Transcript Document

GRB workshop 2008
Nanjing , June 26, 2008
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 ?
flux
α
No synchrotron
 What causes spectral correlations (tracking)?
Unmagnetized medium: a shock
shock
Weibel instability:
Instability induced by anisotropic
particle distribution function
reflected particles
PDF
ep
8
6
4
4
2
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
T 2 > T1
0
-4
-2
T1
-2
0
2
-4
4
(Medvedev & Loeb 1999)
2
0
Weibel shock: 2D PIC e-p, Γ=15
(Simulation by Spitkovsky)
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)
Are shock simulations
relevant for GRBs?
Cooling & Weibel time-scales
Inside the ejecta:
Downstream an internal shock:
Synchrotron
cooling time
Electron/proton
dynamical time
from simulations
Cooling & Weibel time-scales
emission from foreshock ?
shock
prompt
afterglow
Alternative: vorticity-amplified Bfield
Vorticity model
experiment on Richtmeyer-Meshkov instability
(Neiderhaus & Jakobs, experiment)
 Varies with Γ
Requires ~10 eddy turnover times (quite slow)
Clump
density
contrast
Clump
filling
factor
(Sironi & Goodman 2007)
(also see, Nakar et al 2007)
Fermi acceleration and
non-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
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
e-
λ = ℓ/(c/ωp)
l
E
current
B
Reconnection model
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
B
Eind
I0
B
v~c
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:
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 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
Jitter radiation
Radiation in random fields
ws ~ g2 wH
wj ~ g2 c/l
Deflection parameter:
d




eBl
2
mc
… independent of g
(Medvedev, 2000, ApJ)
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)
e-
w┴(t) = random
v = const
(Medvedev, ApJ, 2000; 2006)
Radiation vs Θ
B-field is anisotropic:
B=(Bx , By) is random,
Bz=0
n
z
x
v
Θ
observer
(Medvedev, Silva, Kamionkowski 2006; Medvedev 2006)
Face-on view
(credit: Hededal, Haugbolle, 2005)
Oblique view
(credit: Hededal, Haugbolle, 2005)
Spectra vs. viewing angle
Log Fν
n0
n1
synch.
<Bk
2>
~
n-h
k-η
n-h-1
Log ν
(Medvedev 2006; S. Reynolds, S. Pothapragada, Medvedev, in prep.)
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”
Statistics is large:
About 30% of over 2700 GRBs (or over 5500 individual spectra)
violate synchrotron limit at low energies
P(ω) ~ ω+1
(Medvedev, 2000)
(Preece, et al., ApJS, 2000, Kaneko, et al, ApJS, 2006)
Jet viewing angle effect
Jet opening angle
Jet axis
Θjet
Θobs
Surfaces of
equal times
To observer
“Tracking” GRBs
Also, “hardness – intensity” correlation ;
Also, “tracking behavior”
● =α
◊ = Epeak
― = Flux
t1 , bright,
aberration
high Epeak,
α~0
t2 , intermediate
~1/γ
Θ~Θlab~0
α~ -2/3
t3 , faint,
Θ~π/2, Θlab~1/γ
low Epeak,
α~ -1
Prompt spectral variability
soft index vs. time
a single pulse
flux
α
α
R/(2Γ2c)
α=1/3
Fν ~ να
0.001
1
0.1 t (s) 10
1000
0.1
flux @ Epeak vs. soft index
1
prompt
0.01
Polarization may be
expected, if jet is
misaligned
0.001
high-latitude
0.0001
(Medvedev, 2006)
(Pothapragada, Reynolds, Medvedev, in prep)
Multi-peak prompt GRB
(Kaneko, et al. ApJS 2006; PhD thesis)
(Pothapragada, Medvedev, work in progress)
Afterglow spectra & lightcurves
Peak frequencies are:
νm,jitt ~ νm,synch √εB,-3
Flat (jitter) vs. ν1/3 (synch)
spectrum between the peak and
self-absorption frequency
1. Synchrotron Wind
and Jitter ISM
models are
indistinguishable;
2. Jitter Wind model
has two breaks
(Medvedev, Lazzati, Morsony, Workman, ApJ, 2007)
(Morsony, Workman, Lazzati, Medvedev 2008,
to be submitted tomorrow)
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)