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Gamma-Ray Bursts (GRBs) and collisionless shocks Ehud Nakar. Krakow Oct. 6, 2008. Gamma-Ray Bursts. Flash of g -rays that last several seconds – the prompt emission. NASA. NASA web site. long lasting decaying radio-optical-X-ray emission – the afterglow. Fox et. al., 05.

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slide2

Gamma-Ray Bursts

Flash of g-rays that last several seconds – the prompt emission

NASA

NASA web site

long lasting decaying radio-optical-X-ray emission – the afterglow

Fox et. al., 05

slide3

Longs & shorts

Kouveliotou et al. 1993

?

Short GRBs

Unknown – possibly NS-NS or BH-NS coalescence

Long GRBs

collapse of a massive star

slide4

Prompt emission - observations (long GRBs)

  • Duration 1-1000s
  • 1052-1054 erg (isotropic equivalent)

1050-1052 erg/s (isotropic equivalent)

  • ~0.01-2 MeV photons

Non-thermal spectrum;

very high energy tail

(at least up to GeV)

  • Rapid variability

(less than 10ms)

slide5

g-rays

Inner

Engine

Relativistic

Wind

(p-e- or p-e+-e- or EM)

Internal

dissipation

106cm

1013-1016cm

Prompt emission in the fireball model

G>100

slide6

Prompt emission - theory (long GRBs)

The emission source is internal dissipation within a relativistic outflow, G>100!

Radiation process – Unknown

Leading candidates are synchrotron and IC

Outflow composition and magnetization – Unknown

Unmagentized pair plasma is unlikely

Collisionless shocks ? – only if the outflow is baryonic

 mildly relativistic internal shocks

slide7

Afterglow - Observations

Peaks in X-ray first (minutes-hour) , then in optical (hours-days) and finally in radio (days-years)

Temporal & spectral structure: Broken power law

B, V, R, I

Fn

n

t (days)

Galama et al. 99

Stanek et al. 99

slide8

g-rays

Inner

Engine

Relativistic

Wind

(p-e- or p-e+-e- or EM)

Internal

dissipation

106cm

1013-1016cm

The internal-external fireball model

Afterglow

External

Shock

1016-1018cm

slide9

External shock afterglow model

Hydrodynamics:

A relativistic blast-wave that propagates into a perfect fluid (shocked fluid energy concentrated in – DR ~ R/g2)

  • Blast wave decelerates while shoveling mass - gR-3/2 (for a constant external density).
  • The burst emission ionize and destruct dust in the circum-burst medium  upstream is ionized, unmagnetized, p-e plasma.

g

Shocked

plasma pressure

upstream

pressure

R/g2

slide10

Radiation modeling:

  • Shock crossing  electron acceleration N(g)  g-p for g>gm
  • ee - fraction of electrons energy out of the internal energy at the shock crossing
  • eB - fraction magnetic field energy out of the internal energy at any time
  •  synchrotron + Synchrotron Self-Compton radiation
  • The model fit for five free parameters:
  • Ek, n, p, ee and eB
the basic slow cooling synchrotron afterglow spectrum and its time evolution

t-1/2

t-3/2

t0

The basic (slow cooling) Synchrotron Afterglow Spectrum and its time evolution:

Low energy

Fnn-1/3

Observations

Model

Fn

Sari et al 1998

Galama et al. 99

n

Synch self Absorption

High Energy Fnn-p/2

slide12

The typical parameters that fit the data

ee ~ 0.1

eB ~ 0.01-0.001

p = 2-2.7

Ek,iso = 1052-1054 erg (Comparable to Eg,iso)

n ~ 0.01-10 cm-3 (expected in ISM)

slide13

Typical scales

shock Lorentz factor - G~100 @ t=100s

G~10 @ t=1 day

G~2 @ t=1 month

(t – observer time since the burst)

B Downstream Bd~ mG-G

B Upstream Bu~ mG (eB,up~10-9)

Width of shocked plasma ~1012cm @ t=100s

~1016cm @ t=1week

Skin depth ~107 cm

slide14

Main microphysical assumptions in the basic model:

  • The shock is thin compared to the emitting region.
  • Electrons are coupled to the protons just through the shock.
  • All Electrons are accelerated – relaxing this assumption can change the best fit parameters by a factor f<mp/me (Eichler & Waxman 05)
  • ee and eB are constant in time and space – eB cannot drop significantly far in the downstream (Rossi & Rees 02)
slide15

Afterglow observations strongly suggest that weakly magnetized relativistic collisionless shocks:

  • Generate magnetic field with ~10-4-10-2 of equipartition.
  • This magnetic field survives long after crossing the shock (>107 skin depths).
  • Polarization indicate that the magnetic field is anisotropic on large scales with ratio ~2:1
  • Efficiently accelerate electrons (in equipartitoin with protons energy) at least up to TeV

Note: External shock is the most popular and successful afterglow model. But, it is not the only model and it cannot explain all afterglow observations in all bursts.

slide16

Short GRBs

  • Prompt emission is similar to long GRBs
  • About dozen observed afterglows (mostly in X-ray) suggest a similar mechanism and physical properties as in long GRB afterglows
  • The progenitor is an old stellar system and therefore the expected circum burst medium is the interstellar medium – unaffected by massive stellar wind.

The ability of collisionless shocks to generate field an accelerate particles is not unique to upstream which is shaped by stellar wind (e.g., with high density clumps)

Nakar 07

slide17

Magnetic field generation in GRB external shocks

Equipartion field on a skin depth scale is thought to be generated in unmagnetized shocks by the Weibel instability (Moiseev & Sagdeev 63; Kazimura et al 98; Medvedev & Loeb 99, …)

But … without sustaining process it is expected to decay over a similar scale (Gruzinov 01; Chang et al., 08)

How can the shock generate strong magnetic field

that survives over ~109 skin depths?

slide18

Suggested processes:

  • Interaction of the thermal plasma (upstream and/or
  • downstream) with accelerated particles via kinetic instabilities (e.g., recent numerical results by Keshet et al. 08
  • and Spitkovsky 08)
  • Amplification of the downstream field via downstream vorticity generated by
    • Density inhomogeneity in the upstream (e.g., Sironi & Goodman 07)
    • Angular energy anisotropy of decelerating blast wave (Milosavljevic, Nakar & Zhang 07)
  • Interaction between streaming protons and the upstream plasma via nonresonant streaming instability (e.g., Bell 2004, Milosavljevic & Nakar 06, Reville et al 06, …)
slide19

shock frame

Upstream frame

~R/G

~R/G2

G

p

p

p

e

e

upstream

upstream

Generation of upstream density inhomogeneies by streaming protons(Couch, Milosavljevic & Nakar 2008)

assumption: protons are accelerated in the shock by Fermi process

`

IC cooling grantee that if protons are accelerated to gp>103 then protons stream farther upstream then electrons

slide20

Nonresonant streaming instability amplifies the magnetic field and produces density inhomogeneities (e.g., Bell 04)

  • Even if the field is not amplified by orders of magnitude (e.g., Pelletier et al 08), density contrast of order unity is generated. Such contrast is enough in order to amplify the downstream field to the observed levels by generating downstream vorticity.
  • In GRB external shocks there is enough time to generate order unity density contrast even if the seed field is the pre-existing mG field
slide21

Summary

  • GRB prompt emission may be a result of mildly relativistic collisionless shocks (if GRB jets are baryonic).
  • GRB external shocks are unmagnetized ultra-relativistic collisionless shocks and are the prime candidates to be the source of the observed afterglows, in which case these shocks:
    • Generate long lasting magnetic field to sub-equipartition level
    • Efficiently accelerate electrons at least to Tev energies
  • Several processes were suggested as the source of the generated magnetic field in these shocks. None of which is confirmed yet.
slide23

g dn/dg

g

Are all the electrons need to be accelerated?

ee fee

eB feB

E E/f

n n/f

If only a fraction me/mp<f<1 is accelerated the above mapping results in similar fit to f=1 (Eichler & Waxman 05).

slide24

Can the magnetic field decay after the shock?

No decay

No decay

Decay after

crossing 1%

Decay after

crossing 1%

A decay of the magnetic field after the plasma crosses much less than 1% of the shocked shell is hard to explain by the observations (Rossi & Rees 02)