GRB workshop 2008 Nanjing , June 26, 2008

Mikhail Medvedev (KU)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

synch

rotr

on

Unmagnetized medium: a shock

p

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)

-4

-2

0

2

4-4

-2

0

2

4

0

2

4

6

8

-4

-2

0

2

4

T2 > T1

T1

PDF

Weibel instability:

Instability induced by anisotropic particle distribution function

Weibel shock: 2D PIC e-p, Γ=15

(Simulation by Spitkovsky)

Magnetized outflow: reconnectionSmall-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 Are shock simulations

relevant for GRBs?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

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 andFermi acceleration and

non-Fermi heating of electronsnon-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-

l

B

λ = ℓ/(c/ωp)

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 εe and typically <10%

-- shielding (Debuy) length, ℓ, varies with the distance to the shock

Reconnection modelPerhaps, “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

∳ Eind•dℓ=∂Φ/∂t

B

B

Eind

~< 2I0

I0

I0

Uelectron ~ e Eind l ~ e (v/c)B λ(c/ωpp)

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

Typical size of the reconnection region ~ filament size ~ c/ωpp

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 εe εB 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 afterglowsUsing 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 radiationJitter radiation

Radiation in random fields

j ~ 2 c/

s ~ 2 H

… independent of 2mceB

(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) = r0 + c t

particle experiences random acceleration w┴(t)

e-

v = const

w┴(t) = random

(Medvedev, ApJ, 2000; 2006)

Radiation vs ΘB-field is anisotropic:B=(Bx , By) is random,

Bz=0

(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)

n

z

xv 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 Fν

Log ν

synch.

<Bk2> ~ k-η

Jitter spectra from 3D PIC

(Hededal, PhD thesis 2005)

Bulk Lorentz factor = 15PDF: 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

Jet viewing angle effect

Jet axis

To observer

Surfaces of equal times

Jet opening angle

Θobs

Θjet

“Tracking” GRBs

● = α

◊ = Epeak

― = Flux

~1/γ

t1 , bright,

high Epeak,

α~0

Θ~Θlab~0

t2 , intermediate

α~ -2/3

aberration

t3 , faint,

low Epeak,

α~ -1

Θ~π/2, Θlab~1/γ

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

Prompt spectral variability

α

Fν ~ να

0.001 0.1 t (s) 10 1000

soft index vs. time

R/(2Γ2c)

α=1/3

a single pulse

(Medvedev, 2006)

(Pothapragada, Reynolds, Medvedev, in prep)

flux

α

1

0.001

0.0001

1

0.01

0.1

flux @ Epeak 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. ν1/3 (synch) spectrum between the peak and self-absorption frequency

Peak frequencies are:

νm,jitt ~ νm,synch √εB,-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 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)