Can we probe the Lorentz factor of gamma-ray bursts from GeV-TeV spectra integrated over internal shocks ? Junichi Aoi　(YITP, Kyoto Univ.) co-authors: Kohta Murase Keitaro Takahashi Kunihito Ioka Shigehiro Nagataki the method for proving the Lorentz factor of GRB. TeV particle astrophysics 2009 15/July/09

Gamma-ray bursts: prompt emission highly variable light curve　~0.1 sec → cδT ~ 3×109cm High energy photons ε~ 1 MeV emission from compact region Compactness problem Large number density of high energy photons nγ~1026 cm-3 Optically thick against gg → e+e- high energy photons can not escape from emission region. conflict with observations ~1MeV

Gamma-ray bursts: prompt emission highly variable light curve　~0.1 sec → cδT ~ 3×109cm High energy photons ε~ 1 MeV emission from compact region Compactness problem Large number density of high energy photons nγ~1026 cm-3 Optically thick against gg → e+e- One solution: blue shift with relativistic outflows In this case, there may be also cutoff due to gg → e+e- There is no cutoff observation. ~ecut ~1MeV

Importance of cufoff energy observation gg → e+e- : electron-positron pair-production optical depth against gg → e+e- definition of cutoff energy tgg(ecut)=1 ‘ solve these equations for Γ inside of emission region low energy photon high energy photon cutoff energy is important to constrain the Lorentz factor.

Internal shock model relativistic outflow Compact object Jet Rs~1013~1015cm (1) relativistic outflow from a system including compact object E~1051erg (2) Inhomogeneous part collides with each other. (3) shock dissipation bulk kinetic energy 　 → internal energy (4) emission from accelerated electron

our study previous study our study emission from a single shell time independent calculating energy spectrum of emission from multiple shells using the internal shock model consider electron-positron pair production;　 γγ→e+e- . examine a time-integrated spectrum aim: probe the Lorentz factor of a GRB from the time-integrated spectrum

method A ・・・ fluctuation of initial released energy by collision N shells (Γ,n,l,r), spherical symmetry, equal separation Random initial Lorentz factor (log-normal distribution) A ・・・ fluctuation of initial 　　Lorentz factor distribution released energy by collision energy, momentum conservation Γs Γm Γr inelastic collision Calculate Eint for every collisions 1. calculate a spectrum of emission from a single shell 2. sum up spectra from each shell　 →　compare this spectrum with sensitivity curve of Fermi

result ~energy spectrum~ energy spectra of a single pulse z=1, luminosity=1052erg s-1 There is cutoff due to pair production in each spectrum gg → e+e- Flux is lower than a sensitivity curve when emission comes from broad region. We have to sum up (time integrate) spectra

result ~energy spectrum~ time-integrated 　energy spectrum z=1, luminosity=1052erg s-1 No pair-production cutoff (Rem：Cutoff around 1011eV is due to Cosmic Infrared Background.) Slope becomes softer above some energy. pair-break energy cutoff is smeared by summation fluctuation of initial Lorentz factor distribution features large A: slope gradually becomes softer at large energy. large A: pair-break energy is smaller than for small A. shells collide at smaller radius for large A.

On estimate of Lorentz factors Cutoff is hidden by emission from multiple shells Cutoff is smeared. Maximum energy photon does not give the lower limit of Lorentz factor. We can use a pair-break energy instead of cutoff energy. ~ the minimum cutoff energy in two shell collision Γtrue: true value Γupper: derived from pair-break energy Γco: derived from maximum energy advantages The pair-break energy is produced by the inner collision with a short pulse. It is smaller than a (maximum) cutoff energy in general. It can be smaller than the CIB attenuation energy. This spiky pulse is easier to observe than a broad pulse.

Comparison with recent observation of Fermi GRB080916C There is not observation of a cutoff energy and a pair-break energy. observed maximum energy is 3 GeV in the main pulse light curve observed by Fermi there is a single pulse at time interval (b). (abdo+ 09) minimum Lorentz factor ~ 890 light curve observed by INTEGRAL There are multi pulses at time interval (b). Assume a pair-break energy is determined by one of them. assume there is a pair-break energy Lorentz factor (Greiner+ 09)

conclusion The conventional exponential cutoff should be modified to a steepened power-law in practical observations that integrate emissions from different internal shocks. There may be a pair-break energy around ~1 GeV. 　　This break energy may be observed by Fermi We can use the pair-break energy to probe the Lorentz factor of GRBs. The smearing effect generally reduce the previous estimates of the Lorentz factor. GRB 080916C: The Lorentz factor can be ~ 600, which is below but consistent with the previous result of ~900.