Mikhail V. Medvedev (KU)

Transcription

1 Students (at KU): Sarah Reynolds, Sriharsha Pothapragada Mikhail V. Medvedev (KU) Collaborators: Anatoly Spitkovsky (Princeton) Luis Silva and the Plasma Simulation Group (Portugal) Ken-Ichi Nishikawa (U. Alabama, Huntsville) Aake Nordlund and his group (Niels Bohr Institute, Copenhagen, Denmark) Marcel Grossmann 12 Paris, France, 17 July 2009

2 Outline Gamma-Ray Bursts Baryonic & Poynting flux outflows with small-scale field (Weibel) Basics of Jitter radiation Modeling a GRB prompt emission Prompt emission: tracking & correlations Electron heating, CRs, foreshock, etc.

3 GRB Standard model Internal/External Shock Model fireball prompt emission afterglow -rays ISM X-rays optical radio internal shock (collision of shells) external shock

4 Ubiquitous Weibel-Fried instability: sub-larmor-scale fields

5 Weibel instability (Medvedev & Loeb, 1999, ApJ) For electron streams x B current filamentation B - field produced J z J y shock plane

6 Weibel shock: 2D PIC e - p, Γ=15 P-parallel, protons P-parallel, electrons (Simulation by Spitkovsky)

7 Poynting-flux driven ejecta (Lyutikov & Blandford 2003)

8 Magnetized outflow: reconnection Small-scale field generation (Weibel instability) at a reconnection site see talks at this conference Non-relativistic electron-positron pair plasma (Swisdak, Liu, J. Drake, ApJ, 2008) Relativistic electron-positron pair plasma (Zenitani & Hesse, PoP, 2008)

9 Jitter radiation: connection to observations

10 Jitter radiation particle is highly relativistic ɣ>>1 deflection angle << beaming angle ~1/ (Medvedev, ApJ, 2000; 2006)

11 Extreme 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 - w (t) = random v = const (Medvedev, ApJ, 2000; 2006)

12 Jitter radiation spectrum Jitter radiation is equivalent to convolution of steep spectra from particles moving at different angles with respect to the line-of-sight (credit: K.-I. Nishikawa)

13 Anisotropic emissivity Radiation spectrum depends on angle and B-field spatial spectrum Peak frequency depends on correlation scale λ and not on just B B-field is anisotropic: B =(B x, B y ) is random, B z =0 n z x v Θ (Medvedev, Silva, Kamionkowski 2006; Medvedev 2006) observer

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

15 (credit: Hededal, Haugbolle, 2005) Oblique view

16 Spectra vs. viewing angle Log F ν 90 deg 0 deg synch. <B k2 > ~ k -η Log ν (Medvedev 2006; S. Reynolds, S. Pothapragada, Medvedev, 2009, submitted.)

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

18 Synchrotron Line of Death Statistics is large: About 30% of GRBs violate synchrotron limit at low energies P(ω) ~ ω (Medvedev, 2000) (Kaneko, et al, ApJS, 2006)

19 A canonical pulse Light travel time + relativistic aberration and Doppler boost + anisotropic (angle-dependent) jitter emission spectrum Θ~π/2, Θ lab ~1/γ Jet opening angle Jet axis Θ jet Θ~Θ lab ~0 Θ obs To observer Surfaces of equal times (Medvedev, Pothapragada, Reynolds, 2009, on astro-ph)

20 Modeling prompt GRBs 1. Calculate canonical lightcurve & spectra for a single emission episode (pulse) 2. Make a fake GRB: N=100 pulses at random times and with random peak fluxes 3. Fit with Band function (Medvedev, Pothapragada, Reynolds, 2009, on astro-ph)

21 Predictions Possible polarization signal at t~r/(2γ 2 c) if jet is misaligned with LoS by ~1/Γ Spectral hardening below peak energy at very late times, t ~ few s

22 Are shock simulations relevant for GRBs?

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

24 Cooling & Weibel time-scales shock (Medvedev & Spitkovsky, 2009, in press) prompt prompt, afterglow, large strong Γ-internal explosion

25 Self-similar foreshosk model with CR generated B-field

26 downstream The model y B(γ(x)) x=0 x n CR n CR n CR x 1 x 2 >x 1 x 3 >x 2 γ 1 γ γ 2 > γ 1 γ γ 3 > γ 2 γ B B B λ(γ) λ(γ) λ(γ) (Medvedev & Zakutnyaya, ApJ, 2009)

27 Self-similar foreshock Consequences Assume steady state and neglect nonlinear effects: large effect region of pre-conditioning upstream is strongly of upstream magnetized on Weibel instability enough nonlinear to feedback explain efficient of B-fields acceleration (Li & Waxman, 2006) large-scale CR distribution fields function long life-time increase Shock radiative structure efficiency of afterglow shocks source CR of acceleration magnetic fields in galaxy clusters, at LSS formation shocks time evolution (Medvedev, of generated Silva, Kamionkovski, fields 2005) B-field spectrum near a shock Typical field within ΔR ~ R/(2Γ 2 ): (Medvedev & Zakutnyaya, ApJ, 2009)

28 Fermi acceleration and non-fermi electron heating

29 Fermi acceleration (e +/- shock) (Spitkovsky 2008)

30 Electron heating density ions ε e ~30% electrons Electron heating= 50%(cross-shock electrostatic potential) + 50%(intrinsic heating by Weibel turbulence)?

31 Electrostatic model 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 -- reversible on short time-scale -- irreversible in the long term: virialization of electrons in the potential + time-variable potential λ = l/(c/ω p ) E e - l current B (Medvedev, 2006)

32 (Hededal, et al, 2005, PhD) Electron "heating"

33 Self-similar shock model Current filament merger model (Medvedev, et al 2005) z size ~ separation ~ R 0 current I 0 Coalescence: I N ~ I 0 2 N, R N ~ R 0 2 N/2 x y is generalized by Keshet, et al (2007) to include evolution of PDF

34 Reconnection model Reconnection events during current coalescence can 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/ω pp B ~< 2I 0 E ind dl= Φ/ t U electron ~ e E ind l ~ e (v/c)b λ(c/ω pp ) E ind and if the filling factor is not too small (not << 1), then, again: I 0 v ~ c B I 0

35 Extrapolating to afterglow 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 s B yields s=0.49+/-0.07 (Medvedev, 2006)

36 Radiation polarization properties

37 Polarization of Afterglows Beamed ejecta (jet) (Medvedev & Loeb 1999) GRB polarization of optical transient (Covino at al. 1999; Wijers et al. 1999)

38 Polarization Scintillation (Medvedev & Loeb 1999; Medvedev 2000)

39 Polarization Scintillatons of GRBs Flux vs. time DISS to RISS transition in GRB (Frail, Waxman, Kulkarni 1999) No detection yet; upper limit : < > < 10%

40 Summary Gamma-Ray Bursts Baryonic & Poynting flux outflows with small-scale field (Weibel) Jitter radiation from sub-larmor scale fields Prompt emission: tracking & correlations Energization of electrons, acceleration, foreshock physics