1. 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 Murase Shigehiro Nagataki Kunihito Ioka TeV Particle Astrophysics 2008 26 Sep. 2008

2. Observations of gamma-ray bursts Light curve Energy spectrum duration: 1sec~1000sec (Long GRB) complicated and irregular profiles fast 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

3. standard model Compact object Internal shock →synchrotron rad. prompt emission Jet R s ~10 13 ~10 15 cm Shell’s gamma-factor  > 100 We do not know Collision radius R s, gamma-factor well. It is important to extract information about these quantities from observation.

4. 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.

5. 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e BB Parametarized by

6.  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.

7. 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)

8. Our study Multiple shock model (numerical calculation) assume  cut is determined by  interaction. How is the energy spectrum smoothed? Is this smoothing observable? ?

9. 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 energy    cut 

10. test calculation calculate the light curve to test the numerical calculation code. This figure shows the characteristics of GRB like Kobayashi et al.(‘97).

11. 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 1 shell 2 shell 3

12. 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.

13. 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

14. 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.