GRB workshop 2008 Nanjing, June 26, 2008 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)

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

Unmagnetized medium: a shock p e-e- shock reflected particles 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) T 2 > T 1 T1T1 PDF Weibel instability: Instability induced by anisotropic particle distribution function

Weibel instability … current filamentation … x y z J J B … B - field produced … (Medvedev & Loeb, 1999, ApJ)  n) 1/2 ms,  n) 1/2 km shock plane Consider electron streams (Fried’59)…

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

Magnetized outflow: reconnection Small-scale field generation (Weibel instability) at a reconnection site (Swisdak, Liu, J. Drake 2007, APS DPP meeting) [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

Are shock simulations relevant for GRBs?

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

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

τ baryon =1 τ pair =1 radiative effiiciency Weibel internal shock efficiency If present 2D PIC simulations describe shock structure accurately and If the internal shock model is right and we estimated the relevant parameters correctly, then: One should observe MeV prompt emission with GLAST Caveats: 2D vs. 3D simulations too small simulation box for a foreshock  flux – hardness correlation obs. flux

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

Fermi acceleration and non-Fermi heating of electrons

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

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

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

Electrostatic model current E e-e- l B λ = ℓ/(c/ω p ) 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 ε e and typically <10% -- shielding (Debuy) length, ℓ, varies with the distance to the shock

Reconnection model 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) v ~ c ∳ E ind dℓ=∂Φ/∂t B B E ind ~< 2I 0 I0I0 I0I0 U electron ~ e E ind l ~ e (v/c)B λ(c/ω pp ) and if the filling factor is not too small (not << 1), then, again: Typical size of the reconnection region ~ filament size ~ c/ω pp

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 ε e ε B 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)

For afterglows Using ε e & ε B from Panaitescu (2005) we infer the value of λ for:  best fit model (lowest χ 2 )  all good models (χ 2 /d.o.f. < 4) Fit ε e ~ ε B s yields s=0.49+/-0.07

Jitter radiation

Radiation in random fields  j ~  2 c/  s ~  2  H … independent of  (Medvedev, 2000, ApJ) Deflection parameter: 

Jitter regime When  1, one can assume that  particle is highly relativistic ɣ>>1  particle’s trajectory is piecewise-linear  particle velocity is nearly constant r(t) = r 0 + c t  particle experiences random acceleration w ┴ (t) e-e- v = const w ┴ (t) = random (Medvedev, ApJ, 2000; 2006)

Jitter radiation. Theory The dominant contribution to the integral comes from small angles Small-angle approximation Lienard-Wichert potentials Spectral power (Landau & Lifshitz, 1963; Medvedev, ApJ, 2000)

Jitter radiation. Theory (cont.) where Fourier image of the particle acceleration from the 3D “ (vxB) acceleration field ” Lorentz force B-field spectrum Ensemble-averaged acceleration spectrum (Landau & Lifshitz, 1963; Medvedev, ApJ, 2000; Fleishman, ApJ, 2006, Medvedev, ApJ, 2006)

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

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

Oblique view (credit: Hededal, Haugbolle, 2005)

Spectra vs. viewing angle (Medvedev 2006; S. Reynolds, S. Pothapragada, Medvedev, in prep.)     Log F ν Log ν synch. ~ k -η

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

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

Jitter radiation. 3D model Spectral power of radiation B-field spectra in xy & z (Medvedev, ApJ, 2006) Electron’s acceleration spectrum 2α ~ 4 2α-2β ~ -2.6 κ┴κ┴

Jet viewing angle effect Jet axis To observer Surfaces of equal times Jet opening angle Θ obs Θ jet

“Tracking” GRBs ● = α ◊ = E peak ― = Flux ~1/γ t 1, bright, high E peak, α~0 Θ~Θ lab ~0 t 2, intermediate α~ -2/3 aberration t 3, faint, low E peak, α~ -1 Θ~π/2, Θ lab ~1/γ Also, “ hardness – intensity ” correlation ; Also, “ tracking behavior ”

Prompt spectral variability α F ν ~ ν α t (s) soft index vs. time R/(2Γ 2 c) α=1/3 a single pulse (Medvedev, 2006) (Pothapragada, Reynolds, Medvedev, in prep) flux α E peak vs. soft index high-latitude prompt Polarization may be expected, if jet is misaligned

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

Afterglow spectra & lightcurves Flat (jitter) vs. ν 1/3 (synch) spectrum between the peak and self-absorption frequency Peak frequencies are: ν m,jitt ~ ν m,synch √ε B,-3 (Medvedev, Lazzati, Morsony, Workman, ApJ, 2007) (Morsony, Workman, Lazzati, Medvedev 2008, to be submitted tomorrow) 1.Synchrotron Wind and Jitter ISM models are indistinguishable; 2.Jitter Wind model has two breaks

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 ε e ~ √ε B 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)