1. 1/39 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

2. 2/39 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

3. 3/39 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

4. 4/39 Accelerated particles emit waves at shocks Schematic GRB from a massive stellar progenitor (Meszaros, Science 2001) Prompt emission Polarization ? Simulation box

5. 5/39 3-D simulation Z X Y jet front jet 85×85×640 grids (not scaled) 380 Million particles injected at z = 25Δ Weibel inst

6. 6/39 Collisionless shock Electric and magnetic fields created self- consistently by particle dynamics randomize particles jet ion jet electronambient electron ambient ion jet ∂B/∂t = –  E ∂E/∂t =  B – J dm 0 γv/dt = q(E +v  B) ∂ρ/∂t + J = 0 (Buneman 1993)

7. 7/39 Weibel instability x  ev z  B x jet J J current filamentation generated magnetic fields Time: τ = γ sh 1/2 /ω pe  21.5 Length: λ = γ th 1/2 c/ω pe  9.6Δ (Medvedev & Loeb, 1999, ApJ) (electrons)

8. 8/39 Perpendicular current J z (arrows:J z,x ) ω pe t = 59.8 ≈ 6msec jet Weibel instability jet front (Nishikawa et al. 2005) at Y = 43Δelectron-positron γ= 15 (B) n ISM = 1/cm 3 ω pe -1 ≈ 0.1msec c/ω pe = 5.3 km L ≈ 300 km

9. 9/39 BxBx at Y = 43Δ ⋆ ⋆ ⋆ Blue X = 33 Δ Red X = 43 Δ Green X = 53 Δ X/Δ Y/ Δ Evolution of B x due to the Weibel instability jet Weibel instability jet front ω pe t = 59.8 (convective instability) (Nishikawa et al. 2005) el-positron γ= 15 (B)

10. t = 59.8ω e -1 10/39 Magnetic field generation and particle acceleration with narrow jet (u || = γv || = 12.57) electron-ion ambient ε Bmax = 0.061 electron-positron ambient ε Bmax = 0.012 (Ramirez-Ruiz, Nishikawa, Hededal 2007) red dot: jet electrons blue dots: ambient (positrons and ions) jet electrons ambient positrons ambient ions BB

11. ) 3-D isosurfaces of density of jet particles and J z for narrow jet (γv || =12.57) jet electrons (blue), positrons (gray) electron-positron ambient electron-ion ambient -J z (red), magnetic field lines (white) t = 59.8ω e -1

12. 12/39 Isosurfaces of z-component of current density ) for narrow jet ( γ v || = 12.57) electron-ion ambient plasma electron-positron ambient plasma (+J z : blue, -J z :red) local magnetic field lines (white curves)

13. ) 3-D isosurfaces of z-component of current J z for narrow jet (γv || =12.57) electron-ion ambient -J z (red), +J z (blue), magnetic field lines (white) t = 59.8ω e -1 Particle acceleration due to the local reconnections during merging current filaments at the nonlinear stage thin filamentsmerged filaments

14. 14/39 Ion Weibel instability (Hededal et al 2004) E  B acceleration electron trajectory ion current

15. 15/39 arrows: E x, E y (Z/Δ= 430) Acceleration due to the quasi-DC electric field created by the current channel JzJz nene arrows: B x, B y electron-positron jet 3 < γ < 100 X/Δ Y/ Δ t = 59.8ω pe B and E are nearly perpendicular into electron-positron ambient plasma

16. 16/39 Fermi acceleration (self-consistent with turbulent magnetic field) Fermi acceleration has been done with self-consistent magnetic fields (Spitkovsky ApJ 2008) ω pe t = 8400 density εBεB Av.density Av. ε B electron x-v x particle trajectories ϒ ω pe t ϒ -2.4 particle spectrum at ω pe t = 10 4 ϒ

17. 17/39 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

18. 18/39 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)

19. 19/39 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)

20. 20/39 Synchrotron radiation from gyrating electrons in a uniform magnetic field β β n n  B β  β  electron trajectories radiation 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/ω pe = 8.5, 74.8, 654.

21. 21/39 Radiation from collisionless shock GRB Shock simulations Hededal Thesis: Hededal & Nordlund 2005, submitted to ApJL (astro-ph/0511662) Power ☺ observer

22. 22/39 293 475 Initial tω pe =0tω pe = 2.5 Preliminary uncompleted JzJz Particle trajectories (selected) Partial spectra (viewing angles: 0°,5°,- -30°) Accumulated spectrum over all angles 0° (head on) 30° So far the calculation has been done 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)

23. 23/39 232 473 Initial tω pe tω pe = 62.5 Preliminary uncompleted JzJz Particle trajectories (selected)Partial spectra (viewing angles: 0°,5°,- -30°) Assembled spectrum) 0° (head on) 5° 30° So far the calculation has been done for 2500 steps (10,000steps). The rest of calculation will be completed in a month or so. for detail, see Nishikawa et al. 2008 (astro-ph/0802.2558)

24. 24/39 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).

25. 25/39 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. 26/39 Gamma-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

27. 27/39 GRB progenitor emission relativistic jet Fushin Raishin (Tanyu Kano 1657) (shocks, acceleration) (god of wind) (god of lightning)

28. 28/39 M87

29. 29/39 Pair-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)

30. 30/39 Initial parallel velocity distributions of pair- created jets (e  ) (into ambient pair plasma) A: γ = (1–(v j /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 (m i /m e = 20) Schematic initial parallel velocity distribution of jets Growth times of Weibel instability: τ B’ ≪ τ A’ ≪ τ B ≈ τ A B A 12.6

31. 31/39 BxBx at Y = 43Δ ⋆ ⋆ ⋆ Blue X = 33 Δ Red X = 43 Δ Green X = 53 Δ X/Δ Y/ Δ Evolution of B x due to the Weibel instability jet Weibel instability jet front ω pe t = 59.8 (convective instability) (Nishikawa et al. 2005) el-positron γ= 15 (B)

32. 32/39 narrow jet electron-ion broad jet electron-ion  B = E B /E ke (shocked region: 300<z<600) Comparisons among four cases narrow jet e ± pair broad jet e ± pair j z (j x, j z ) B2B2 0.0257 0.0275 0.0060 0.0045 A’ B’ A B (Ramirez-Ruiz, Nishikawa, Hededal 2007) t = 59.8ω e -1

33. Momentum distributions of jet electrons injected into pair ambient plasma 33/39 parallel perpendicular solid curves: t = 20.8ω e -1, dashed curves: t = 59.8ω e -1 (Ramirez-Ruiz, Nishikawa, Hededal 2007) red curves: broad jet, blue curves: narrow jet

34. 34/39 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=μ= -2 0 2 2d slice of magnetic filed 3D jitter radiation with  = 3 electrons

35. ) 3-D isosurfaces of z-component of current J z for narrow jet (γv || =12.57) electron-ion ambient electron-positron ambient -J z (red), +J z (blue), magnetic field lines (white) t = 59.8ω e -1

36. 36/39 ) Isosurfaces of jet particles for narrow jet ( γ v || = 12.57) electron-positron ambient plasma electron-ion ambient plasma jet electrons (blue), positrons (gray)