GRB workshop 2008                                                                                   ...
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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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GRB workshop 2008 Nanjing , June 26, 2008

GRBs and relativistic shocks

Mikhail Medvedev (KU)

Students (at KU):

Sarah Reynolds,

Sriharsha Pothapragada


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)


Davide Lazatti, B. Workman, D. Morsony (U.Colorado Boulder)

Motivation Nanjing , June 26, 2008

  • 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)?



No synchrotron

Unmagnetized medium a shock
Unmagnetized medium: a shock Nanjing , June 26, 2008


shock reflected particles



T2 > 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)

Weibel shock 2d pic e p 15
Weibel shock: Nanjing , June 26, 2008 2D PIC e-p, Γ=15

(Simulation by Spitkovsky)

Magnetized outflow reconnection
Magnetized outflow: reconnection Nanjing , June 26, 2008

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)

Are shock simulations Nanjing , June 26, 2008

relevant for GRBs?

Cooling weibel time scales
Cooling & Weibel time-scales Nanjing , June 26, 2008

Inside the ejecta:

Synchrotron cooling time

Electron/proton dynamical time

Downstream an internal shock:

from simulations

Cooling weibel time scales1
Cooling & Weibel time-scales Nanjing , June 26, 2008

emission from foreshock ?




Alternative vorticity amplified bfield
Alternative: vorticity-amplified Bfield Nanjing , June 26, 2008

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)

Fermi acceleration and Nanjing , June 26, 2008

non-Fermi heating of electrons

Fermi acceleration e shock
Fermi acceleration (e Nanjing , June 26, 2008 +/- shock)

(Spitkovsky 2008, astro-ph)

Electron heating
Electron heating Nanjing , June 26, 2008

Bulk electrons are gradually accelerated through the foreshock, before the main shock compression

(scheme based on Anatoly’s simulations)

Electron acceleration
Electron “acceleration” Nanjing , June 26, 2008

(Hededal, et al, 2005, PhD

A. Nordlund talk)

Electrostatic model
Electrostatic model Nanjing , June 26, 2008






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)

Reconnection model
Reconnection model Nanjing , June 26, 2008


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)


and if the filling factor is not too small (not << 1), then, again:




Other … Nanjing , June 26, 2008

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)

For afterglows
For afterglows Nanjing , June 26, 2008

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


Jitter radiation Nanjing , June 26, 2008

Radiation in random fields
Radiation in random fields Nanjing , June 26, 2008

ws ~ g2wH

wj ~ g2 c/l

Deflection parameter:


… independent of g

(Medvedev, 2000, ApJ)

Jitter regime
Jitter regime Nanjing , June 26, 2008

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


v = const

(Medvedev, ApJ, 2000; 2006)

Radiation vs
Radiation vs Nanjing , June 26, 2008 Θ

B-field is anisotropic:

B=(Bx , By) is random,








(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)

Face on view
Face-on view Nanjing , June 26, 2008

(credit: Hededal, Haugbolle, 2005)

Oblique view
Oblique view Nanjing , June 26, 2008

(credit: Hededal, Haugbolle, 2005)

Spectra vs viewing angle
Spectra vs. viewing angle Nanjing , June 26, 2008


Log Fν




<Bk2> ~ k-η


Log ν

(Medvedev 2006; S. Reynolds, S. Pothapragada, Medvedev, in prep.)

Jitter spectra from 3d pic
Jitter spectra from 3D PIC Nanjing , June 26, 2008

1/3 (synch.)

Bulk Lorentz factor = 15

PDF: Thermal +non-thermal (p=2.7)

(Hededal, PhD thesis 2005)

Synchrotron line of death
Synchrotron “Line of Death” Nanjing , June 26, 2008

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)

Jet viewing angle effect
Jet viewing angle effect Nanjing , June 26, 2008

Jet opening angle

Jet axis


To observer


Surfaces of equal times

Tracking grbs
“Tracking” GRBs Nanjing , June 26, 2008

t1, bright,

high Epeak,



t2, intermediate

α~ -2/3



t3, faint,

low Epeak,

α~ -1

Θ~π/2, Θlab~1/γ

Also, “hardness – intensity” correlation ; Also, “tracking behavior”

● = α

◊ = Epeak

― = Flux

Prompt spectral variability
Prompt spectral variability Nanjing , June 26, 2008


soft index vs. time









Fν ~ να

0.001 0.1 t (s) 10 1000

a single pulse



flux @ Epeak vs. soft index


Polarization may be expected, if jet is misaligned


(Medvedev, 2006)

(Pothapragada, Reynolds, Medvedev, in prep)

Multi peak prompt grb
Multi-peak prompt GRB Nanjing , June 26, 2008

(Kaneko, et al. ApJS 2006; PhD thesis)

(Pothapragada, Medvedev, work in progress)

Afterglow spectra lightcurves
Afterglow spectra & lightcurves Nanjing , June 26, 2008

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)

Conclusions Nanjing , June 26, 2008

  • 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)