The acceleration and radiation in the internal shock of the gamma-ray bursts ~Smoothing Effect on the High-Energy Cutoff by Multiple Shocks~

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The acceleration and radiation in the internal
shock of the gamma-ray burstsSmoothing Effect
on the High-Energy Cutoff by Multiple
Shocks

• Junichi Aoi
• (Yukawa Institute for Theoretical Physics)
• collaborator
• Kohta Murase
• Shigehiro Nagataki
• Kunihito Ioka

TeV Particle Astrophysics 2008 26 Sep. 2008
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Observations of gamma-ray bursts
Light curve
Energy spectrum
no cut-off observation
Cohen et al. (97)
Fishman et al.(94)
Characterized by power-law and break energy
(Band et al. (93) )
duration 1sec1000sec (Long GRB) complicated
and irregular profiles fast rise and
quasi-exponential decay
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standard model
Shells gamma-factor g gt 100
Compact object
Jet
Internal shock ?synchrotron rad. prompt
emission
Rs10131015cm
We do not know Collision radius Rs, gamma-factor
well. It is important to extract information
about these quantities from observation.
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Introduction

• Study radiation from the gamma-ray burst using
  the Internal shock model.

Aim

• Effect of multiple shocks on the cut-off energy
• know physical quantities such as collision radius
  from the cut-off energy.

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Internal shock model
Kinetics energy of shells
dissipation
Jet

• Internal energy
• proton
• electron
• magnetic field

ee
eB
Parametarized by
Relativistic shock acceleration
Power-law energy spectrum Synchrotron emission
Forward shock
Reverse shock
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g - g interaction
it is necessary to discuss whether radiation can
escape from a shell.
g - g interaction occurs at a shell in which
particles are accelerated.

low energy photon
Optical depth
high energy photon
b photon index x numerical factor 0.1
tgg(ecut)1
Define cut-off energy
Only consider gg interaction (Rezzaque et al.
(04) )
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Preceding studies

• g-g interaction
• e.g. Baring Harding (97), Lithwick Sari
  (01),
• Peer Waxman (04), Razzaque, Meszaros
  Zhang (04)
• Cut-off
• Li Waxman (08)
• possibility of smoothing effect of
  cut-off
• Gupta Zhang (08)
• Murase Ioka (08)
• method to calculate the collision
  radius from observation of
• cut-off energy and gamma-factor of a
  shell.
• (e.g. gamma-factor is observed by
  annihilation line of electron
• and positron)

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Our study
?

• Multiple shock model (numerical calculation)
• assume ecut is determined by g-g interaction.
• How is the energy spectrum smoothed?
• Is this smoothing observable?

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method

• use multiple shock model by Kobayashi et al.
  (97)
• calculate flux from each shell and integrate
  them

Radiation from one of shells
1. assumption synchrotron emission fast
cooling (strong mag.field)
p can be calculated by shock acceleration theory
Observation (preece et al. (00) )
2. assumption We set a1, nb300 keV
(typical value of observation)
3. Calculate cut-off energy
tgg(ecut)1
break energy
Power-law index a
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test calculation
calculate the light curve to test the numerical
calculation code.
This figure shows the characteristics of GRB like
Kobayashi et al.(97).
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Result energy spectrum
Energy spectrum of radiation coming from each
shell
shell 1 shell 2 shell 3
There is energy cut-off originate from g-g
interaction.
If we can observe the energy spectrum (including
cut-off) and gamma-factor.
We can calculate the collision radius.
But, observable spectrum is an integrated
spectrum.
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Result energy spectrum
Energy spectrum of radiation coming from all
shells
There is no exponential decay, but steep
power-law.
Does we extract information from this energy
spectrum?
YES!
the beginning of the steepening corresponds to
the cut-off of the one shell which collide at the
smallest collision radius.
cut-off energy pulse duration ? collision
radius and gamma-factor
Fermi satellite may observe this steep power-law
spectrum.
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conclusion

• Fermi the energy range 10keV 300 GeV
• There is no observation of cut-off in the GRB
  energy spectrum.
• We calculate the energy spectrum of GRB.
• We use the multiple shock model.
• The energy spectrum becomes steep in the high
  energy range. It is the steep power-law spectrum.
• cut-off energy may be in the energy range of
  Fermi.
• The collision radius may be determined by
  observation.
• The start of the steepening
  the smallest radius
• The end of the steepening the
  largest radius

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future work
Our calculation is not completed.

• Inverse compton
• Reacceleration
• In this study we assume electrons becomes
  cold immediately. But, electrons may be
  accelerated by shock before they become cold.