3-D RPIC simulations of relativistic jets: Particle acceleration, magnetic field generation, and emission

1
3-D RPIC simulations of relativistic jets
Particle acceleration, magnetic field
generation, and emission
Ken Nishikawa National Space Science
Technology Center/Center for Space Plasma and
Aeronomic Research (UAH) (email
ken-ichi.nishikawa_at_nsstc.nasa.gov) Collaborators
E. Ramirez-Ruiz (UCSC) P. Hardee (Univ. of
Alabama, Tuscaloosa) Y. Mizuno (NPPFNSSTC/MSFC) C.
Hededal (Niels Bohr Institute) G. J. Fishman
(NASA/MSFC )

Nishikawa et al. 2006, ApJ 642,
1274 Ramirez-Ruiz, Nishikawa, Hededal, 2006,
submitted
Santa Cruz Institute for Particle Physics
Seminar, April 17, 2007
2
Outline of talk

• Jet formation from black hole and its
  observations
• Motivations
• 3-D particle simulations of relativistic jets
• electron-positron, (a pair jet created by
  photon annihilation)
• ? 5 (electron-ion), 15, 4 lt ? lt100
• Recent 3-D particle simulations of relativistic
  jets
• pair jet into pair and electron-ion ambient
  plasmas
• ? 12.57, 1 lt ? lt30
• Calculation of radiation based on particle
  trajectories
• Summary of current 3-D simulations (Weibel
  Instability)
• Future plans of our simulations of relativistic
  jets

3
Jets from binary stars
(Schematic figure)
Accretion disk
BH or NS
Accretion stream
Jets

• General Relativistic MHD
• General Relativistic PIC

Mass donor star
4
M87
Mass of black hole 3 billion solar
masses Resolve 100 m
Halca
5
Observations of M87
Shocks?
nonthermal electrons, enhanced magnetic
field, jitter radiation (Medvedev 2000, 2006
Fleishman 2006)?
6
Motivations

• Study particle acceleration at external and
  internal shocks in relativistic jets
  self-consistently with kinetic effects
• Study structures and dynamics of collisionless
  shocks caused by instabilities at the jet front
  and transition region in relativistic jets
• Estimate synchrotron/jitter radiation from
  accelerated particles
• Examine possibilities for afterglows in gamma-ray
  bursts with appropriate ambient plasmas

7
Simulation box
Accelerated particles emit waves at shocks
8
Necessity of 3-D full particle simulation for
particle acceleration

• MHD simulations provide global dynamics of
  relativistic jets including hot spots
• MHD simulations include heating due to shocks,
  however do not create high energy particles (MHD
  simulation test particle (Tom Jones))
• In order to take account of acceleration, the
  kinetic effects need to be included
• Test particle (Monte Carlo) simulations can
  include kinetic effects, but not
  self-consistently
• Particle simulations provide particle
  acceleration (?) with (?e, ?B) and emission
  self-consistently. However, due to the
  computational limitations, particle-in-cell (PIC)
  simulations covers only a small part of the full
  jet.
• Particle simulations can provide synchrotron and
  jitter radiation from ensemble of each particle
  (electron and positron) motion in electromagnetic
  fields.

9
injected at z 25?
3-D simulation
X
jet
Weibel inst
Y
Weibel inst
Z
8585640 grids (not scaled) 380 Million particles
jet front
10
Collisionless shock
?B/?t ??E ?E/?t ??B J dm0?v/dt q(E
v?B) ??/?t ?J 0
Electric and magnetic fields created
self-consistently by particle dynamics randomize
particles
(Buneman 1993)
jet
jet electron
ambient electron
ambient ion
jet ion
11
Weibel instability
Time t ?sh1/2/?pe ? 21.5 Length ?
?th1/2c/?pe ? 9.6?
current filamentation
jet
generated magnetic fields
J
J
?evz ? Bx
(electrons)
x
(Medvedev Loeb, 1999, ApJ)
12
3-D Simulations of Weibel instability
Counter-steaming electron-positron shells
Electron-ion plasma for a long time for
nonlinear stage (Frederiksen at al. 2004, ApJL
Hededal et al. 2004, ApJL)
(Silva et al. 2003, ApJL)
electrons
ions
(Jaroschek, Lesch, Treumann, ApJ, 2005)
(Spitkovsky 2006)
13
Initial parallel velocity distributions of
pair-created jets
Schematic initial parallel velocity distribution
of jets

• A ? (1(vj/c)2)1/2 5
• B ? (1(vj/c)2)1/2 15
• C 4 lt ? lt 100 (distributed cold jet)
• (pair jet created by photon
• annihilation, ??? e?)
• A ? 5 (electron-ion)

B
A
C
Growth times of Weibel instability t A t A tB
tC
14
Perpendicular current Jz (arrowsJz,x)
nISM 1/cm3
?pe-1 0.1msec
at Y 43?
electron-positron ? 15 (B)
c/?pe 5.3 km
?pet 59.8 6msec
L 300 km
jet
jet front
Weibel instability
(Nishikawa et al. 2005)
15
Evolution of Bx due to the Weibel instability
(convective instability)
el-positron ? 15 (B)
?pet 59.8
at Y 43?
Y/?
Bx
?
?
?
jet
X/?
Blue X 33 ? Red X 43 ? Green X 53 ?
jet front
Weibel instability
(Nishikawa et al. 2005)
16
Bx component generated by current channels at t
59.8?pe
el-ion ? 5
el-positron 4 lt?lt100
430
el-positron ? 15
el-positron ? 5
17
Total magnetic field energy (Bx2 By2 Bz2)
averaged in the x-y plane
B2
B?2
B?2
(t 59.8?pe)
el-ion ? 5
el-positron 4 lt?lt100
el-positron ? 15
el-positron ? 5
movie
18
??V?- ?V? phase space of jet electrons at t
59.8?pe
el-pos 4 lt?lt 100
Z/? 120
Z/? 150
Z/? 350
Z/? 580
Z/? 450
Z/? 550
19
Magnetic field energy and parallel and
perpendicular velocity space along Z
?pet 59.8
Linear stage
Nonlinear stage
Jet head
Nonlinear stage
Nonlinear stage
Nonlinear stage
Jet head
Jet head
10
0.8
5
? 5
2
2
0.4
0.2
0.0
0.5
15
0.8
B2
10
?V?
?V?
? 15
2
2
0.4
0.0
0.5
0.2
100
0.8
10
4lt? lt100
10
0.4
2
0.0
0.5
0.2
Z/?
Z/?
Z/?
20
Ion Weibel instability
ion current
E ? B acceleration
electron trajectory
(Hededal et al 2004)
21
EB acceleration due to the current channel
(Z/? 430)
electron-ion jet ? 5
t 50.7?pe
ne
Jz
arrows Ex, Ey
arrows Bx, By
Y/?
Y/?
X/?
X/?
B and E are nearly perpendicular
22
EB acceleration and deceleration
(Z/? 430)
t 50.7?pe
electron-ion jet ? 5
Jz
arrows Ex, Ey
(EB)z
arrows Bx, By
Y/?
Y/?
X/?
X/?
both electrons (and positrons) are accelerated in
this region
E and B are nearly perpendicular
23
Parallel and perpendicular velocity distributions
at ?pet 59.8
1/3
1/3
F(?V?)
F(?V?)
? 5
? 15
4 lt ? lt 100
? V?
?V?
24
Initial parallel velocity distributions of
pair-created jets (e?) (into ambient pair plasma)
Schematic initial parallel velocity distribution
of jets

• A ? (1(vj/c)2)1/2 12.57
• B 1 lt ? lt 30
• (distributed cold jet)
• (pair jet created by photon
• annihilation, ??? e?)
• Aand B injected into ambient electron-ion
  plasma

A
B
12.6
Growth times of Weibel instability t B t A
tB tA
25
Comparisons among four cases
?B (shocked region 300ltzlt600)
jz (jx, jz)
B2
A
narrow el-ion
B
broad el-ion
A
narrow el-po
B
broad el-po
26
All pair plasmas
Bx
B2
? 12.57
1lt?lt30
3lt?lt100
27
Present theory of Synchrotron radiation

• Fermi acceleration (not self-consistent
  simulation)
• (particles are crossing at the shock surface
  many times and
• accelerated, the strength of turbulent
  magnetic fields are assumed)
• The strength of magnetic fields is assumed based
  on the equipartition (magnetic field is similar
  to the thermal energy) (?B)
• The density of accelerated electrons are assumed
  by the power low (F(?) ?p p 2.2?) (?e)
• Synchrotron emission is calculated based on p and
  ?B
• There are many assumptions in this calculation

28
Self-consistent calculation of radiation

• Electrons are accelerated by the
• electromagnetic field generated by the
• Weibel instability (without the assumption
  used in test-particle simulations for Fermi
  acceleration)
• Radiation is calculated by the particle
  trajectory in the self-consistent magnetic field
• This calculation include Jitter radiation
  (Medvedev 2000, 2006) which is different from
  standard synchrotron emission

29
Radiation from collisionless shock
New approach Calculate radiation from
integrating position, velocity, and acceleration
of ensemble of particles (electrons and positrons)
Hededal, Thesis 2005 (astro-ph/0506559)
30
3D jitter radiation (diffusive synchrotron
radiation) with a ensemble of mono-energetic
electrons (? 3) in turbulent magnetic fields
(Medvedev 2000 2006, Fleishman 2006)
2d slice of magnetic filed
3D jitter radiation with ? 3 electrons
-2
µ
0
2
Hededal Nordlund (astro-ph/0511662)
31
Radiation from collisionless shock
?
observer
Power
Shock simulations
GRB
Hededal Thesis
Hededal Nordlund 2005, submitted to ApJL
(astro-ph/0511662)
32
Summary

• Simulation results show Weibel instability which
  creates filamented currents and density along the
  propagation of jets.
• Weibel instability may play a major role in
  particle acceleration in relativistic jets.
• The magnetic fields created by Weibel instability
  generate highly inhomogeneous magnetic fields,
  which is responsible for Jitter radiation
  (Medvedev, 2000, 2006 Fleishman 2006).
• For details see Nishikawa et al. ApJ, 2003, 2005,
  2006, Hededal Nishikawa ApJ, 2005, and
  proceeding papers (astro-ph/0503515, 0502331,
  0410266, 0410193)

33
Future plans for particle acceleration in
relativistic jets

• Further simulations with a systematic parameter
  survey will be performed in order to understand
  shock dynamics
• In order to investigate shock dynamics further
  diagnostics will be developed
• Simulations with large systems will be performed
  with the codes parallelized with OpenMP and MPI
• Investigate synchrotron (jitter) emission, and/or
  polarity from the accelerated electrons and
  compare with observations (Blazars and gamma-ray
  burst emissions)
• Develop a new code implementing synchrotron loss
  and/or inverse Compton scattering

34
Gamma-Ray Large Area Space Telescope (GLAST)
(will be launched in November 2007)http//www-gl
ast.stanford.edu/
Compton Gamma-Ray Observatory (CGRO)
Burst And Transient Source Experiment (BATSE)
(1991-2000) PI Jerry Fishman

• Large Area Telescope (LAT) PI Peter Michaelson
• 20 MeV to about 300 GeV
• GLAST Burst Monitor (GBM) PI Chip Meegan (MSFC)
  
• X-rays and gamma rays with energies
  between 5 keV and
• 25 MeV (http//gammaray.nsstc.nasa.gov/gbm
  /)
• The combination of the GBM and the LAT provides
• a powerful tool for studying gamma-ray
  bursts, particularly for time-resolved
  spectral studies over a very large energy band.

35
GRB progenitor
relativistic jet
Fushin
(god of wind)
emission
(shocks, acceleration)
Raishin
(Tanyu Kano 1657)
(god of lightning)
36
Three-dimensional GRPIC Simulation of Jets from
Accretion Disks

• Background
• Accrete3D was developed to study the
  self-consistent
• evolution of the jet from the accretion disk.
• GRPIC Considerations
• GRMHD is a fluid approximation
• Particle motion is self-consistent (not ideal
  fluid)
• Dynamics of charged particle separation (not
  frozen)
• Questions in Disk-Jet Dynamics/Simulation
• What is the acceleration mechanism?
• Why is the jet collimated?
• Can the disk-jet system become steady
  self-consistently?

37
General relativistic extension of
particle-in-cell code Tensor form of Maxwells
equations Tensor form of Newton-Lorentz
equation Bz -6x104 pairs, 32x32x64 grids
38
Evolution of accretion disk with kinetic processes
39

• Disk Instabilities
• We have conducted a preliminary analysis on the
  plasma mode and density structure within the
  disk.
• There is no electric field at T 0.
• The first row is the density profile within the
  disk. The density
• structure develops waves as the jet develops.
• The second row shows the growth of m 4 for
  the z-component of the electric field . As the
  jet fully develops the instabilities grow within
  the disk.
• The third row shows the mode amplitude of the
  instability.

40
Summary and Further Development There appears
to be mode coupling between the disk and the jet
within the simulation. We see some of the same
instabilities within the disk electric field
within the jet region. The low grid resolution
prevents an in-depth analysis of the density
modes. We will increase the number of particles
to study the density fluctuations and to test the
correspondence with the field modes. We will
include studies of the particle heating and work
done by the field on the particles. Using MPI,
we will make the code parallel.
41
?V?- ?V? phase space of jet electrons at t
59.8?pe
el-pos 4 lt?v?lt 100
Z/? 120
(24 in ?10Z/?)
Z/? 150
Z/? 250
Z/? 350
Z/?450
Z/?550
Z/?580
42
Longer simulation of electron-ion jet injected
into unmagnetized plasma
t 59.8?pe
?v
Bx
jet front
Jy
43
Scientific objectives

• How do shocks in relativistic jets evolve in
  accelerating particles and emission?
• How do 3-D relativistic particle simulations
  reveal the dynamics of shock front and transition
  region?
• What is the main acceleration mechanism in
  relativistic jets, shock surfing, wakefield,
  Fermi models or stochastic processes?
• Obtain spectra and time evolutions from
  simulations and compare with observations
• Understand observations from GLAST (GBM) based on
  simulation and theoretical studies

44
Electron acceleration by ion Weibel instability
G15, mi/me 16
P 2.7
injected
acceleration
(Hededal et al. 2004)
45
Phase space distributions of elctrons
?pe t 59.8
ele-pos
ele-ion
Jet head
jet
Nonlinear stage
Linear stage
ambient
46
Parallel and perpendicular velocity space of
ambient electrons along Z
?pet 59.8
parallel
perpendicular
8
8
Jet head
4
? 5
1
0
Nonlinear stage
8
8
?V?
?V?
4
? 15
1
0
Linear stage
8
8
4 lt? lt100
4
1
0
Z/?
Z/?
47
Electron jet velocity distributions
?pe t 59.8
ele-ion
ele-pos
parallel
perpendicular
48
Evolutions of magnetic fields
?pe t 59.8
? 5
x/? 38 y/? 33 (blue) 43 (red) 53 (green)
ele-ion
B2 B?2
B?2
ele-pos
linear grow
nonlinear stage
49
at Y 43?
Generated magnetic field Bx along Z direction
Blue X 33 ? Red X 43 ? Green X 53 ?
4 lt ? lt 100 (distributed cold jet)
1.0
t 39.0/?pe
t 28.6/?pe
? 1.0
30
Weibel instability grows
1.0
t 58.5/?pe
t 48.1/?pe
Z/?
? 1.0
30
600
30
600
50
(Z/? 430)
t 59.8?pe
electron-ion jet ? 5
ne
arrows Ex, Ey
arrows Bx, By
arrows Ex, Ey
Jz
Jz
Y/?
X/?
jet ?
(EB)z
arrows Bx, By
(EB)z
arrows Jx, Jz
(Y/? 25)
X/?
Y/?
Z/?
0
X/?
51
nISM 1/cm3
Electron density (arrows Bz, Bx)
?pe-1 0.1msec
electron-positron jet (? 15) (B)
c/?pe 5.3 km
?pet 62.4
L 300 km
jet
Weibel instability
jet front
(Nishikawa et al. 2005)
52
EB acceleration and deceleration in x-y plane
(Z/? 430)
el-ion ? 5
el-positron 10lt ?lt100
(EB)z
arrows Bx, By
el-positron ? 5
el-positron ? 15
53
Jz and (EB)z in the nonlinear stage in the x-y
plane
?pe t 59.8
z/?430
ele-ion
ele-pos
arrows
? ion current channel
?
Jz
Ex, Ey
?
? electron current channel
?
EB force accelerate and decelerate particles
(EB)z
Bx, By
?
(EB)z ß? vz/c 0.8 ? 5
?
Bx, By
?
54
(EB)z in the moving frames in the x-y plane
?pe t 59.8 ? 5
z/?430
z/?250
ß? vz/c
ele-ion
ele-pos
ele-ion
ele-pos
0.98
0.8
0.6
x/?
x/?
x/?
x/?
55
Z/? - ?V?phase space of jet electrons at t
59.8?pe
el-ion ? 5
el-pos 4 lt?lt 100
el-pos ? 5
el-pos ? 15
56
Z/? - ?V? phase space of ambient electrons at t
59.8?pe
el-ion ? 5
el-pos 4 lt?lt 100
el-pos ? 5
el-pos ? 15
57
Z/? - ?V? phase space of ambient electrons at t
59.8?pe
el-ion ? 5
el-pos 4 lt?lt 100
el-pos ? 5
el-pos ? 15
58
Jz at the linear and nonlinear stages
color electron density
?pe t
linear stage
electron-ion
19.5
elongated current channels are generated
59.8
nonlinear stage
electron-positron
19.5
current channels are shorter and bent
59.8
arrows electron flux
z/?430
(Nishikawa et al 2005)
59
Electron acceleration at t 59.8?pe
el-ion ? 5
el-positron ? 5
el-positron ? 15
parallel
1
1
10
10
10
1
?v?
perpendicular
1
10
1
10
1
10
?v?
60
Frequency spectrum of radiation emitted by a
relativistic electron
If ? 1, ??c,? 0
(Jackson 1999 Rybicki Lightman 1979)
61
at Y 43?
Generated magnetic field Bx along Z direction
Blue X 33 ? Red X 43 ? Green X 53 ?
t 28.6/?pe
1.0
B
A
? 1.0
Bx
1.0
D
C
? 1.0
30
300
30
300
Z/?
62
Parallel velocity distributions of jets (?v?)
Red front half Blue rear half
t 28.6/?pe
accelerated
107
107
B
A
100
1
10
10
1
F(?v?)
106
106
D
C
100
10
1
1
100
100
10
?v?
decelerated
63
Relationship between the total magnetic field
energy and particle acceleration
64
? 15
4 lt ? lt 100
65
Perturbed current density Jy (Z X plane)
t 28.6/?pe
Arrows (Jz, Jx)
Weibel instability
jet
A
B
C
D
Z 230? (the next sheet shows Jz in
the X Y plane)
66
Perturbed current density Jz (X Y plane)
Arrows (Bx, By)
t 28.6/?pe
Z 230?
80
B
A
Current filaments
20
Y/?
80
D
C
20
80
20
80
20
X/?
67
Jz component generated by current channels (x-y
plane) at t 59.8?pe
arrows Bx, By
el-ion ? 5
el-positron 4 lt?lt100
161.5
76.1
el-positron ? 5
el-positron ? 15
22.6
?
?
?
-22.6
75.1
68
Comparison between electron-ion and
electron-positron
?pet 23.4
no-ambient magnetic field
shocked
injection
eBk 0.4510-4
UBsh /UBin 1,140
ele-ion
Uthe,j,sh /Uthe,j,in 1.02
eBk 1.0210-2
UBsh / UBin 6,080
ele-pos
Uthe,j,sh/Uthe,j,in 2.12
(Nishikawa et al. 2005)
69
Electron acceleration
(parallel injection)
strong magnetic field reduces the growth
rates
1 10 20 1500
injected
(Hededal Nishikawa 2005)
70
Magnetosonic shock structure in 1-D system
reflected
Buneman instability
Uix/U0
ion
Uex/U0
electron
Ue/U0
motional electric field
Ey/E0
Ey v0B0
trapped
Bz/B0
Ex/E0
ßeßi0.01 ?pe/?ce 19 mi/me20
U0 0.25c (0.375c) VA/c0.012
X/(c/?pe)
X/(c/?pe)
MA 32 ?0 1.03
(Hoshino Shimada, 2002, ApJ)
71
EB acceleration due to the current channel
(Z/? 430)
electron-positron jet 4 lt ? lt 100
t 50.7?pe
ne
Jy
arrows Ex, Ey
arrows Bx, By
Y/?
Y/?
X/?
X/?
B and E are nearly perpendicular
72
EB acceleration and deceleration
(Z/? 430)
Jz
arrows Ex, Ey
(EB)z
arrows Bx, By
Y/?
Y/?
X/?
X/?
both electrons and positrons are accelerated in
this region
E and B are nearly perpendicular
73
Schematic topology of magnetic field with
current channel (xz- plane)
t 16/?pe
Deflected jet electrons
Weibel instability
Magnetic field lines with loops created by
current channels
Reconnection ?
Initial setup
(Hededal Nishikawa 2004)
74
Electron vz?- z
t 30/?pe
?pe/?c 20
Ambient electrons (grey)
Jet electrons (black)
injected
(Hededal Nishikawa 2004)
75
Electron acceleration in perpendicular injection
t 30/?pe
injected
?pe/?c 1500
40 20 5
accelerated
(Hededal Nishikawa 2004)
76
1-D simulations of positron acceleration (Hoshino
et al. 1992)
Maser instability
electron
Ex
Ey
positron
proton
Bz
reflected jet
jet
( EM/KE)
precursor
positrons accelerated due to the resonance
injected
77
Illustration of the electron surfing mechanism

• How does this mechanism work in
  the 3-D shock transition regions?

78
Density and Jz in x-y plane
?pet 23.4
electron skin depth
density
JZ
4.8?
Y/?
9.6?
X/?
(Nishikawa et al. 2005)
79
Flat jet injected parallel to B

• Electron-ion jet, mi/me 20
• ? vj/c 0.9798, vet/c 0.1
• ? nj /na ? 0.741
• ? (1(vj/c)2)1/2 5
• vje 3vet, vji 3vit, vit /c 0.022
• ?pe/Oe 2.89, VA/c 0.0775, MA 12.65
• ?e (8pneTe/B2) 1.66
• ?pe?t 0.026, rj 40 ?x ? 10?ce (infinite)
• ?e 1.389?, ?i 6.211?

80
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81
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82
A Flat jet injected into an unmagnetized plasma

• Electron-positron jet, mp/me 1
• ? vj/c 0.9798, vet/c 0.1
• ? nj /na ? 0.741
• ? (1(vj/c)2)1/2 5
• vje 0.1vet, vjp 0.1vpt
• ?pe?t 0.013
• ?ce c/?pe 9.6?, ?e vet/?pe 0.96?

83
A Flat jet injected into an unmagnetized plasma

• Electron-positron jet, mp/me 1
• ? nj /na ? 0.741, vet vpt 0.1 c
• vje 0.1vet, vjp 0.1vpt (cold jet)
• ?pe?t 0.013
• ?ce c/?pe 9.6? (electron skin depth)
• ?e vet/?pe 0.96? (electron Debye length)
• ? grid size ( 1)

84
Electron-positron jet injected
electron-ion ambient plasma
electron-positron ambient plasma
85
M87
86
Z/?-?V? phase space for jet electrons at t
59.8?pe
el-ion ? 5
el-pos 4 lt?lt 100
el-pos ? 15
el-pos ? 5