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

Junichi Aoi (Yukawa Institute for Theoretical Physics)collaborator:Kohta MuraseShigehiro NagatakiKunihito IokaTeV Particle Astrophysics 2008 26 Sep. 2008

Observations of gamma-ray bursts

Light curve Energy spectrum

duration: 1sec~1000sec (Long GRB)complicated and irregular profilesfast rise and quasi-exponential decay

Characterized by power-law and break energy (Band et al. (’93) )

Cohen et al. (’97)Fishman et al.(’94)

no cut-off observation

standard model

Compact object

Internal shock→synchrotron rad. prompt emission

Jet

Rs~1013~1015cm

Shell’s gamma-factor > 100

We do not know Collision radius Rs, gamma-factor well.It is important to extract information about these quantitiesfrom observation.

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.

Internal shock model

Forward shockReverse shock

Jet

Kinetics energy of shells

dissipation

Internal energy•proton•electron•magnetic field

Relativistic shock acceleration

Power-law energy spectrum

Synchrotron emission

e BParametarized by

interaction

low energy photon

high energy photon

Optical depth

Only consider interaction(Rezzaque et al. (’04) )

Define cut-off energy

: photon index: numerical factor ~0.1

cut

interaction occurs at a shell in which particles are accelerated.it is necessary to discuss whether radiation can escape from a shell.

Preceding studies

• interaction e.g. Baring & Harding (’97), Lithwick & Sari (’01), Pe’er & 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)

Our study

• Multiple shock model (numerical calculation)

• assume cut is determined by interaction.

• How is the energy spectrum smoothed?• Is this smoothing observable?

?

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

Power-law index break energy

Observation (preece et al. (’00) )

2. assumption: We set =1, b=300 keV

(typical value of observation)

1. assumption: synchrotron emission fast cooling (strong mag.field)

Radiation from one of shells

p can be calculated by shock acceleration theory

3. Calculate cut-off energycut

test calculation

calculate the light curve to test the numerical calculation code.

This figure shows the characteristics of GRB like Kobayashi et al.(‘97).

Result ~energy spectrum~

Energy spectrum of radiation coming from each shell

There is energy cut-off originate from 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.

shell 1shell 2shell 3

Result ~energy spectrum~

Energy spectrum of radiation coming from all shells

cut-off energy + pulse duration collision radius and gamma-factor

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.

Fermi satellite may observe this steep power-law spectrum.

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

future work

• Inverse compton• Reacceleration In this study we assume electrons

becomes cold immediately. But, electrons may be accelerated by shock before they become cold.

Our calculation is not completed.