Ken Nishikawa. What is Plasma? 2. Simulation methods. 3. Fluid (GRMHD) Simulations Global Dynamics of Plasmas

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1 Ken Nishikawa National Space Science & Technology Center/UAH 1. Basic Plasma Physics What is Plasma? 2. Simulation methods Macroscopic and Microscopic Processes 3. Fluid (GRMHD) Simulations Global Dynamics of Plasmas 4. Kinetic (RPIC) Simulations Kinetic Dynamics of Plasmas 5. Radiation Standard radiation model Self-consistent model "GRB Physics at Kavli Institute for Astronomy and Astrophysics (KIAA), May 18-22, /39

2 Collaborators: M. Medvedev (Univ. of Kansas) B. Zhang (Univ. Nevada, Las Vegas) P. Hardee (Univ. of Alabama, Tuscaloosa) J. Niemiec (Institute of Nuclear Physics PAN) Y. Mizuno (Univ. Alabama in Huntsville/CSPAR) Å. Nordlund (Neils Bohr Institute) J. Frederiksen (Neils Bohr Institute) ) H. Sol (Meudon Observatory) M. Pohl (Iowa State University) DHHartmann(Clemson D. H. Hartmann Univ.) ) M. Oka (UAH/CSPAR) G. J. Fishman (NASA/MSFC ) 2/39

3 Outline of talk Motivations Radiation i from two electrons Recent 3 D particle simulations of relativistic jets * e ± pair jet into e ± pair, γ= 15 New initial results of radiation from electrons based on particle trajectories Summary Future plans of our simulations of relativistic jets 3/39

4 Good dtext tbooks for radiation Classical Electrodynamics, by Jackson, J. D., Interscience, e ce, 1999 Radiative Processes in Astrophysics, by Rybicki, G. B., & Lightman, A. P., John Wiley & Sons, New York, 1979 Radiation Processes in Plasmas, by Bekefi, G., Wiley & Sons, New York, 1966 The Classical Theory of Fields, by Landau, L. D., Pergamon Press, /39

5 1. 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, Martins et al. 2009) The strength of magnetic fields is assumed based on the equipartition (magnetic field is similar to the thermal energy) (ε B ) The density of accelerated e ated electrons eecto saeassu are assumed by the power law (F(γ) = γ p ; p = 2.2?) (ε e ) Synchrotron emission is calculated based on p and ε B There are many assumptions in this calculation 5/39

6 Synchrotron Emission: radiation from accelerated adapted by S. Kobayashi 6/39

7 Slf Self consistent calculation l of radiation i 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 d 2000, 2006) which h is different from standard synchrotron emission Some synchrotron radiation from electron is reported (Nishikawa et al (astroph/ ; ; ) 7/39

8 Radiation from collisionless shock observer wer Pow GRB Shock simulations Hededal Thesis: Hededal & Nordlund 2005, submitted to ApJL (astro-ph/ ) 8/39

9 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/ ) Nishikawa et al (astro-ph/ ) 9/39

10 Synchrotron radiation from gyrating electrons in a uniform magnetic field electron trajectories B β β n β β n radiation electric field observed at long distance observer spectra with different viewing angles time evolution of three frequencies f/ω theoretical synchrotron spectrum pe = 8.5, 74.8, 654. Rybicki, G. B., & Lightman, A. P. 1979, Radiative Processes in Astrophysics, John Wiley & Sons, New York 10/39

11 Cyclotron radiation γ = 15 Angle dependence of radiation Radiation ratio at θ = 0 and π/2 (74.4) from Landau & Lifshitz, The Classical Theory of Fields, /39

12 Cyclotron emission of an electron in helical motion resultant electric field β 2 = β P 2 + β 2 = x = ω β sinθ ω 0 v P c v c γ = (1 β 2 ) 1/2 ω 0 = eb 0 m 0 γ y = mω 0 ω(1 β P cosθ) η m (ω,v,θ) = e2 ω 2 8π 2 ε 0 c 1 cosθ β P sinθ 2 J 2 2 m (x) + β J m 2 (x) δ(y) J m dj m (x)/dx 0 even θ = 0 G. Bekefi, Radiation Processes in Plasma, 1966, John Wiley & Sons, Inc 12/39

13 Synchrotron radiation from propagating electrons in a uniform magnetic field electron trajectories radiation electric field observed at long distance B θ observer gyrating spectra with different viewing angles θ Γ = 4.25 Nishikawa et al. astro-ph/ /39

14 A E B F C D (Nishikawa et al. astro-ph/ ) 14/39

15 Case A (Nishikawa et al. astro-ph/ ) 15/39

16 Case B (Nishikawa et al. astro-ph/ ) 16/39

17 Case C (Nishikawa et al. astro-ph/ ) 17/39

18 Case D (Nishikawa et al. astro-ph/ ) 18/39

19 Case E (Nishikawa et al. astro-ph/ ) 19/39

20 Case F (Nishikawa et al. astro-ph/ ) 20/39

21 3D jitter radiation (diffusive synchrotron radiation) with a ensemble of mono-energetic electrons (γ = 3) in turbulent magnetic fields (Medvedev 2000; 2006, Fleishman 2006) μ= -2 2d slice of magnetic filed 3D jitter radiation with γ = 3 electrons 0 2 Hededal & Nordlund (astro-ph/ ) 21/39

22 3-D simulation with MPI code Y injected at z = 25Δ Z grids (not scaled) 1.2 billion particles jet front ambient plasma X 22/39

23 Phase space of electrons red: jet electrons, blue: ambient electrons Phase space of electrons in the x/ γv x at t = 3250ω pe -1. Red dots show jet electrons which are injected from the left with γv x =15 (Nishikawa et al. ApJL, submitted, 2009, arxiv: ) 23/39

24 Shock velocity and bulk velocity trailing shock (reverse shock) contact discontinuity leading shock (forward shock) jet electrons Fermi acceleration? total electrons ambient electrons 24/39

25 Shock formation, forward shock, reverse shock v ts =0.56c v cd =0.76c total ambient v jf =0.996c jet ε B ε E () (a) electron density and d(b) electromagnetic field energy (ε B, ε E ) divided by the total kinetic energy at t = 3250ω -1 pe (Nishikawa et al. ApJL, submitted, 2009 arxiv: ) 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. 25/39

26 Radiation from collisionless shock observer wer Pow GRB Shock simulations Hededal Thesis: Hededal & Nordlund 2005, submitted to ApJL (astro-ph/ ) 26/39

27 Jitter radiation from electrons by tracing trajectories self-consistently using a small simulation system initial setup for jitter radiation select electrons (12,150) 150) in jet and ambient 27/39

28 final condition for jitter radiation 15,000 steps 1 dt = ω pe ω n = 100 θ n = 2 Δxjet jt= 75Δ 1 Δt jitt = 75 ω pe 28/39

29 Calculated spectra for jet electrons and ambient electrons γ = 15 θ =0 and 5 Case D γ = /39

30 Summary Simulation i 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. The magnetic fields created by Weibel instability generate highly inhomogeneous magnetic fields, which is responsible for jitter radiation (Medvedev, 2000, 2006; Fleishman 2006). 30/39

31 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 Simulations with magnetic field may accelerate particles further? In order to investigate shock dynamics further diagnostics will be developed d 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) 31/39

32 Gamma Ray Large Area Space Telescope (GLAST) (launchedonjune 11, 2008) glast.stanford.edu/ stanford Compton Gamma-Ray Observatory (CGRO) Burst And Transient Source Experiment (BATSE) ( ) 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 GLAST Burst Monitor (GBM) PI: Bill Paciaas (UAH) (Chip Meegan (Retired;USRA)): X rays and gamma rays with energies between 8 kev and 25 MeV ( 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. 32/39

33 GRB progenitor relativistic jet Fushin (god of wind) (Tanyu Kano 1657) emission (shocks, acceleration) Raishin as (god of lightning) 33/39

34 Schematic GRB from a massive stellar progenitor Simulation box (Meszaros, Science 2001) Prompt emission Polarization? Accelerated particles emit waves at shocks 34/39

35 Collisionless shock Electric and magnetic fields created selfconsistently by particle dynamics randomize particles jet (Buneman 1993) B/ t = E E/ t = B J dm 0 γv/dt = q(e +v B) ρ/ t + J = 0 jet electron jet ion ambient electron ambient ion 35/39

36 Weibel instability generated magnetic fields current filamentation J jet Time: τ = γ sh 1/2/ω pe 21.5 Length: λ = γ 1/2 th c/ω pe 9.6Δ J x ev z B x (electrons) (Medvedev & Loeb, 1999, ApJ) 36/39

37 Perpendicular current J z (arrows:j z,x ) n ISM = 1/cm 3 electron-positron γ= 15 (B) at Y = 43Δ ω pe t = msec jet ω -1 pe 0.1msec c/ω pe = 5.3 km L 300 km Weibel instability jet front (Nishikawa et al. 2005) 37/39

38 3-D isosurfaces of density of jet particles and Jz for narrow jet (γv =12.57) electron-ion ambient t = 59.8ω e -1 jet electrons (blue), positrons (gray) -J z (red), magnetic field lines (white) electron-positron ambient

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