1. Particle acceleration and the microphysics of gamma-ray burst shocks
Ehud Nakar
California Institute of Technology
APCTP 2007
Feb. 23

2. Outline Observations The internal-external fireball model
Particle acceleration in internal and reverse shocks.
Magnetic field generation and particle acceleration in the external shock
Summary

3. 10 keV-1 MeV photons (prompt emission)
Observations
10 keV-1 MeV photons (prompt emission) 
F
Non-thermal spectrum (best fitted by a broken power law, Peaking at ~0.1-1Mev)
Highly variable temporal structure
Time
Flux
Isotropic equivalent energy of a burst ~

4. Gamma-ray burst afterglows
X-ray
Flux
Fox et. al., 05
Optical
Time
Soderberg et. al., 06
Broken power-law spectrum and broken power-law light curve

5. + + GRBs (longs & shorts) are highly relativistic sources: High Rapid
Luminosity
1052erg/s
Rapid
Variability
dt~10ms
Hard (>MeV)
nonthermal
Spectrum + +
The emitting source must be relativistic in order to avoid high pair-production opacity!

6. Poynting flux dominated flow Particle acceleration
The Fireball Model
Prompt emission
Collimated
Baryonic flow
emEk
Goodman 86’
Paczynski 86’
Shemi & Piran 90’, …
Internal Shocks cm
synchrotron
-rays
(Rees & Meszaros 94’, …)
Compact
Source
Poynting flux dominated flow
Eem>>Ek
Thompson 94’, Usov 94’, Katz
97’, Meszaros & Rees 97’, …
In the fireball model a source which nature is unknown produce a wind for a duration which is similar to the observed duration of the burst (tens of seconds). This wind carry ~10^52ergs in one of the two forms: A collimated Baryonic flow or a Poynting flux dominated flow. In Baryonic flow ~10^-4 solar masses are accelarated to a Lorentz factor of 100 or so, thus most of the energy is in the kinetik energy of the protons. This flow is collimated with a half opening angle of ~0.1rad. In Poynting flux dominated flow the Baryon load is much smaller and almost all the energy is in the form of Electromagnetic field. In both scenarios the g- ray emission is a result of internal dissipation in the wind. In the baryon dominated flow the internal disipation is due to high variability in the winds velocity and collisions within the wind, these collisions are called internal shocks. In the Poynting flux dominated flows at large radii electromagnetic instabilities are developed which accelerate the paricales. In both cases the observed g-rays are emitted through synchrotron emission.
EM instabilities 
Particle acceleration
(~1016 cm)
synchrotron
-rays
(Lyutikov & Blandford 02)

7. Afterglow (in the fireball model)
Reverse shock††
(~1017 cm)
Relativistic
ejecta
X-rays
Optical
Radio
Baryonic flow
Forward shock†
( cm)
External
medium
Poynting flux dominated flow
Magnetic†††
bubble
X-rays
Optical
Radio
The afterglow is observed when the energy that remain after the g-ray emission is transferred to the circum burst medium. In both the Poynting lux and the baryonic flow a relativistic blast wave called the forward shock is propagating into external matter. After the energy transfer is completed the blast wave develop a self-similar profile called Blandford-Mackee solution – the equivalent to the Newtonian Sedov- Von-Noyman-Taylor solution. Here again the radiation is mainly through synchrotron emission. The main difference between the two scenarios is that in the baryonic flow another shock is developed – the reverse shock.
† Meszaros & Rees 92…
†† Meszaros & Rees 92; Katz 94; Sari & Piran 95…
†††Luytikov & Blandford 2002

8. All shocks are collisionless
The mean free path for binary collisions in the ionized relativistic plasma is much larger than the system
But plasma interactions and shocks are observed on much smaller scales
Collective “collisionless” electromagnetic plasma interactions

9. Energy output of GRBs is comparable to the observed flux of 1020 eV cosmic rays
GRBs are one of the most promising sources of UHECR through diffusive shock acceleration [DSA] (Waxman 1995; Vietri 1995; Milgrom &Usov 1995):

10. Internal shocks and/or reverse shock
Necessary conditions for DSA:
Confinement + acceleration faster than adiabatic cooling (assuming coherent B over R/G):
Larmour radius < R/G 
Unshocked plasma
Magnetization
parameter
Wind
luminosity
CR energy

11. 2) acceleration faster than radiative cooling (e.g., Waxman 01):
tacc<tsynch 
3) optical depth to p production < 1 (Waxman & Bahcall 97,99, Asano 05)
UHECR acceleration is possible in internal or reverse shock if the outflow is mildly magnetized and 100<G<1000

12. External shock afterglow theory
Hydrodynamics:
A relativistic blast-wave that propagates into a perfect fluid resulting in a self-similar profile (Blandford & McKee ‘76) .
All the energy is concentrated in a thin shell after the blast-wave – DR ~ R/g2
The blast-wave decelerates while shoveling increased amount of mass - gR-3/2 (for a constant external density). g
Shocked
plasma
ISM
R/g2
pressure R

13. Main microphysical assumptions
Radiation: synchrotron
Electrons: N(g)  ge-p for ge>gmin
A fraction ee of the internal energy
Magnetic field - a fraction eB of the internal energy
The model fits for five free parameters:
Ek, n, p, ee and eB
Main microphysical assumptions
Thin shock
Shock accelerate electrons and generate magnetic field.
Constant ee and eB (in time and space).

14. The typical parameters that fit the data
ee ~ 0.1
eB ~ (B does not decay in the downstrem)
p = 2-3
Ek,iso = erg (Comparable to Eg,iso)
n ~ cm-3 (expected in ISM)

15. Observations of GRB afterglows (external shocks) suggest:
Relativistic unmagnetized collisionless shocks take place in Nature
What initiates such shocks?
What is their steady-state structure?
Electrons are accelerated
How? What is the their energy distribution?
Long lasting anisotropic magnetic field is generated
How is it generated?
How can it survive for so long?
There are such shocks – what is the process and what is there structure
Synchrotron emission is observed -> electron accelerated to LF higher by orders of magnitude than the shock LF – How?
Magnetic field is generated in the shock (or by the shock) and survive long after the shock. Polarization measurements indicate that the surviving field is anisotropic – How?
There is no definite answer for any of the questions.
The best understanding is of the first one and the rest of them are still open
Magnetic field is also probably generated naturally in the shocks but how is it survives is unclear?
The answers of course can be different for pair plasma and p-e plasma.
I will concentrate on the structure question in pair plasma which is of interest for itself and that may bring us closer to solve the other questions

16. The transverse Wiebel instability
(Weibel 59; Fried 59) e- e- e+ e+ e- e- e+ e+ e- e- e+ e+ e- e- e+ e+

17. The transverse Wiebel instability
(Weibel 59; Fried 59) e+ e- e+ e- J e- e+ e- e+ e+ e- e+ e- J e- e+ e- e+

18. The transverse weibel instability is expected to produce current filaments and build equipartition magnetic field. This field provides collisionallity and produce a shock with the following properties (Moiseev & Sagdeev 63; Kazimura et al 98; Medvedev & Loeb 99, …):
The shock width is ~ls
At the shock eB~10-1
The magnetic field coherence length is ls
The magnetic field is within the shock plane
However – easy come easy go:
A magnetic field on ls scale is expected to decay within ls as well (Grizinov 2001)
R/g2 ~ 109 ls !!!

19. Can upstreaming CRs build up magnetic field on large scales?
high energy electrons cool fast
high energy protons do not cool
Jcr (streaming high energy protons)
Jreturn=Jcr (upstream return current)
Jreturn: a relative motion between the upstream plasma electrons and protons – an unstable configuration (Bell 04, 05)

20. Back-reaction on the shock structure
In weakly magnetized plasma collisionless shocks are believed to rise due to the transverse Weibel instability.
Amplification of the upstream magnetic field may quench the Wiebel instability. Hededal & Nishikawa (2005) find numerically that eB>10-5 quenches the instability in the electrons.
The amplified field may be the dominant confining field, thereby increasing the energy of the CRs.

21. Application to GRBs afterglow
Milosavljevic & Nakar 2006
Our assumptions are not valid once eB~1

22. Observational hint of amplified upstream field
(Li & Waxman 2006)
electrons emitting the X-ray afterglow at ~1day
are accelerated ge~106
tupstream<tIC,cooling
ge/Bus
1/ge
A lower limit on Bus
In several bright bursts Bus>0.2n05/8mG

23. Summary internal and reverse shocks may be the UHECRs source if:
-The outflow is baryonic
-The confining magnetic field is carried by the flow
The afterglow is produced by the external shock –an unmagnetized ultra-relativistic collisionless shock.
-Observations require that this shock generate strong magnetic field and accelerate particles (at least electrons).
- Most popular process for the shock generation is the Weibel instability
- Accelerated CRs may amplify the upstream field (e.g., by the Bell instability) and affect the shock structure.
-UHECRs are highly unlikly to be accelerated in the external shock

24. Thanks!