Radiative Transfer Calculasion for theThermal Radiation from GRB Jets

 Sanshiro Shibata (Konan Univ.)
Collaborator: Nozomu Tominaga (Konan Univ., Kavli IPMU)
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Outline• Introduction– Models for the prompt emission– Thermal emission from GRB jet• Method– Hydrodynamical simulation– Photosphere– Radiative transfer• Results• Summary
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Introduction

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Models for the prompt emission• Internal shock model– A standard scenario for a long time.
– Low Radiative efficiency, line of death problem• 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 jets
• Thermal emission from GRB jets have been investigatedby performing hydrodynamical simulations.
(Lazzati+2009, Mizuta+11, Nagakura+11)• They calculated the light curves and spectra by
superposing blackbody radiation emitted from thephotosphere with τ =1.

progenitor
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jetphotonobserver

photosphere

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Thermal emission from GRB jets
However– The observed photons should be generated in the inner layer
with τ ≫ 1. (e.g., Beloborodov 13)– Radiation intensity can be anisotropic even in the comoving
frame at τ～1. (Beloborodov 11, Aksenov+ 13)

In order to treat the thermal radiation from GRB jets properly,
both the radiative transfer in the jet and complex structure of
the jet and cocoon should be taken into account.

We calculate the radiative transfer in the jet and cocoon.
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Method

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Hydrodynamical simulation
2D relativistic hydrodynamics (Tominaga 2009)Setup– Progenitor: 15Msun WR star (Rprog～2.3×1010cm)– Γ0=5– Θjet=10°
θjet– Ljet=5.3×1050 erg s-1– fth=0.9925 (eint/ρc2=80)
Ljet, fth, Γ0– (log r, θ) = (600, 150) grids
R0
from R0=109cm
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Rprog8

Hydrodynamical simulation
Density [g/cc]

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Snapshot at 40s• We use a snapshot at 40s for the structures ofthe jet and cocoon.
Density ρ [g/cm3]

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Temperature T [K]Supernovae and Gamma-Ray Bursts 2013

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The site of photon production• The effective optical depth τ*
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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Supernovae and Gamma-Ray Bursts 2013for Θ=011Absorption processes• Free-free absorption (e + p + γ → e + p)
(Rybicki&Lightman 79)• Double Compton absorption (γ + γ + e → γ + e)
(Svensson 84)• We assume hν=kT
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Photosphere• τ* to a radius R*• σ’=neσT• α’ depends on ne, nγ, T.
• We assume
andWe find the R* which satisfies τ* = 1
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Photosphere
τ*=1

τs=1

ρ [g/cm3]

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Photosphere
τs=1

τ*=1

ρ [g/cm3]

τ*=1

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Photosphere• The number of photons emitted at the photosphere:Nγ(Θ)=16π2Γ(3)ζ(3)(kT*/hc)3R*2sinΘ*jet

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cocoonSupernovae and Gamma-Ray Bursts 201316

Radiative transfer
Numerical code

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

jetphotonτ*=1

τs～1Photon injection– Spatial distribution: Nγ(Θ)– Planck distribution with local plasma temperatures– Isotropic in the comoving frameWe use a snapshot at t=40s forthe jet and cocoon structure.
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Results

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Observed spectrum• Epeak～450keV• A bump like feature
at low energies• At the low energy,
νFν∝E1.3→Nν∝E-0.7• No high energy PL

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Origin of the bump?

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Comparison with the observations
Kaneko et al 2006

Nothinglow energy index (α)

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high energy index (β)

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peak energy (Epeak)21

Summary

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Summary We calculate radiative transfer for the thermal radiaiton
from GRB jet.
 Both the jet and cocoon components constitute theobserved spectrum.
 The low energy index may be determined by the relative
brightness of these two components.

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