Radiation from accelerated particles in relativistic jets with shocks, shear-flow and reconnections

Transcription

1 Radiation from accelerated particles in relativistic jets with shocks, shear-flow and reconnections Ken Nishikawa Physics/UAH/NSSTC P. Hardee (Univ. of Alabama, Tuscaloosa) Y. Mizuno (National Tsing Hua University, Taiwan) I. Duţan (Institute of Space Science, Rumania) B. Zhang (Univ. Nevada, Las Vegas) M. Medvedev (Univ. of Kansas) A. Meli (Univ. of Gent) E. J. Choi (KAIST) K. W. Min (KAIST) J. Niemiec (Institute of Nuclear Physics PAN) Å. Nordlund (Niels Bohr Institute) J. Frederiksen (Niels Bohr Institute) H. Sol (Meudon Observatory) M. Pohl (U Potsdam/DESY) D. H. Hartmann (Clemson Univ.) A. Marscher (Boston Univ.) J. Gómez (IAA, CSIC) XXVII Texas Symposium on 1/39 Relativistic Astrophysics Dallas, TX, December 8-13, 2013

2 Outline 1. Magnetic field generation and particle acceleration in kinetic Kelvin-Helmholtz instability 2. Self-consistent radiation method using PIC simulations 3. Synthetic spectra in shocks generated by the Weibel instability 5. Strong magnetic field amplification with colliding jets with magnetic fields 6. Acceleration in recollimation shock 7. Summary 8. Future plans

3 Simulations of Kinetic Kelvin-Helmholtz instability with counter-streaming flows (γ 0 = 3, m i /m e =1836) magnetic field lines electron density Ä Ä Ä Ä Alves et al. (2012), Grismayer et al. (2013)

4 Simulations of KHI with core and sheath jets RMHD, no wind ω=0.93, time=60.0 case of V theath = 0 Mizuno, Hardee & Nishikawa, ApJ, 662, 835, 2007

5 New KKHI simulations with core and sheath jets in slab geometry γ j = 15, m i /m e = 20 B y B y Nishikawa et al econf C (arxiv: ) J x B y

6 Electric field generation by KKHI with real mass ratio γ j = 15, m i /m e = 1836, t = 30/ω pe t = 70/ω pe E z B y E z (Nishikawa et al. Annales Geophysicae, 2013)

7 Motion of the electrons across the shear surface produce electric currents which generate magnetic field t = 30/ω pe γ j = 1.5, m i /m e = 20 J x B y

8 B y in the x z plane γ = 15 m i /m e = 1386 tω pe = 70 m i /m e = 1 tω pe = 200

9 KKHI with electron-positron jet (core-sheath scheme) γ= 15 B y t = 200/ω pe B y B z (Nishikawa et al. in preparation, 2013c)

10 Generation of magnetic field in electron-positron jet-sheath plasmas B y t = 200/ω pe B y J x with arrows (B y, B z ) no DC magnetic field is found at this time (Nishikawa et al. in preparation, 2013c)

11 Magnetic Field Generation and Particle Energization at Relativistic Shear Boundaries in Collisionless Electron-Positron Plasmas (2D simulation) p 0 = p x /mc tω e = p 0 = 5 B x (Liang et al. 2013)

12 frequency limit the dispersion relation can be written as er the solution for transverse E&M waves from eq.(14). Provide Study of the relativistic velocity shear interface KKHI instability rse wave γ am ω p,am dispersion ωp,j 2 t(ω relat kv am ion ) 2 associat + γ jt ω p,j ed t ωp,am(ω 2 with avelocity kv jt ) 2 shear 0. surf ect quadratic of parallel equation magnetic fields on KKHI. We will look at this cas p,am)ω qual 2 densities 2(γ am ω p,j with t kv am (A) + γ jt count ω p,am i(kx kv er-st jt ωt) )ω+ reaming (γ ω p,j and t k 2 Vam 2 (B + ) γ jtω uneq p,am iven eturnby to the general dispersion relation, eq.(8): (kv ω) 2 where ω p 4πne 2 / γ 3 m,perturb flow direction, and the prime de e Within each medium on eit be written as: (γ am (k 2 ω c 2 p,j t kv + γ 2 am ωp 2 + γ jt ω 2 p,am ) 1/ 2 kv jt ) (kv ± i (γ amω ω) 2 p,j t γ jt ω p,am [(kv + ω) 2 ) 1/ 2 ωp+ 2 ] (γ am ω p,j t + γ jt ω p,am ) (γ am ω p,j t + γ jt ω p,am ) k(v jt V am ) al part +(k 2 gives c 2 + the γ+ 2 ω2 phase p+ velocity ω2 ) 1/ 2 (kv and + the ω) imaginary 2 [(kv part (kv ω) 2 gives ωp 2 ]= 0. + the ω) tem 2 + y shows the dependence of the growth rate on the velocity (kv densities with count er-st reaming velocities + ω) 2 (k 2 differenc c 2 Low-frequency limit + γ n the case where V (V - =0) am =0 e case ω in Alves (γ jtω p,am et / al. ω p,j (2012) and t ) where we set V = V + = V an I not e (1+ before γ jt ω I p,am st / art ω p,j t ) kv (γ jt ω p,am / ω p,j t ) 1/ 2 jt ± i hat t here (1+ is γ jt a ω p,am t ypo / ω p,j in t ) kv jt. t he t ext in dispersion o see that therelat phase ion velocity [eq.(1)] increases (Nishikawa where andt heir thetemporal al. 2013a,b) k kc/ growth ω p+ shoul rate (kv ω) 2 +

13 Dispersion relation for longitudinal electron mode of KKHI n j = n a γ j = 5 γ j = 15

14 Kinetic Kelvin-Helmholtz Instability 1. Static electric field grows due to the charge separation by the negative and positive current filaments 2. Current filaments at the velocity shear generate magnetic field transverse to the jet along the velocity shear 3. Jet with high Lorentz factor with core-sheath case generate higher magnetic field even after saturated in the case counter-streaming case with moderately relativistic jet 4. Non-relativistic jet generate KKHI quickly and magnetic field grows faster than the jet with higher Lorentz factor 5. For the jet-sheath case with Lorentz factor 15 the evolution of KKHI does not change with the mass ratio between 20 and Strong magnetic field affects electron trajectories and create synchrotron-like (jitter) radiation which is in progress 7. KKHI need to be investigated with shocks (jets need to be injected to ambient plasma)

15 Schematic GRB from a massive stellar progenitor Simulation box (Meszaros, Science 2001) Prompt emission Polarization? Accelerated particles emit waves at shocks 24/39

16 3-D simulation with MPI code Y injected at z = 25Δ Z grids (not scaled) 1.2 billion particles jet front 25/39 ambient plasma X

17 Collisionless shock Electric and magnetic fields created selfconsistently by particle dynamics randomize particles jet (Buneman 1993) B / t = -Ñ E E / t = Ñ B - J dm 0 g v / dt = q(e + v B) r / t + ÑiJ = 0 jet electron jet ion 26/39 ambient electron ambient ion

18 Weibel instability generated magnetic fields current filamentation J jet Time: τ = γ sh 1/2/ω pe 21.5 Length: λ = γ th 1/2 c/ω pe 9.6Δ J x ev z B x (electrons) 27/39 (Medvedev & Loeb, 1999, ApJ)

19 3-D isosurfaces of z-component of current Jz for narrow jet (γv =12.57) electron-ion ambient t = 59.8ω -1 e -J z (red), +J z (blue), magnetic field lines (white) Particle acceleration due to the local reconnections during merging current filaments at the nonlinear stage thin filaments merged filaments

20 Shock velocity and bulk velocity trailing shock trailing edge contact discontinuity (CD) leading shock (forward shock) leading edge jet electrons Fermi acceleration? total electrons ambient electrons 32/39

21 Shock formation, forward shock, reverse shock v rs =0.56c v cd =0.76c total ambient (c) v jf =0.996c jet ε B ε E (a) electron density and (b) electromagnetic field energy (ε B, ε E ) divided by the total kinetic energy at t = 3250ω pe -1 Time evolution of the total electron density. The velocity of the jet front is ~c, the predicted contact discontinuity speed is 0.76c, and the velocity of the reverse shock is 0.56c. (Nishikawa et al. ApJ, 698, L10, 2009)

22 Present theory of Synchrotron radiation Fermi acceleration (Monte Carlo simulations are not self- consistent; particles are crossing the shock surface many times and remain accelerated, the strengths of turbulent magnetic fields are assumed), Some simulations exhibit Fermi acceleration (Spitkovsky 2008) The strength of magnetic fields is estimated based on equipartition - magnetic field energy is comparable to the thermal energy): ε B ~ u(t) The distribution of accelerated electrons is approximated 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!

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

24 Self-consistent calculation of radiation Electrons are accelerated by the electromagnetic field generated by the Weibel instability and KKHI (without the assumption used in test-particle simulations for Fermi acceleration) Radiation is calculated using the particle trajectory in the self-consistent turbulent magnetic field This calculation includes Jitter radiation (Medvedev 2000, 2006) which is different from standard synchrotron emission Radiation from electrons in our simulation is reported in Nishikawa et al. Adv. Sci. Rev, 47, 1434, 2011.

25 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/ ) Sironi & Spitkovsky, 2009, ApJ Martins et al. 2009, Proc. of SPIE Vol Frederiksen et al. 2010, ApJL 41/39

26 Synchrotron radiation from gyrating electrons in a uniform magnetic field electron trajectories B β β β n β n radiation electric field observed at long distance observer spectra with different viewing angles time evolution of three frequencies theoretical synchrotron spectrum 43/39 f/ω pe = 8.5, 74.8, 654.

27 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 (helical) θ γ = /39 Nishikawa et al. astro-ph/

28 Synchrotron vs. `Jitter (a) Synchrotron emission assumes large-scale homogeneous magnetic fields (b) `Jitter radiation (Medvedev 2000) occurs where the gyro-radius is larger than the randomness of turbulent magnetic fields 45/39

29 46/39 (Nishikawa et al. astro-ph/ )

30 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 49/39

31 final condition for radiation 15,000 steps dt = n ω = w pe n θ = 2 Δx jet = 75Δ 75Δ -1 t r = 75 w pe 50/39

32 Calculated spectra for jet electrons and ambient electrons a = λe δb /mc 2 < 1 (λ: the length scale and δb is the magnitude of the fluctuations) γ = 15 θ = 0 and 5 q g = 3.81 high frequency due to turbulent magnetic field Case D Bremesstrahlung (ballistic) γ = /39 Nishikawa et al (arxiv: )

33 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) μ= -2 2d slice of magnetic field 3D jitter radiation with γ = 3 electrons /39 Hededal & Nordlund (astro-ph/ )

34 Dependence on Lorentz factors of jets θ = 0 5 q g = 3.81 γ = 15 θ = 0 5 q g = 0.57 γ = 100 Narrow beaming angle 53/39

35 Observations and numerical spectrum a GRB C b c d e a 1 a 1 Abdo et al. 2009, Science 54/39 Nishikawa et al. 2010

36 Radiation in a larger system at early time System size: Electron-positron: γ = 15 Sampled particles 115,200-1 w pe (a)150 t w pe -1-1 (b) 200 w pe t 275 w pe 56/39 Nishikawa et al. in progress

37 Summary for synthetic spectra Synthetic spectra provide self-consistent from electrons in turbulent magnetic fields In order to compare with observational spectra further investigation is necessary Kinetic Kelvin-Helmholtz instability is also need to be included for obtaining synthetic spectra We need to implement more realistic GRB jet conditions with Lorentz factor, density, temperature, etc.

38 GRB progenitor (collapsar, merger, magnetar) Gravitational waves relativistic jet Fushin (god of wind) EM emission (shocks, acceleration) Raishin (god of lightning) 58/39 (Tanyu Kano 1657)