Junichi Aoi (YITP, Kyoto Univ.) co-authors: Kohta Murase Keitaro Takahashi

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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/

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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. - PowerPoint PPT Presentation

Transcript of Junichi Aoi (YITP, Kyoto Univ.) co-authors: Kohta Murase Keitaro Takahashi

Page 1: 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

Page 2: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

• 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

Page 3: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

• 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

Page 4: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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

Page 5: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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

Page 6: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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

Page 7: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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

Page 8: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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

Page 9: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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.

Page 10: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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.

Page 11: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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)

Page 12: Junichi Aoi (YITP, Kyoto Univ.)     co-authors:       Kohta Murase       Keitaro Takahashi

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.