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Random walks of photons in relativistic flow and its application to gamma-ray burst

Sanshiro Shibata (Konan Univ.)
Collaborators: Nozomu Tominaga (Konan Univ., Kavli IPMU) Masaomi Tanaka (NAOJ)
.

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Outline
· · · · Introduction Random walks in relativistic flow Application to gamma-ray burst Summary

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Introduction

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Gamma-Ray Burst (GRB)

L

Prompt emission
-rays (100keV) L,iso1052erg /s T0.1-1000s

Afterglow
x-ray, optical, radio,...

Relativistic jet
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t
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Models for the prompt emission
· Internal shock model
­ A standard scenario for a long time. ­ Some problems about the radiative efficiency and the low energy photon index

· Photospheric (thermal emission) model
­ Thermal emission from relativistic jets ­ (possibly) high radiative efficiency ­ Some GRBs exhibit blackbody like feature (e.g., GRB090902B).
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(Ryde et al 2010)

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Thermal emission from GRB jet
progenitor
observer
photon

jet

Photosphere (=1)

· · · ·

Photons are not produced at the photosphere We have to calculate radiative transfer We need to know where the photons are produced We construct the expression for effective optical depth in relativistic flow considering random walk process in relativistic flow
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Random walks in relativistic flow

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Random walks of photons
· Displacement of a photon
· The average net displacement

v · The second term is 0 in the static medium · But it is not 0 in the relativistic flow
(due to the relativistic beaming effect)
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Random walks of photons
· Taking into account relativistic effect

· If we set

and introduce

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Comparison with numerical simulation
· Monte-Carlo simulation of photon propagation · Calculate number of scatterings

0=10-103

=10-3102
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Comparison with numerical simulation

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The effective optical depth
· The effective optical depth
For the static medium
*
(Rybicki & Lightman 79)

For the relativistic medium

, In the non-relativistic limit, In the relativistic limit, 2
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for =0
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Application to Gamma-Ray Burst

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Calculation method
Hydrodynamical simulation Estimation of the photon production site Radiative transfer simulation

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Hydrodynamical simulation
2D relativistic hydrodynamics Setup
­ ­ ­ ­ ­ ­
(Tominaga 2009)

Progenitor: 15Msun WR star (Rprog2.3в1010cm) 0=5 jet=10° jet Ljet=5.3в1050 erg s-1 fth=0.9925 (eint/c2=80) Ljet, fth, 0 (log r, ) = (600, 150) grids R0 from R0=109cm
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R

prog

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Hydrodynamical simulation

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Hydrodynamical simulation
· We use a snapshot at 40s for the structures of the jet and cocoon.
Density [g /cm3]

Temperature T [K]

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The photon production site
· * to a radius R
*

· 'electron scattering · ' includes
­ Free-free absorption (e + p + e + p) ­ Double Compton absorption ( + + e + e)

We find the R* which satisfies * = 1
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The photon production site
*=1
s=1

[g /cm3]

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The photon production site
*=1
s=1

[g /cm3]

*=1

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The photon production site
· The number of emitted photons:

jet
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cocoon
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Radiative transfer
Numerical code
progenitor
observer
photon

­ Monte Carlo method ­ Calculate Compton scattering ­ Photons are injected at *=1

jet

*=1

s1

Photon injection
­ Spatial distribution: N() ­ Planck distribution with local plasma temperatures ­ Isotropic in the comoving frame We use a snapshot at t=40s for the jet and cocoon structure.
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Results

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Observed spectrum
· Epeak450keV · A bump like feature at low energies · At the low energy, FE1.3 NE-0.7 · No high energy PL

E

1.3

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Origin of the bump?

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Comparison with the observations
Kaneko et al 2006

Nothing

low energy index ()

high energy index ()

peak energy (E

peak)

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Summary

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Summary
We constructed the expression for effective optical depth in relativistic flow. We calculated radiative transfer for the thermal radiaiton from GRB jet. Both the jet and cocoon components constitute the observed spectrum. The low energy index may be determined by the relative brightness of these two components.

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