also Mastichiadis

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(also Mastichiadis Kazanas 2005)Spectra and
Time Variability
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Similarity of GRB/Nuclear Piles

• The similarity of GRB to a Nuclear Pile is more
  than incidental
• 1. They both contain lots of free energy stored
  in
• Nuclear Binding Energy (nuclear pile)
• Relativistic Protons or Magnetic Field (GRB)
• 2. The energy can be released explosively once
  certain conditions (identical in both cases) are
  fulfilled.

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• There are (at least) two outstanding issues with
  the prompt GRB emission (Piran 2004)
• A. Dissipation of the RBW free energy. Energy
  stored in relativistic ps or B-field. Sweeping
  of ambient protons stores significant amount of
  energy in ps anyway. Necessary to store energy
  in non-radiant form, but hard to extract when
  needed.
• B. The presence of Epeak 0.1 1.0 MeV. If
  prompt emission is synchrotron by relativistic
  electrons of Loretnz factor (LF) same as shock Ep
  G4, much too strong to account for the
  observations.

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• We propose a model that can resolve both these
  issues simultaneously. The model relies
• 1. On a radiative instability of a relativistic
  proton plasma with B-fields due to the
  internally produced sychrotron radiation.
• 2. On the amplification of the instability by
  relativistic motion and reflection of the
  internally produced radiation by upstream located
  matter.

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Pg ee- eB Bg
R
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bG61 100 GeV photons bG41 1 MeV
photons bG21 10 eV O-UV photons
RBW
Mirror
'Mirror'
R/G2
Rel. Blast Wave
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bG61 100 GeV photons bG41 1 MeV
photons bG21 10 eV O-UV photons
RBW
Mirror
'Mirror'
Rel. Blast Wave
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• We have modeled this process numerically. We
  assume the presence of scattering medium at R
  1016 cm and of finite radial extent.
• We follow the evolution of the proton, electron
  and photon distribution by solving the
  corresponding kinetic equations.
• We obtain the spectra as a function of time for
  the prompt GRB emission.
• The time scales are given in units of the
  comoving blob crossing time Dco/c R / G2c 2
  R16/G2.6 sec.

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The kinetic equations are solved on the RBW rest
frame with pair production, synchrotron, IC
losses, escape in a spherical geometry of radius
R/G and proton density n n0 G. The protons are
assumed to be injected at energy Ep mpc2 G.
These are the following
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• Spectra (Mastichiadis Kazanas 2005)

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Distribution of LE indices
a
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The spectra of doubly scattered component
(Mastichiadis DK (2005))
S1, a-1
S2, a0
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120 G
12 G
1.2 G
0.12 G
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Eiso of the three different spectral components
as a function of B for G400 and np105 cm-3. x
103 denotes the relative g-ray O-UV
normalization of GRB 990123, 041219a.
1 MeV
100 GeV
X 103
O-UV
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• Epeak as a function of the magnetic field B

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Variations

• If the mirror is in relative motion to the RBW
  then the kinematic threshold is modified to b G3
  G2rel 2 Grel is the relative LF between the
  RBW and the mirror.
• The value of Epeak is again 1 MeV, however the
  synchrotron and IC peaks are higher and lower by
  G2rel than G2 .
• In the presence of accelerated particles the
  threshold condition is satisfied even for Glt
  (2/b)1/5. This may explain the time evolution of
  GRB941017 (Gonzalez et al. 04)
• GRB flux is likely to be highly polarized (GRB
  031206, Coburn Boggs 03).
• This model applicable to internal shock model
  (photons from downstream shell instead of
  mirror).

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Then ....
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Shock Mirror Geometry
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formation region, generally not much different
than the
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