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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Mikhail Medvedev (KU)

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Mikhail medvedev ku

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)


Motivation

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

Unmagnetized medium: a shock

PDF

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)


Weibel shock 2d pic e p 15

Weibel shock: 2D PIC e-p, Γ=15

(Simulation by Spitkovsky)


Magnetized outflow reconnection

Magnetized outflow: reconnection

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)


Mikhail medvedev ku

Are shock simulations

relevant for GRBs?


Cooling weibel time scales

Cooling & Weibel time-scales

Inside the ejecta:

Synchrotron cooling time

Electron/proton dynamical time

Downstream an internal shock:

from simulations


Cooling weibel time scales1

Cooling & Weibel time-scales

emission from foreshock ?

shock

afterglow

prompt


Alternative vorticity amplified bfield

Alternative: vorticity-amplified Bfield

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)


Mikhail medvedev ku

Fermi acceleration and

non-Fermi heating of electrons


Fermi acceleration e shock

Fermi acceleration (e+/- shock)

(Spitkovsky 2008, astro-ph)


Electron heating

Electron heating

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

(scheme based on Anatoly’s simulations)


Electron acceleration

Electron “acceleration”

(Hededal, et al, 2005, PhD

A. Nordlund talk)


Electrostatic model

Electrostatic model

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)


Reconnection model

Reconnection model

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

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 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

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


Mikhail medvedev ku

Jitter radiation


Radiation in random fields

Radiation in random fields

ws ~ g2wH

wj ~ g2 c/l

Deflection parameter:

d

… independent of g

(Medvedev, 2000, ApJ)


Jitter regime

Jitter regime

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)


Radiation vs

Radiation vs Θ

B-field is anisotropic:

B=(Bx , By) is random,

Bz=0

n

z

x

Θ

v

observer

(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)


Face on view

Face-on view

(credit: Hededal, Haugbolle, 2005)


Oblique view

Oblique view

(credit: Hededal, Haugbolle, 2005)


Spectra vs viewing angle

Spectra vs. viewing angle

n0

Log Fν

n1

synch.

n-h

<Bk2> ~ k-η

n-h-1

Log ν

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


Jitter spectra from 3d pic

Jitter spectra from 3D PIC

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”

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

Jet opening angle

Jet axis

Θjet

To observer

Θobs

Surfaces of equal times


Tracking grbs

“Tracking” GRBs

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


Prompt spectral variability

Prompt spectral variability

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)


Multi peak prompt grb

Multi-peak prompt GRB

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

(Pothapragada, Medvedev, work in progress)


Afterglow spectra lightcurves

Afterglow spectra & lightcurves

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

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)


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