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Gamma-Ray Bursts and unmagnetized relativistic collisionless shocks Ehud Nakar Caltech

Gamma-Ray Bursts and unmagnetized relativistic collisionless shocks Ehud Nakar Caltech. Outline - Gamma-Ray bursts – observational constraints on relativistic, unmagnetized collisionless shocks - Electro-static layer in relativistic, unmagnetized collisionless shocks in pair plasma

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Gamma-Ray Bursts and unmagnetized relativistic collisionless shocks Ehud Nakar Caltech

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  1. Gamma-Ray Bursts and unmagnetized relativistic collisionless shocks Ehud Nakar Caltech

  2. Outline - Gamma-Ray bursts – observational constraints on relativistic, unmagnetized collisionless shocks - Electro-static layer in relativistic, unmagnetized collisionless shocks in pair plasma Milosavljevic, Nakar & Spitkovsky, ApJ 2006 - Constraints on particle acceleration in galaxy cluster merger shocks (M=2-3, mildly magnetized collisionless shocks) Nakar, Milosavljevic, & Nagai, in preparation

  3. Gamma-Ray Bursts Flash of g-rays of several seconds NASA web site Weeks of decaying radio-X-ray emission – The afterglow Fox et. al., 05

  4. Schematic model Relativistic wind Compact engine Internal Dissipation External shock g-rays Afterglow

  5. The afterglow – Emission from an ion-electron plasma shocked in a relativistic (or mildly relativistic) collisionless unmagnetaized shock. Relativistic: Lorentz factor from 100 to 1.1 Collisionless: Upstream density ~1 prticle/cm-3 lcollision~ 1025cm ;system size R~ 1018cm Unmagnetized: Emitting region width: R/G~1015-1018cm Plasma skin depth: ls~107-108 cm Upstream Larmor radius: RL,p~1012 cm (upstream B~mG)

  6. Radiation model • Synchrotron • Electrons: N(g)  ge-p for ge>gmin • A fractioneeof the internal energy • Magnetic field - a fractioneBof the internal energy • The model fits for five free parameters: • Ek, n, p, ee and eB • Main microphysical assumptions • Thin shock • Accelerated electrons and generated magnetic field. • Constantee and eB (in time and space).

  7. The typical parameters that fit the data ee ~ 0.1 eB ~ 0.01-0.001 (B does not decay in the downstrem) p = 2-3 Ek,iso = 1052-1054 erg (Comparable to Eg,iso) n ~ 0.01-10 cm-3 (expected in ISM) At early time (~1hr after the burst) this simple theory often does not work. Theoretical insights on the microphysics is of great need!

  8. GRB afterglow observations (external shocks) suggest: • Relativistic unmagnetized collisionless shocks take place in Nature • What initiates such shocks? • What is their steady-state structure? • Electrons are accelerated to a power-law at least up to TeV • How? • Does ee andp vary in time , space or initial conditions? • Long lasting anisotropic magnetic field is generated • How is it generated? • How can it survive for so long? • What is the source of anisotropy?

  9. Moiseev & Sagdeev 63 What is the source of colissionality in an unmagnetized plasma? • Weibel instability (Weibel 59; Fried 59) • 2D numericalsimulations of • relativistic electron-positron beams • show filmentation (e.g., Lee & Lampe 73) • Weibel instability is suggested as the mechanism responsible for astrophysical relativistic unmagnetized collisionless shocks (Medvedev & Loeb 99; Gruzinov & Waxman 99) • Extensive numerical effort with 3D PIC simulationssupports this idea(Silva et al; Nordlund et al.; Liang et al.; Jaroschek et al.; Nishikawa et al.; Spitkovsky et al;)

  10. 3D simulations in pair (and low mass ratio) plasma: • Skin depth (ls)current filaments are generated (The magnetic field coherence length is ls) • At the shock eB~10-1 • The magnetic field is within the shock plane • Particles start thermalization and the magnetic field start decaying. • But, 3D simulations do not answer yet (partial list): • What is the steady-state shock structure? • What is the fate of the generated field far in the downstream? • Are particles accelerated and how? • What is the back reaction of accelerated particles on the shock? • Does the same mechanism works in e-p plasma? Are electrons and protons coupled in the shock?

  11. Electro-static layer in the steady-state structure of unmagnetized relativistic pair plasma collsionless shock (Milosavljevic, Nakar & Spitkovsky 06)

  12. G ~G/2 G e- G G ~G e- e- G G ~G/2 ~G/2 G G G The steady-state shock structure Structure guideline: Filamentation arises where cold upstream plasma and hot counter-stream plasma interpenetrate Cold upstream Shock layer Hot downstream ~G e+ G e+ e- ~G/2 e- e+ e- e+ e+ e- e+ ~G/2 ~G/2 e+ e+ e- ~G/2 e- G e- e+ e+ b=1/3 All the discussion is in the shock frame

  13. Two stages in the shock structure: • Laminar charge separation layer: • A nearly maximal charge separation of the upstream • takes place in the first generation of filaments • producing a quasi-static 2D structure • II) Turbulent compression layer • Unstable and interacting filaments produce a 3D turbulent layer that isotropize and compress the plasma

  14. J e+ Counter-stream Upstream e- e+ e+ E J e+ e- e- e+ E e- J E e+ e+ e- e+ The charge separation layer Filamentation: l What prevents the counterstream particles from escaping the shock layer into the upstream? rus>>rcs  E·J<0 The first generation of filaments may functions as a diode protecting the upstream from the downstream

  15. J e+ Hot Counter-stream Cold Upstream e- E e+ e+ J e+ e- e- e+ E e- E e+ e+ e- e+ J l x0 The first generation of filaments l>RL A quasi-static 2D structure with E|| may be constructed An electrostatic layer with |f0| ~ Gmc2  , eB~1 A small fraction (<nus/G2) of the counterstream escapes to the upstream

  16. Additional properties of the charge-separation layer: • Width: ls<<D~(rus/rcs)1/2ls <G ls • Initial deceleration and spreading of the momentum distribution function • Almost no upstream compression • B||<<B • A small fraction (<nus/G2) of the CS particles escapes the shock into the upstream • At x=x0: • Maximal charge separation: r/n~1 • Maximal electromagnetic energy: eB~1 • RL,us~l~ls • I~ (Gmc3/q) - the Alfven current

  17. X0 Size: [200×32×32]ls Simulation by Anatoly Spitkovsky Jx Numerical Precursor Not a steady-state!!!

  18. X0 y/ls <|r|/qn> ncs/nus <gb||,us> x/ls

  19. Shock structure - Conclusions • Two stages in the shock structure: • Quasi-static 2Dcharge separation layer: • f~mec2G • r/n~1 • eB~1 • Some counterstream particles do escape to the upstream – candidates for particle acceleration • II) Dynamic 3D compression layer • Unstable interacting filaments • Decaying eB • B||~B

  20. Main open questions • Far in the upstream: What is the fate of the escaping counter stream particles? Are they accelerated? Do they affect the shock structure (e.g, Milosavljevic & Nakar 06)? • Far in the downstream: what fraction of the generated magnetic fields survive? • What is the structure p-e- shocks?

  21. Thanks!

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