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Mikhail Medvedev (KU)

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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:

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)

- 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

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)

(Simulation by Spitkovsky)

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

relevant for GRBs?

Inside the ejecta:

Synchrotron cooling time

Electron/proton dynamical time

Downstream an internal shock:

from simulations

emission from foreshock ?

shock

afterglow

prompt

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

non-Fermi heating of electrons

(Spitkovsky 2008, astro-ph)

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

(scheme based on Anatoly’s simulations)

(Hededal, et al, 2005, PhD

A. Nordlund talk)

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)

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

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)

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

Jitter radiation

ws ~ g2wH

wj ~ g2 c/l

Deflection parameter:

d

… independent of g

(Medvedev, 2000, ApJ)

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)

B-field is anisotropic:

B=(Bx , By) is random,

Bz=0

n

z

x

Θ

v

observer

(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)

(credit: Hededal, Haugbolle, 2005)

(credit: Hededal, Haugbolle, 2005)

n0

Log Fν

n1

synch.

n-h

<Bk2> ~ k-η

n-h-1

Log ν

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

1/3 (synch.)

Bulk Lorentz factor = 15

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

(Hededal, PhD thesis 2005)

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 opening angle

Jet axis

Θjet

To observer

Θobs

Surfaces of equal times

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

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)

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

(Pothapragada, Medvedev, work in progress)

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)

- 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)