The 2 nd Joint Kyoto-NTU High Energy Theory Workshop Welcome!
Junichi Aoi (YITP, Kyoto Univ.) co-authors: Kohta Murase Keitaro Takahashi
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Transcript of Junichi Aoi (YITP, Kyoto Univ.) co-authors: Kohta Murase Keitaro Takahashi
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
TeV particle astrophysics 2009 15/July/09
• highly variable light curve ~0.1 sec → cδT ~ 3×109cm
• High energy photons ε~ 1 MeV
Gamma-ray bursts: prompt emission
emission from compact region
Compactness problemLarge number density of high energy photons nγ~1026 cm-3
Optically thick against → e+e-
~1MeV
high energy photons can not escape from emission region.
conflict with observations
• highly variable light curve ~0.1 sec → cδT ~ 3×109cm
• High energy photons ε~ 1 MeV
Gamma-ray bursts: prompt emission
emission from compact region
Compactness problemLarge number density of high energy photons nγ~1026 cm-3
Optically thick against → e+e-
One solution: blue shift with relativistic outflows
In this case, there may be also cutoff due to → e+e-
There is no cutoff observation. ~1MeV ~cut
Importance of cufoff energy observation → e+e- : electron-positron pair-
production
low energy photon
high energy photon
inside of emission region
definition of cutoff energy cut
optical depth against → e+e-
cutoff energy is important to constrain the Lorentz factor.
solve these equations for Γ
‘
Internal shock model
Compact object
Jet
relativistic outflow
(1)relativistic outflow from a system including compact object E~1051erg
(2)Inhomogeneous part collides with each other.
Rs~1013~1015cm
(3)shock dissipation bulk kinetic energy → internal energy (4)emission from accelerated electron
our study
• 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
previous study our study
•emission from a single shell•time independent
aim: probe the Lorentz factor of a GRB from the time-integrated spectrum
method
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
Γr
Γs
Γm
inelastic collision
energy, momentum conservation
Calculate Eint for every collisions
1. calculate a spectrum of emission from a single shell2. sum up spectra from each shell → compare this spectrum with sensitivity curve of Fermi
result ~energy spectrum~
energy spectra of a single pulse
There is cutoff due to pair production in each spectrum → e+e-
Flux is lower than a sensitivity curve when emission comes from broad region.
We have to sum up (time integrate) spectra
z=1, luminosity=1052erg s-1
result ~energy spectrum~
time-integrated energy spectrum
No pair-production cutoff(Rem : Cutoff around 1011eV is due to Cosmic Infrared Background.)
Slope becomes softer above some energy.
cutoff is smeared by summation
fluctuation of initial Lorentz factor distribution
z=1, luminosity=1052erg s-1
1. large A: slope gradually becomes softer at large energy.2. large A: pair-break energy is smaller than for small A.
features
pair-break energy
shells collide at smaller radius for large A.
On estimate of Lorentz factors
Cutoff is hidden by emission from multiple shellsCutoff is smeared.
We can use a pair-break energy instead of cutoff energy.~
the minimum cutoff energy in two shell collision
advantages1. The pair-break energy is produced by the inner collision with a short pulse.
2. It is smaller than a (maximum) cutoff energy in general. It can be smaller than the CIB attenuation energy.
Maximum energy photon does not give the lower limit of Lorentz factor.
Γtrue: true valueΓupper: derived from pair-break energyΓco: derived from maximum 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 Fermithere is a single pulse at time interval (b).
There are multi pulses at time interval (b). Assume a pair-break energy is determined by one of them.
light curve observed by INTEGRAL
minimum Lorentz factor ~ 890
assume there is a pair-break energy
Lorentz factor
(abdo+ 09)
(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.