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Particle-in-cell simulations of GRB shocks

Ken Nishikawa

National Space Science & Technology Center/CSPAR (UAH)Meudon Observatory (visiting)

(email: ken-ichi.nishikawa-1@nasa.gov)

Collaborators:

M. Medvedev (Univ. of Kansas) B. Zhang (Univ. Nevada, Las Vegas) P. Hardee (Univ. of Alabama, Tuscaloosa)Y. Mizuno (Univ. Nevada, Las Vegas/CSPAR)H. Sol (Meudon Observatory)D. H. Hartmann (Clemson Univ.) G. J. Fishman (NASA/MSFC ) R. Preece (NSSTC/UAH)

2008 Nanking GRB Conference, Nanjing, China, June 23-27, 2008

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Outline of talk• Motivations• 3-D particle simulations of relativistic jets * electron-positron, (a pair jet created by photon annihilation) = 5 (electron-ion), 15, 4 < <100• Recent 3-D particle simulations of relativistic jets * e±pair jet into e±pair and electron-ion ambient plasmas

= 12.57, 1 < <30 (avr ≈ 12.6)• New simulations of Fermi acceleration• Summary of current 3-D simulations (Weibel

Instability)• Future plans of our simulations of relativistic jets Calculation of radiation based on particle trajectories

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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

• Calculate synchrotron/jitter radiation from accelerated particles without assumesions

• Examine possibilities for spectra and their variations in relativistic jets

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Accelerated particles emit waves at shocks

Schematic GRB from a massive stellar progenitor(Meszaros, Science 2001)

Prompt emission Polarization ?

Simulation box

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3-D simulation

Z

X

Y

jet front

jet

85×85×640 grids

(not scaled)

380 Million particles

injected at z = 25Δ

Weibel inst

Weibel inst

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Collisionless shockElectric and magnetic fields created self-consistently by particle dynamics randomize particles

jet ion

jet electron ambient electronambient ion

jet

∂B/∂t = – E

∂E/∂t = B – J

dm0γv/dt = q(E +vB)

∂ρ/∂t + •J = 0

(Buneman 1993)

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Weibel instability

xevz Bx

jet

J

J

current filamentation

generated magnetic fields

Time: τ = γsh

1/2/ωpe 21.5 Length: λ = γth

1/2c/ωpe 9.6Δ

(Medvedev & Loeb, 1999, ApJ)

(electrons)

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Perpendicular current Jz (arrows:Jz,x)

ωpet = 59.8 ≈ 6msec

jet

Weibel instability jet front

(Nishikawa et al. 2005)

at Y = 43Δelectron-positron γ= 15 (B)

nISM = 1/cm3

ωpe-1 ≈ 0.1msec

c/ωpe = 5.3 km

L ≈ 300 km

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Bx

at Y = 43Δ

⋆⋆ ⋆

Blue X = 33 ΔRed X = 43 ΔGreen X = 53 Δ

X/Δ

Y/Δ

Evolution of Bx due to the Weibel instability

jet

Weibel instabilityjet front

ωpet = 59.8(convective instability)

(Nishikawa et al. 2005)

el-positron γ= 15 (B)

t = 59.8ωe-1 10/39Magnetic field generation and particle

acceleration with narrow jet (u|| = γv|| = 12.57)

electron-ionambientεBmax = 0.061

electron-positronambientεBmax = 0.012

(Ramirez-Ruiz, Nishikawa, Hededal 2007)

red dot: jet electronsblue dots: ambient (positrons and ions)

jet electrons

jet electrons

ambient positrons

ambient ions

B

3-D isosurfaces of density of jet particles and Jz for narrow jet (γv||=12.57))

jet electrons (blue), positrons (gray)

electron-positronambient

electron-ionambient

-Jz (red), magnetic field lines (white)t = 59.8ωe-1

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Isosurfaces of z-component of current density for narrow jet (γv||= 12.57))

electron-ionambient plasma

electron-positronambient plasma

(+Jz: blue, -Jz:red) local magnetic field lines (white curves)

3-D isosurfaces of z-component of current Jz for narrow jet (γv||=12.57))

electron-ion ambient

-Jz (red), +Jz (blue), magnetic field lines (white)

t = 59.8ωe-1

Particle acceleration due to the localreconnections during merging currentfilaments at the nonlinear stage

thin filaments merged filaments

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Ion Weibel instability

(Hededal et al 2004)

E B acceleration

electron trajectory

ion current

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arrows: Ex, Ey

(Z/Δ= 430)

Acceleration due to the quasi-DC electric field created by the current channel

Jz nearrows: Bx, By

electron-positron jet 3 < γ < 100

X/Δ X/Δ

Y/Δ Y/Δ

t = 59.8ωpe

B and E are nearly perpendicular

into electron-positron ambient plasma

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Fermi acceleration (self-consistent with turbulent magnetic field)

Fermi acceleration has been done withself-consistent magnetic fields (Spitkovsky ApJ 2008)

ωpet = 8400

density

εB

Av.density

Av. εB

electron x-vx

particle trajectories

ϒϒ-2.4

particle spectrum at ωpet = 104

ϒ

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Present theory of Synchrotron radiation

• Fermi acceleration (Monte Carlo simulations are not self-consistent; particles are crossing at the shock surface many times and accelerated, the strength of turbulent magnetic fields are assumed), New simulations show Fermi acceleration (Spitkovsky 2008)

• 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

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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

• Some synchrotron radiation from electron is reported (Nishikawa et al. 2008 (astro-ph/0801.4390;0802.2558)

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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)Nishikawa et al. 2008 (astro-ph/0802.2558)

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Synchrotron radiation from gyrating electrons in a uniform magnetic field

β

β

n

n

B

β

β

electron trajectoriesradiation electric field observed at long distance

spectra with different viewing angles

0°

theoretical synchrotron spectrum

1°2°3°

6°

time evolution of three frequencies

4°

5°

observer

f/ωpe = 8.5, 74.8, 654.

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Radiation from collisionless shock

GRB Shock simulations

Hededal Thesis:

Hededal & Nordlund 2005, submitted to ApJL (astro-ph/0511662)

Pow

er

☺observer

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293 475Initial tωpe=0 tωpe = 2.5 Preliminary uncompleted

Jz

Particle trajectories (selected) Partial spectra (viewing angles: 0°,5°,- -30°)

Accumulated spectrum over all angles

0° (head on)

30°

So far the calculation has beendone for 100 steps (10,000steps).The rest of calculation will be completed in a month or so. Due to the short time, some collective motions may cause periodicity in obtained spectrum.for detail, see Nishikawa et al. 2008 (astro-ph/0802.2558)

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Summary• Simulation results show electromagnetic stream

instability driven by streaming e± pairs are responsible for the excitation of near-equipartition, turbulent magnetic fields.

• Ambient ions assist in generation of stronger magnetic fields.

• Weibel instability plays a major role in particle acceleration due the quasi-steady radial electric field around the current filaments and local reconnections during merging filaments in relativistic jets.

• Broadband (not monoenergetic) jets sustain the stronger magnetic field over a longer region.

• The magnetic fields created by Weibel instability generate highly inhomogeneous magnetic fields, which is responsible for jitter radiation (Medvedev, 2000, 2006; Fleishman 2006).

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Future plans for particle acceleration in relativistic jets

• Further simulations with a systematic parameter survey will be performed in order to understand shock dynamics with larger systems

• In order to investigate shock dynamics further diagnostics will be developed

• Investigate synchrotron (jitter) emission, and/or polarity from the accelerated electrons in inhomogeneous magnetic fields and compare with observations (Blazars and gamma-ray burst emissions) (Medvedev, 2000, 2006; Fleishman 2006)

26/39Gamma-Ray Large Area Space Telescope (GLAST)

(launched on June 11, 2008)http://www-glast.stanford.edu/

• Large Area Telescope (LAT) PI: Peter Michaelson:

gamma-ray energies between 20 MeV to about 300 GeV • GLAST Burst Monitor (GBM) PI: Chip Meegan (MSFC): 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.

Burst And Transient Source Experiment

(BATSE) (1991-2000)

PI: Jerry Fishman

Compton Gamma-Ray

Observatory (CGRO)

GLAST

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GRB progenitor

emission

relativistic jet

Fushin

Raishin(Tanyu Kano 1657)

(shocks, acceleration)

(god of wind)

(god of lightning)

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M87

29/39Pair-creation by collisions with lower energy photons: → e+e-

Schematic plot of e± pair cascades triggered by the back-scattering of seed -ray photons on the external medium. (e.g., Piran 1999)

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Initial parallel velocity distributions of pair-created jets (e) (into ambient pair plasma)

• A: γ = (1–(vj/c)2)–1/2 = 12.57 (narrow jet)

• B: 1 < γ < 30

(broad jet)

(pair jet created by photon

annihilation, γ+γ e)

• A’and B’: injected into ambient electron-ion plasma (mi/me = 20)

Schematic initial parallel velocity distribution of jets

Growth times of Weibel instability:

τ B’ ≪ τ A’ ≪τB ≈ τA

B

A

12.6

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Bx

at Y = 43Δ

⋆⋆ ⋆

Blue X = 33 ΔRed X = 43 ΔGreen X = 53 Δ

X/Δ

Y/Δ

Evolution of Bx due to the Weibel instability

jet

Weibel instabilityjet front

ωpet = 59.8(convective instability)

(Nishikawa et al. 2005)

el-positron γ= 15 (B)

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narrow jet

electron-ion

broad jet

electron-ion

B = EB/Eke

(shocked region: 300<z<600)

Comparisons among four cases

narrow jet

e±pair

broad jet

e±pair

jz (jx, jz) B2

0.0257

0.0275

0.0060

0.0045

A’

B’

A

B

(Ramirez-Ruiz, Nishikawa, Hededal 2007)

t = 59.8ωe-1

Momentum distributions of jet electronsinjected into pair ambient plasma

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parallel perpendicular

solid curves: t = 20.8ωe-1, dashed curves: t = 59.8ωe

-1

(Ramirez-Ruiz, Nishikawa, Hededal 2007)

red curves: broad jet, blue curves: narrow jet

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Hededal & Nordlund (astro-ph/0511662)

3D jitter radiation (diffusive synchrotron radiation) with a ensemble of mono-energetic electrons ( = 3) in turbulent magnetic fields (Medvedev 2000; 2006, Fleishman 2006)

μ= -2

0

2

2d slice of magnetic filed

3D jitter radiation with = 3 electrons

3-D isosurfaces of z-component of current Jz for narrow jet (γv||=12.57))

electron-ionambient

electron-positronambient

-Jz (red), +Jz (blue), magnetic field lines (white)t = 59.8ωe-1

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Isosurfaces of jet particles for narrow jet (γv||= 12.57))

electron-positronambient plasma

electron-ionambient plasma

jet electrons (blue), positrons (gray)