Radiation Calculations using RPIC simulations
Ken Nishikawa
National Space Science & Technology Center/UAH
Collaborators:
J. Niemiec (Institute of Nuclear Physics PAN)
M. Medvedev (Univ. of Kansas)
B. Zhang (Univ. Nevada, Las Vegas)
P. Hardee (Univ. of Alabama, Tuscaloosa)
Y. Mizuno (Univ. Alabama in Huntsville/CSPAR)
Å. Nordlund (Neils Bohr Institute)
J. Frederiksen (Neils Bohr Institute)
H. Sol (Meudon Observatory)
M. Pohl (U‐Potsdam/DESY)
D. H. Hartmann (Clemson Univ.)
2nd GTAC workshop
Loa Alomos, August 29 - 31, 2011
1/39
Outline of talk
 Introduction and Weibel instability
 Radiation from two electrons
 New initial results of radiation from jet electrons
which are traced in the simulations selfconsistently
 3-D particle simulations of relativistic jets
* e±pair jet into e±pair, γ= 15 and
* electron-ion (mi/me = 20) into electron-ion γ= 15
shock structures
 Recent simulations with perpendicular magnetic
field with denser jets
 Future plans of our simulations of relativistic jets
2/39
Schematic GRB from a massive stellar progenitor
(Meszaros, Science 2001)
Simulation box
Prompt emission
Polarization ?
Accelerated particles emit waves at shocks
3/39
in RPIC
mixed
Courtesy of L. Stawarz
4/39
3-D simulation
with MPI code
injected at z = 25Δ
Y
Z
X
131×131×4005
grids
(not scaled)
1.2 billion particles
jet front
ambient plasma
5/39
Collisionless shock
Electric and magnetic fields created selfconsistently by particle dynamics randomize
particles
(Buneman 1993)
¶B / ¶t = -Ñ ´ E
¶E / ¶t = Ñ ´ B - J
dm0g v / dt = q(E + v ´ B)
¶r / ¶t + ÑiJ = 0
jet
jet electron
jet ion
ambient electron
ambient ion
6/39
Weibel instability
current filamentation
jet
generated
magnetic fields
Time:
τ = γsh1/2/ωpe ≈ 21.5
Length:
λ = γth1/2c/ωpe ≈ 9.6Δ
J
J
x
evz × Bx
(electrons)
(Medvedev & Loeb, 1999, ApJ)
7/39
Evolution of Bx due to the
Weibel
instability
(convective instability)
el-positron γ= 15 (B)
ωpet = 59.8
Y/Δ
at Y = 43Δ
⋆⋆⋆
Bx
jet
X/Δ
Blue X = 33 Δ
Red X = 43 Δ
Green X = 53 Δ
jet front
Weibel instability
(Nishikawa et al. 2005)
8/39
3-D isosurfaces of z-component of current Jz for narrow jet (γv||=12.57)
electron-ion ambient
t = 59.8ωe-1
-Jz (red), +Jz (blue), magnetic field lines (white)
Particle acceleration due to the local
reconnections during merging current
filaments at the nonlinear stage
thin filaments
merged filaments
Synchrotron Emission: radiation from accelerated
adapted by Kobayashi
(see talks by Draigne,
Derishev, Kobayashi,
Massaro, Curran)
10/39
Radiation from particles in 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)
Nishikawa et al. 2011 ASR
Sironi & Spitkovsky, 2009, ApJ
Martins et al. 2009, Proc. of SPIE Vol. 7359
Frederiksen et al. 2010, ApJL
11/39
Calculation of synchrotron
B
Retarded electric field
Two electron paths
Critical frequency
3
c
w c = g 3 ( ), r = 11.03
2
r
=2309
d 2W|| m0 cq 2w 2 rLq b 2 | K 2/3 ( c / cosqb 2 ) |2
=
(
)
dw dW
12p
c
(cosqb 2 )2
2
wc
q b2 º 2(1- b cosq ), c = w rLq b3 / 3c, rL = g mv / (qB)
Spectra with different viewing angles
12/39
Synchrotron radiation from propagating electrons in a uniform magnetic field
electron trajectories
B
gyrating
radiation electric field observed at long distance
θ
observer
spectra with different viewing angles (helical)
θγ = 4.25°
Nishikawa et al. astro-ph/0809.5067
13/39
Synchrotron versus Jitter radiation
Synchrotron
Dq
•a
• K = ql B / mc2
1
Jitter radiation
Dq
• a
• K = ql B / mc2
1
electron-positron jet in a small system
K
1?
14/39
Line of death in GRB spectra (BATSE and GBM)
Some of spectra of GRB prompt emission
have low-frequency slope a ( f (n ) µ n a )
harder than synchrotron ``line-of-death” α=−2/3
Jitter spectra would have low-frequency slope as
hard as f (n ) µ n 0 (α=0)
synchrotron line of death
long GRBs
short GRBs
(Nava et al. 2011)
GBM/LAT short & long
GRBs
15/39
Radiation from test (accelerated) particles in static turbulent magnetic fields
generated by the Weibel instability in 2D PIC simulation
y
t = 2250w -1
pe
t s = 3000Dt = 135w -1
p
number density
Dt = 0.045w -1
p
test particle simulation in a
fixed snapshot of electromagnetic filed
B2
E2
gb x
gb y
x
jitter radiation
(Sironi & Spitkovsky 2009)
16/39
Radiation from electrons in self-consistent electromagnetic field from a 2D
PIC simulation
Due to the radiation is calculated
in downstream frame the radiation
is isotropic. An additional Lorentz
transformation is required, if the
down-stream medium is moving
with respect to the observer (no
beaming effect is taken account and
they are different from the observed
radiation).
They conclude that jitter regime is
obtained only if with artificially
reduced the strength of the
electromagnetic filed?
(K º qBl / mc2)
This conclusion is due to that radiation
is calculated in downstream frame?
(Sironi & Spitkovsky 2009)
17/39
Importance of Synchrotron radiation calculated in 3-D system
γ = 6, P+ e-
counter-streaming jet, no shock generated
3D
6<t<16
32<t<72
2D
6<t<16
32<t<72
Frederiksen et al. ApJL, 2010
18/39
Radiation from electrons by tracing trajectories self-consistently
using a small simulation system
initial setup for jitter radiation
select electrons
randomly (12,150)
in jet and ambient
19/39
Calculated spectra for jet electrons and ambient electrons
a = λe|δB|/mc2 < 1 (λ: the length scale and |δB| is the magnitude of the fluctuations)
γ = 15
qg = 3.81°
θ = 0° and 5°
high frequency
due to turbulent
magnetic field
Bremesstrahlung (ballistic)
Case D
γ = 7.11
Nishikawa et al. 2009 (arXiv:0906.5018)
20/39
3D jitter radiation (diffusive synchrotron radiation) with a ensemble of
mono-energetic electrons (γ = 3) in turbulent magnetic fields
(Medvedev 2000; 2006, Fleishman 2006) (ballistic)
2d slice of
magnetic field
3D jitter radiation
with γ = 3 electrons
μ= -2
0
2
Hededal & Nordlund (astro-ph/0511662)
21/39
Dependence on Lorentz factors of jets
θ = 0°
5° qg = 3.81°
γ = 15
θ = 0°
5°qg = 0.57
γ = 100
Narrow beaming
angle
22/39
Observations and numerical spectrum
a
b
GRB 080916C
c
d
e
a≈1
a≈1
Abdo et al. 2009, Science
Nishikawa et al. 2010
23/39
Radiation in a larger system
System size: 8000 × 240 × 240
Electron-positron , γ = 15
(Preliminary result)
Sampled particles 115,200
-1
-1
200w pe ≤ t ≤ 275 w pe
24/39
Shock velocity and bulk velocity
trailing shock
(reverse shock)
jet electrons
contact discontinuity
leading shock
(forward shock)
Fermi acceleration ?
total electrons
ambient electrons
25/39
Shock formation, forward shock, reverse shock
vts=0.56c
vcd=0.76c
total
ambient
vjf=0.996c
jet
εB
εE
(a) electron density and (b) electromagnetic
field energy (εB, εE) divided by the total
kinetic energy at t = 3250ωpe-1
(Nishikawa et al. ApJ, 698, L10, 2009)
Time evolution of the total electron density.
The velocity of jet front is nearly c, the predicted
contact discontinuity speed is 0.76c, and the
velocity of trailing shock is 0.56c.
26/39
Comparison with different mass ratio (electron-positron and electron-ion)
electron-positron
electron-ion (mi/me = 20)
X/Δ>2000
27/39
Electron shock surfing acceleration (Sironi & Spitkovsky, 2009, ApJ)
θ = 90
(see Poster: Murphy)
(Amano & Hoshino, 2009, ApJ)
28/39
New simulations with perpendicular magnetic field
(E.J Choi, K. Min, KN, in preparation, 2011)
29/39
Perpendicular magnetic field
(E.J Choi, K. Min, KN, in preparation, 2011)
30/39
Summary
 Simulation results show electromagnetic stream
instability driven by streaming e± pairs are
responsible for the excitation of nearequipartition, turbulent magnetic fields and
a structure with leading and trailing shocks.
 Shock is similar to the shock in simulations with
the constant contact discontinuity.
 The spectrum from jet electrons in a weak
magnetic field in a small system shows a
Bremsstrahlung like spectrum with higher
frequency enhancement with turbulent magnetic
field.
 The magnetic fields created by Weibel instability
generate highly inhomogeneous magnetic fields,
which is responsible for jitter radiation
(Medvedev, 2000, 2006; Fleishman 2006).
31/39
Future plans of our simulations of relativistic jets
• Calculate radiation with larger systems for different
parameters in order to compare with observational data
• Include inverse Compton emission beside synchrotron
radiation to obtain high frequency radiation
• Simulations with magnetic fields including turbulent
magnetic fields with pair plasma and electron-ion
plasma
• Reconnection simulations for additional acceleration
mechanism including magnetic reconnection
• Non-relativistic jet simulations for understanding SNRs
32/39
Gamma-Ray Large Area Space Telescope (FERMI)
(launched on June 11, 2008) http://www-glast.stanford.edu/
Compton Gamma-Ray
Observatory (CGRO)
Burst And Transient
Source Experiment
(BATSE) (1991-2000)
PI: Jerry Fishman
Fermi (GLAST)
All sky monitor
 Large Area Telescope (LAT) PI: Peter Michaelson:
gamma-ray energies between 20 MeV to about 300 GeV
 Fermi Gamma-ray Burst Monitor (GBM) PI: Bill Paciaas
(UAH) (Chip Meegan (Retired;USRA)): X-rays and gamma
rays with energies between 8 keV and 25 MeV
(http://gammaray.nsstc.nasa.gov/gbm/)
The combination of the GBM and the LAT provides a
powerful tool for studying radiation from relativistic jets
and gamma-ray bursts, particularly for time-resolved
spectral studies over very large energy band.
33/39
Jet formation in general relativistic PIC simulation
Keplerian motion of
electrons and positrons
may excite charge separation
instability, then generate
jet
A method for incorporating the Kerr–Schild metric in electromagnetic
particle-in-cell code, M. Watson & K.-I. Nishikawa,
Computer Physics Communications 181 (2010) 1750–1757
34/39
Ion Weibel instability
ion current
E✕B
acceleration
electron trajectory
(Hededal et al 2004)
35/39
Effects of ambient magnetic field and jet Lorentz factor
Energetic jet electrons produce higher frequency waves
Turbulent magnetic fields creates higher frequency waves
36/39
Phase space of electrons
red: jet electrons, blue: ambient electrons
Phase space of electrons in the x/∆−γvx at t = 3250ωpe-1.
Red dots show jet electrons which are injected from the left with γvx =15
(Nishikawa et al. ApJ, 698, L10, 2009)
37/39
final condition for radiation
15,000 steps
dt = 0.005 w pe
-1
nω = 100
nθ = 2
Δxjet = 75Δ
75Δ
tr = 75 w pe
-1
38/39
Shock velocity and structure based on 1-D HD analysis
moving contact discontinuity (CD)
trailing shock
(reverse shock)
leading shock
(forward shock)
in CD frame
nsj / g cd
¢ n j = 3.36
bs = 0.417 g cd¢ = 5.60
(Nishikawa et al. 2009)
4 <G= 3 <5
3
2
3
fixed CD
Density
n2/γ0n1=3.13
bc = 0.47
γ0 = 15
0
(Spitkovsky 2008 (adapted))
39/39
Fermi acceleration (self-consistent with turbulent magnetic field)
ωpet = 8400
density
εB
Fermi acceleration has been done with
self-consistent magnetic fields
(Spitkovsky, ApJ, 2008)
Av.density
Av. εB
particle spectrum at ωpet = 104
electron
x-vx
ωpet
particle trajectories
ϒ-2.4
ϒ
ϒ
40/39