SMA
ALMA

52. BH shadow image (no jet)
Takahashi et al. (2004)
Pu et al. (2014)
a=0
a=0.5
a=0.999
Optically thick
Geometrically thin
i=10 deg
i=85 deg
Optically thin
Geometrically thick
i=85 deg

53. BH shadow image (with jet)
Moscibrodzka et al.(2014)
1mas = 200Rg
0.1mas = 20Rg
Based on 3D GRMHD Simulations of jet formation (HARM3D)
Radiation is calculated by (general relativistic) radiation transfer code in post-process (ray-tracing method)
90 deg
60 deg
30 deg
intensity

54. Other Research
GRMHD simulations of relativistic jet formation from BH-disk system (Mizuno et al. 06b, Hardee et al. 07)
Radiation imaging from BH-disk system (Wu et al. 08)
MHD effect for relativistic shock and additional jet acceleration (Mizuno et al. 08, 09)
Magnetic Field Amplification by relativistic turbulence in propagating relativistic shock (Mizuno et al. 11a, 14a)
Relaxation of Pulsar wind nebulae via CD kink instability (Mizuno et al. 11b)
Relativistic Particle-in-Cell simulations of relativistic jets (Nishikawa et al. 09, 13, 14)

56. M87 Jet & BH Basic facts: D ~ 16.7 Mpc , 1” ~ 80 pc
Marshall et al. (x-ray)
Perlman et al. (optical)
Nuclear region: Mbh ~ 6 x 109 Msol , Rs ~ 0.6 milli-pc
Gebhardt & Thomas (2009)
Biretta, Junor & Livio (2002)
Junor, Biretta & Livio (1999)
Ly, Walker & Wrobel (2004)
Zhou et al. (radio)
1 pc
0.03 pc

57. M87: BH & Jet Collimation Region
Radio Galaxy
FR Type
MBH (M)
D (pc)
RS/as
Collimation Region Size
M87/Vir A I
6.0  109
1.67  107
7.5
0.10 – 10 mas
Cen A
2.0  108
3.4  106
1.2
0.06 – 6 mas
Cyg A II
2.5  109
2.2  108
0.2
2.2 – 44 as
Sgr A GC
2.5  106
8,500
5.9
0.07 – 7 mas
M87 Black Hole & Jet Launching Region Largest Angular Size! 57

58. KHI in Spine-Sheath Jet Global Structure
3D isovolume density at t=60
No wind case
External wind (spine-sheath) case vj
The precession perturbation from jet inlet leads to grow of KH instability and it disrupts jet structure in non-linear phase.
Growth/damp of KH instability and jet structure is different in each cases.

59. KHI in Spine-Sheath Jet Effect of B-field & sheath wind
1D radial velocity profile along jet
ue=0.0
ue=0.5c
ue=0.0
ue=0.5c
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)

60. Jet formation/acceleration mechanism (cont.)
In ideal MHD limit (infinite conductivity), plasma flow (motion) is connected with magnetic field
The rotation of accretion disks or compact objects (BHs / NSs) twisted up the magnetic field into toroidal components
Collapsing, magnetized supernova core (GRBs)
Pulsar magnetosphere
Magnetized accretion disks around neutron stars and black holes
Magnetospheres of rotating black holes
Courtesy to David Meier

61. Jet formation/acceleration mechanism (cont.)
Gas or radiation pressure (Blandford & Rees 1974, O’Dell 1984)
push accretion matter to make and accelerate outflows by pressure gradient
Expansion of magnetic tower (Lynden-Bell & Boily 1994)
Mainly toroidal field from start
Acceleration by magnetic pressure
Magnetocentrifugal acceleration (Blandford & Payne 1982)
Mainly poloidal field anchored to disk or rotating objects
Disk or ergosphere of BH acts like crank
Torque transmitted though poloidal field powers jet
Blandford-Znajek process (Blandford & Znajek 1977)
Directly extract the BH rotating energy and convert to outward Poynting flux
Consider force-free limit (MHD Penrose process is similar mechanism )

62. Acceleration & Collimation in MHD model
Magnetic field line
Assume: in ideal MHD, plasma is attached with magnetic field
Acceleration
Magneto-centrifugal force
Magnetic pressure
Like expansion of spring
Collimation
Magnetic pinch force
Like shrink lubber band
Centrifugal force
Accretion disk
outflow (jet)
accretion
Jets
Magnetic field lines
Magnetic field lines

63. Effects of external confinement
2D RMHD simulations (Komissarov et al. 2009)
Parabolic (z ∝ r2)
Conical (z ∝ r)
Lorentz factor
Some part of jets can convert Poynting flux to Kinetic Energy but most can’t.
Energy conversion is too slow to become kinetic energy dominated, it is unreasonably long distance = inconsistent of observations.
We need to consider some sort of dissipation (rapid energy conversion)

64. Rarefaction Acceleration
If the external confined media is suddenly disappeared and jet becomes free expansion (parabolic => conical), the rarefaction wave is formed and propagates in the jets during the transition from jet boundary.
Rarefaction wave converts jet thermal and magnetic energies to jet kinetic energy efficiently (e.g., Aloy & Rezzolla 2006; Mizuno et al. 2008; Komissarov et al ), so-called rarefaction acceleration
The mechanism is favor for GRBs and may be possible for AGNs.
stationary feature by recollimation shock?
Komissarov et al. 2010
Rarefaction wave propagates from the jet boundary
Change channel shape from parabolic to conical
Lorentz factor

65. Magnetic Reconnection
Ideal MHD gives frozen in magnetic fields.
Resistive MHD (non-ideal MHD) allows diffusion of fields.
Magnetic reconnection is the process of a rapid rearrangement of magnetic field topology.
Magnetic reconnection occurs through diffusion in narrow current sheets.
Magnetic energy could be converted to thermal and kinetic energies
Problem: how differently oriented magnetic field lines could come close each other?
Global MHD instability
Alternating B-field formed at jet beginning.

66. Magnetic Reconnection (cont.)
Dissipation of alternating magnetic fields in the jet (e.g., Giannios & Spruit 05,07; Giannios 06,08; McKinney & Uzdensky 2012) j B 
Alternating polarity by misaligned dipole field
multipolar field (local closed field)
Ordered field broken by instability
Mckinney & Uzdensky (2012)

67. Advantage of Magnetic Reconnections
Magnetic reconnection easily provides large radiative efficiencies and strong variability inferred in AGNs and GRBs.
Reconnection at high s produces relativistic “jets in a jet”; this could account for the fast TeV variability of blazars (Giannios et al 2010)
Questions: why fast reconnection occur in jets?
If we consider anomalous resistivity in small dissipation region, we get fast reconnection. But we do not know what is anomalous resistivity.
This is still unsolved problem in physics.

68. Why we need to develop RRMHD
Quite often numerical simulations using ideal RMHD exhibit violent magnetic reconnection.
The magnetic reconnection observed in ideal RMHD simulations is due to purely numerical resistivity
Fully depends on the numerical scheme and resolution.
To control of magnetic reconnection according to a physical model of resistivity, numerical codes solving the resistive RMHD (RRMHD) equations are highly desirable.
We have newly developed RRMHD code

69. Observed Jet structure
Global structure of M87 jet (Asada & Nakamura 2012)
The parabolic structure (z ∝ r1.7) maintains over 105 rs, external confinement is worked.
The transition of streamlines presumably occurs beyond the gravitational influence of the SMBH (= Bondi radius)
Stationary feature HST-1 is a consequence of the jet recollimation due to the pressure imbalance at the transition
In far region, jet stream line is conical (z ∝ r)
Parabolic streamline
(confined by ISM?)
Conical streamline
(unconfined, free expansion)
Over-collimation at HST-1 stationary knot (recollimation shock?)
HST-1 region

70. Observed Jet structure (cont.)
In M87 jet, the asymptotic acceleration from non-relativistic (0.01c) to relativistic speed (0.99c) occurs over rs
This is very slow acceleration = consistent with theoretical results?
The absence of bulk-Comptonization spectral signatures in blazars implies that Lorentz factors >10 must be attained at least ~1000 rg (Sikora et al. 05).
But according to spectral fitting, jets are already matter-dominated at ~1000 rg (Ghisellini et al 10).
Transition of Sub- to super-luminal motion in M87 jet
Asada & Nakamura (2014)