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Gamma-Ray Bursts and unmagnetized
relativistic collisionless shocks
Ehud Nakar
Caltech
Outline
- Gamma-Ray bursts – observational constraints on
relativistic, unmagnetized collisionless shocks
- Electro-static layer in relativistic, unmagnetized
collisionless shocks in pair plasma
Milosavljevic, Nakar & Spitkovsky, ApJ 2006
- Constraints on particle acceleration in galaxy cluster
merger shocks (M=2-3, mildly magnetized
collisionless shocks)
Nakar, Milosavljevic, & Nagai, in preparation
Gamma-Ray Bursts
Flash of g-rays of several seconds
NASA web site
Weeks of decaying radio-X-ray
emission – The afterglow
Fox et. al., 05
Schematic model
Compact
engine
Relativistic
wind
Internal
Dissipation
External
shock
g-rays
Afterglow
The afterglow – Emission from an ion-electron plasma
shocked in a relativistic (or mildly relativistic)
collisionless unmagnetaized shock.
Relativistic: Lorentz factor from 100 to 1.1
Collisionless: Upstream density ~1 prticle/cm-3
lcollision~ 1025cm ; system size R~ 1018cm
Unmagnetized:
2
B
9  B 
1


 B ,upstream ~
~
10
n
 mG 
nm p c 2


2
Emitting region width:
R/G~1015-1018cm
Plasma skin depth:
ls~107-108 cm
Upstream Larmor radius: RL,p~1012 cm (upstream B~mG)
Radiation model
Synchrotron
•Electrons: N(g)  ge-p for ge>gmin
A fraction e of the internal energy
•Magnetic field - a fraction B of the internal energy
The model fits for five free parameters:
Ek, n, p, e and B
Main microphysical assumptions
•Thin shock
•Accelerated electrons and generated magnetic field.
•Constant e and B (in time and space).
The typical parameters that fit the data
e ~ 0.1
B ~ 0.01-0.001 (B does not decay in the downstrem)
p = 2-3
Ek,iso = 1052-1054 erg (Comparable to Eg,iso)
n ~ 0.01-10 cm-3 (expected in ISM)
At early time (~1hr after the burst) this simple
theory often does not work. Theoretical insights on
the microphysics is of great need!
GRB afterglow observations (external shocks) suggest:
• Relativistic unmagnetized collisionless shocks take
place in Nature


What initiates such shocks?
What is their steady-state structure?
• Electrons are accelerated to a power-law at least up
to TeV


How?
Does e and p vary in time , space or initial conditions?
• Long lasting anisotropic magnetic field is generated



How is it generated?
How can it survive for so long?
What is the source of anisotropy?
What is the source of colissionality in an
unmagnetized plasma?
Moiseev & Sagdeev 63
•Weibel instability (Weibel 59; Fried 59)
•2D numerical simulations of
relativistic electron-positron beams
show filmentation (e.g., Lee & Lampe 73)
•Weibel instability is suggested as the mechanism
responsible for astrophysical relativistic
unmagnetized collisionless shocks (Medvedev & Loeb 99;
Gruzinov & Waxman 99)
•Extensive numerical effort with 3D PIC
simulations supports this idea (Silva et al; Nordlund et al.;
Liang et al.; Jaroschek et al.; Nishikawa et al.; Spitkovsky et al;)
3D simulations in pair (and low mass ratio) plasma:
• Skin depth (ls) current filaments are generated (The
magnetic field coherence length is ls)
• At the shock B~10-1
• The magnetic field is within the shock plane
• Particles start thermalization and the magnetic field start
decaying.
But, 3D simulations do not answer yet (partial list):
• What is the steady-state shock structure?
• What is the fate of the generated field far in the downstream?
• Are particles accelerated and how?
• What is the back reaction of accelerated particles on the
shock?
• Does the same mechanism works in e-p plasma? Are electrons
and protons coupled in the shock?
Electro-static layer in the steady-state
structure of unmagnetized relativistic
pair plasma collsionless shock
(Milosavljevic, Nakar & Spitkovsky 06)
The steady-state shock structure
Structure guideline:
Filamentation arises where cold upstream plasma and
hot counter-stream plasma interpenetrate
Cold upstream Shock layer
G
+
e
ee+
e-
G
G
G
G
e
G
+
e
e-
G
+
e
e-
G
G
e
Hot downstream
G
+
e
e
e+
e e+ e+
e+
e- e+
e-
~G
b=1/3
All the discussion is in the shock frame
Two stages in the shock structure:
I) Laminar charge separation layer:
A nearly maximal charge separation of the upstream
takes place in the first generation of filaments
producing a quasi-static 2D structure
II) Turbulent compression layer
Unstable and interacting filaments produce a 3D turbulent
layer that isotropize and compress the plasma
The charge separation layer
Upstream
e-
E
l
e+
e+
e+
J e+
e+
J
e- e-
e-
E
E e-
Counter-stream
e+
J
e
e+
Filamentation:
 cs 
 us
G
2
+
What prevents the counterstream particles from
escaping the shock layer into the upstream?
us>>cs  E·J<0
The first generation of filaments may functions as a diode
protecting the upstream from the downstream
Cold
Upstream
l
E
e-
e
e+
e+ J
Hot
Counter-stream
e- e -
e+ E
E
Je+
+
ee-
e+
J
e
e+
+
x0
The first generation of filaments l>RL
A quasi-static 2D structure with E|| may be constructed
An electrostatic layer with |f0| ~
Gmc2 
 ( x0 )
~ 1, B~1
qn( x0 )
A small fraction (<nus/G2) of the counterstream
escapes to the upstream
Additional properties of the chargeseparation layer:
•Width: ls<<D~(us/cs)1/2ls < G ls
•Initial deceleration and spreading of the
momentum distribution function
•Almost no upstream compression
•B||<<B
•A small fraction (<nus/G2) of the CS particles
escapes the shock into the upstream
At x=x0:
•Maximal charge separation: /n~1
•Maximal electromagnetic energy: B~1
•RL,us~l~ls
•I~ (Gmc3/q) - the Alfven current
Simulation by
Anatoly Spitkovsky
Size: [200×32×32]ls
X0
Jx
Numerical
Precursor
Not a steady-state!!!
X0
y/ls

x

qE x dx (= f )
<gb||,us
ncs/nus
<||/qn>
Gmc2
x/ls
Shock structure - Conclusions
Two stages in the shock structure:
I) Quasi-static 2D charge separation layer:
• f~mec2G
• /n~1
• B~1
• Some counterstream particles do escape to the
upstream – candidates for particle acceleration
II) Dynamic 3D compression layer
• Unstable interacting filaments
• Decaying B
• B||~B
Main open questions
•Far in the upstream: What is the fate of the
escaping counter stream particles? Are they
accelerated? Do they affect the shock structure (e.g,
Milosavljevic & Nakar 06)?
•Far in the downstream: what fraction of the
generated magnetic fields survive?
•What is the structure p-e- shocks?
Thanks!