Gamma-Ray Bursts and unmagnetized relativistic collisionless shocks

Ehud NakarCaltech

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

NASA web site

Gamma-Ray Bursts

Flash of -rays of several seconds

Fox et. al., 05

Weeks of decaying radio-X-ray emission – The afterglow

Compactengine

Relativistic wind

InternalDissipation

-rays Afterglow

Externalshock

Schematic model

The afterglow – Emission from an ion-electron plasma shocked in a relativistic (or mildly relativistic) collisionless unmagnetaized shock.

Relativistic: Lorentz factor from 100 to 1.1Collisionless: Upstream density ~1 prticle/cm-3

lcollision~ 1025cm ; system size R~ 1018cm

Unmagnetized:

Emitting region width: R/~1015-1018cm Plasma skin depth: s~107-108 cmUpstream Larmor radius: RL,p~1012 cm (upstream B~G)

1

2

92

2

, 10~~

n

G

B

cnm

B

pupstreamB

Radiation model

Synchrotron

•Electrons: N() e-p

for e>min 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 Eiso

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?

•Weibel instability (Weibel 59; Fried 59)

•2D numerical simulations of relativistic electron-positron beamsshow 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;)

What is the source of colissionality in an unmagnetized plasma?

Moiseev & Sagdeev 63

3D simulations in pair (and low mass ratio) plasma:

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?

• Skin depth (s) current filaments are generated (The magnetic field coherence length is s)• At the shock B~10-1

• The magnetic field is within the shock plane• Particles start thermalization and the magnetic field start decaying.

Electro-static layer in the steady-state structure of unmagnetized relativistic

pair plasma collsionless shock(Milosavljevic, Nakar & Spitkovsky 06)

The steady-state shock structureStructure guideline:Filamentation arises where cold upstream plasma and hot counter-stream plasma interpenetrate

e+

e+

e-

e-

Cold upstream

e+

e+

e-

e-

e+

e-

e+

e+

e-e

e+

e+

e-

e

Shock layer

Hot downstream

e-

e+

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 upstreamtakes place in the first generation of filamentsproducing a quasi-static 2D structure

II) Turbulent compression layerUnstable and interacting filaments produce a 3D turbulent layer that isotropize and compress the plasma

What prevents the counterstream particles from escaping the shock layer into the upstream?

Filamentation:

e+

e+

e+ e+

e+

e+e+

e+

e-

e-

e-

e-

e-J

J

J Counter-streamUpstream

E

E

E

2 us

cs

us>>cs E·J<0

The first generation of filaments may functions as a diode protecting the upstream from the downstream

The charge separation layer

The first generation of filaments >RL

A quasi-static 2D structure with E|| may be constructed

An electrostatic layer with | ~ mc2 , B~1

e+

e+

e+ e+

e+

e+e+

e+

e-

e-

e-

e-

e-J

J

J HotCounter-stream

ColdUpstream

E

E

E

x0

A small fraction (<nus/2) of the counterstream escapes to the upstream

1~)(

)(

0

0

xqn

x

Additional properties of the charge-separation layer:•Width: s<<~(us/cs)1/2s < s

•Initial deceleration and spreading of the momentum distribution function•Almost no upstream compression•B||<<B

•A small fraction (<nus/2) 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~s

•I~ (mc3/q) - the Alfven current

X0

Jx

Not a steady-state!!!

Size: [200×32×32]s

NumericalPrecursor

Simulation by Anatoly Spitkovsky

u

s

x/s

ncs/n

us

2

)(

mc

dxqEx

x

y/ s

X0

/qn

>

Shock structure - ConclusionsTwo stages in the shock structure:

I) Quasi-static 2D charge separation layer:• ~mec2• /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!