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Mikhail Medvedev (KU)

GRB workshop 2008 Nanjing , June 26, 2008. GRBs and relativistic shocks. Mikhail Medvedev (KU). Students (at KU): Sarah Reynolds, Sriharsha Pothapragada. Simulations:

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Mikhail Medvedev (KU)

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  1. GRB workshop 2008 Nanjing , June 26, 2008 GRBs and relativistic shocks Mikhail Medvedev (KU) Students (at KU): Sarah Reynolds, Sriharsha Pothapragada Simulations: Ken-Ichi Nishikawa (U. Alabama, Huntsville) Anatoly Spitkovsky (Princeton) Luis Silva and the Plasma Simulation Group(Portugal) Aake Nordlund and his group (Niels Bohr Institute, Copenhagen, Denmark) Theory: Davide Lazatti, B. Workman, D. Morsony (U.Colorado Boulder)

  2. Motivation • Whence magnetic fields ? • Whence electron heating/acceleration ? • Is emission non-synchrotron (why α>-2/3 sometimes)? • Why α’s are clustered about α=-1 ? • What causes spectral correlations (tracking)? flux α No synchrotron

  3. Unmagnetized medium: a shock PDF shock reflected particles e- p T2 > T1 T1 Weibel instability: Instability induced by anisotropic particle distribution function Generation of small-scale fields via filamentation of electron and proton currents at the shock front, on the microscopic level due to the Weibel instability (Medvedev & Loeb 1999)

  4. Weibel shock: 2D PIC e-p, Γ=15 (Simulation by Spitkovsky)

  5. Magnetized outflow: reconnection Small-scale field generation (Weibel instability) at a reconnection site [top] The reconnection site overview and the emergence of the out-of-plane B-field [right] Theoretical (solid line) and measured (stars) growth rate of the Weibel instability (Swisdak, Liu, J. Drake 2007, APS DPP meeting)

  6. Are shock simulations relevant for GRBs?

  7. Cooling & Weibel time-scales Inside the ejecta: Synchrotron cooling time Electron/proton dynamical time Downstream an internal shock: from simulations

  8. Cooling & Weibel time-scales emission from foreshock ? shock afterglow prompt

  9. Alternative: vorticity-amplified Bfield experiment on Richtmeyer-Meshkov instability (Neiderhaus & Jakobs, experiment) Vorticity model  Varies with Γ Clump density contrast Clump filling factor Requires ~10 eddy turnover times (quite slow) (Sironi & Goodman 2007) (also see, Nakar et al 2007)

  10. Fermi acceleration and non-Fermi heating of electrons

  11. Fermi acceleration (e+/- shock) (Spitkovsky 2008, astro-ph)

  12. Electron heating Bulk electrons are gradually accelerated through the foreshock, before the main shock compression (scheme based on Anatoly’s simulations)

  13. Electron “acceleration” (Hededal, et al, 2005, PhD A. Nordlund talk)

  14. Electrostatic model e- l E current B Motion of electrons in electrostatic fields of ion currents – local acceleration -- all electrons go trough filaments, but at different times  lengthen cooling time by filling factor -- the efficiency depends on εeand typically <10% -- shielding (Debuy) length, ℓ, varies with the distance to the shock λ = ℓ/(c/ωp)

  15. Reconnection model Eind v ~ c Perhaps, “reconnection” events during current coalescence may accelerate electrons -- “permanent” acceleration of electrons -- the efficiency depends on the filling factor of the filaments -- the characteristic energy is, again, ~ eBl (as in the electrostatic model) Typical size of the reconnection region ~ filament size ~ c/ωpp ∳ Eind•dℓ=∂Φ/∂t ~< 2I0 Uelectron ~ e Eind l ~ e (v/c)B λ(c/ωpp) B and if the filling factor is not too small (not << 1), then, again: I0 B I0

  16. Other … Other electron heating mechanisms: --- interaction of electrons with low-hybrid waves (not seen in 2D simul.) --- run-away pinching of ion channels (not accurate in 2D simul.) --- role of plasma instabilities of ion filaments (Buneman, two-stream, ion-sound, kinetic kink, ….) 2D geometry affects how current filaments merge  2D simulations are dangerous for making conclusions Parameters εeεB may vary depending on shock & upstream conditions -- Lorentz factor (if it is not >>1) -- back-reaction of CR on shock structure (which may depend on CR confinement, hence upstream B-field) -- upstream composition (He abundance, metallicity) -- post shock turbulence: MHD & hydro -- vorticity generation – Goodman, MacFadyen, (ApJ, J. Fluid Mech)

  17. For afterglows Using εe & εB from Panaitescu (2005) we infer the value of λ for:  best fit model (lowest χ2)  all good models (χ2/d.o.f. < 4) Fit εe ~ εBs yields s=0.49+/-0.07

  18. Jitter radiation

  19. Radiation in random fields ws ~ g2wH wj ~ g2 c/l Deflection parameter: d … independent of g (Medvedev, 2000, ApJ)

  20. Jitter regime When d << 1, one can assume that • particle is highly relativistic ɣ>>1 • particle’s trajectory is piecewise-linear • particle velocity is nearly constant r(t) = r0 + c t • particle experiences random acceleration w┴(t) w┴(t) = random e- v = const (Medvedev, ApJ, 2000; 2006)

  21. Radiation vs Θ B-field is anisotropic: B=(Bx , By) is random, Bz=0 n z x Θ v observer (Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)

  22. Face-on view (credit: Hededal, Haugbolle, 2005)

  23. Oblique view (credit: Hededal, Haugbolle, 2005)

  24. Spectra vs. viewing angle n0 Log Fν n1 synch. n-h <Bk2> ~ k-η n-h-1 Log ν (Medvedev 2006; S. Reynolds, S. Pothapragada, Medvedev, in prep.)

  25. Jitter spectra from 3D PIC 1/3 (synch.) Bulk Lorentz factor = 15 PDF: Thermal +non-thermal (p=2.7) (Hededal, PhD thesis 2005)

  26. Synchrotron “Line of Death” Statistics is large: About 30% of over 2700 GRBs (or over 5500 individual spectra) violate synchrotron limit at low energies P(ω) ~ ωa+1 (Medvedev, 2000) (Preece, et al., ApJS, 2000, Kaneko, et al, ApJS, 2006)

  27. Jet viewing angle effect Jet opening angle Jet axis Θjet To observer Θobs Surfaces of equal times

  28. “Tracking” GRBs t1, bright, high Epeak, α~0 aberration t2, intermediate α~ -2/3 Θ~Θlab~0 ~1/γ t3, faint, low Epeak, α~ -1 Θ~π/2, Θlab~1/γ Also, “hardness – intensity” correlation ; Also, “tracking behavior” ● = α ◊ = Epeak ― = Flux

  29. Prompt spectral variability 1 soft index vs. time 1 0.1 0.01 α R/(2Γ2c) 0.001 α=1/3 0.0001 Fν ~ να 0.001 0.1 t (s) 10 1000 a single pulse flux α flux @ Epeak vs. soft index prompt Polarization may be expected, if jet is misaligned high-latitude (Medvedev, 2006) (Pothapragada, Reynolds, Medvedev, in prep)

  30. Multi-peak prompt GRB (Kaneko, et al. ApJS 2006; PhD thesis) (Pothapragada, Medvedev, work in progress)

  31. Afterglow spectra & lightcurves Peak frequencies are: νm,jitt ~ νm,synch√εB,-3 • Synchrotron Wind and Jitter ISM models are indistinguishable; • Jitter Wind model has two breaks Flat (jitter) vs. ν1/3 (synch) spectrum between the peak and self-absorption frequency (Medvedev, Lazzati, Morsony, Workman, ApJ, 2007) (Morsony, Workman, Lazzati, Medvedev 2008, to be submitted tomorrow)

  32. Conclusions • Magnetic field with small spatial coherence length are ubiquitous. They form due to the Weibel instability via the current filament formation • Fermi acceleration is likely present, as indicated by PIC simulations. Electron non-Fermi heating is efficient, with εe ~ √εB and the electron energy density is comparable to the proton energy density; but more understanding is needed in B-field evolution and acceleration/heating in the foreshock  larger and longer PIC simulations are needed • Radiation emitted by electrons in Weibel-generated magnetic fields – Jitter radiation – has spectral properties that make it more favorable over synchrotron models. The Weibel+Jitter shock model can be tested against GRB data: e.g., spectral variability and afterglow lightcurves • More understanding is still needed for external shocks of afterglows (Weibel vs vorticity models, post-shock turbulence) and prompt emission (magnetized outflows)

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