Photospheric thermal radiation from
GRB collapsar jets
1.Gamma-ray burst (GRB)
2.Model
3.Hydrodynamics
4.Thermal radiation
Light curve, spectrum,
5.Summary

Akira MIZUTA(KEK)
AM, Nagataki, Aoi(ApJ, 732 26, 2011)
AM + (in prep)

素核宇融合による計算基礎物理学の進展研究会
＠合歓の郷 2011.12.05

原子核研究講義録
相対論的流体方程式の数値解法 I ('11春) II ('11秋), III('12春：予定)
http://www2.yukawa.kyoto-u.ac.jp/~mizuta/

Notes on the numerical method to solve special
relativistic hydrodynamic equations based on theresume prepared for the seminar last year.
In Japanese.
I appreciate the participants for giving me so manyquestions. Any comments, questions, and suggestions
are welcome.

Gamma-ray Burst (GRB) :The most energetic
explosion after Big-Bang●transient event (~10 s, gamma-ray~ a few hundred KeV)
explosion energy~1052erg
From relativistic collimated jet
Lorentz factor 100-1000●No typical light curve pattern.
Time variability in milli to a few sec.
Divided into two groups in durationof the radiation
long burst v.s. short burst●cosmological event
GRB 090423 z=8.2
GRB 090429B z=9.4 ? (~600 million
year after Big-Bang)Good tool to study high redshift
Universe, c.f normal SN up to z~1.2

td:0.5sec

td:5sec

td:40sec

td:100sec

Event #

shortlongduration

William et al. (1999) ApJS
distribution of GRB duration fromBATSE catalog

At least some of Long GRBs are special typeof supernova explosions of massive stars.
short burst ?

long burst

Binary merger

Kyoto Univ.

NASA/sonoma state univ.
Sekiguchi-san's talkKiuchi-san's talk

GRB980425/SN1998bw
GRB030329/SN2003dh
XRF060218/SN2006aj
GRB091127/SN2009nz
XRF100316D/SN2010bh

Central engine
Kajino-san's talkNagataki-san's talkSpectrum of GRB prompt emission
Band function: Broken power-law
Eα+2

GRB090902B
Abdo+(20009)

Eβ+2E3

GeV component

Planckian
GRB990123 Briggs et al. (1999)
Non-thermal radiation is expected.
How can the photospheric
There is no theoretical model
radiation
seen ?band.
to explainthermal
the index
for lowbe
energyThermal radiation; light curve, spectrum
viewing angle effect--jet like explosion
Hydrodynamics of jet propagation
Spectrum fittingfunction
Photospheric
thermalradiation
Band function (Band et al. 1993)

α =1:single
temperature Planck
Similar withPlanck
typical α

GRB090902B Ryde et al (2010,2011) thermal-like component
was found.

Hydrodynamic simulations (time dependent, jet )+photospheric thermal radiation by post process--find a photosphere (optical depth =1)--black body radiation (local temp + Lorentz boost)
Quantitative discussion is possible !!
-direct comparison with light curves, spectrum, etc.
Mizuta +'11,Lazzati et al. '09 '11, Nagakura+ '11
To estimate non-theremal radiation ( synchrotron emission )so many assumptions are necessary.
– Spectrum for non-thermal electrons(f(E) ひれい E-alpha)– When, where and how much are electrons accelerated ?
– Strength of magnetic fieldLj=5.e50 erg/s [0:100s] Opening angle 10 degrees
Γ0=50, ε0/c2=80 (h0~106) Γ_max~h0Γ 0(Bernoulli's principle)

2D (r x θ) axisymmetric, progenitor 14_sum,R*=4.e10cm (Woosley & Heger(2006)) + wind (r>R*) ρ ∝ r-2
2D-rela- hydro code(constant specific heat ratio=4/3)Mizuta et al. (2004,2006) + MPI

Lj=5.e50 erg/s [0:100s] Opening angle 10 degrees
Γ0=50, ε0/c2=80 (h0~106) Γ_max~h0Γ 0(Bernoulli's principle)

2D (r x θ) axisymmetric, progenitor 14_sum,R*=4.e10cm (Woosley & Heger(2006)) + wind (r>R*) ρ ∝ r-2
2D-rela- hydro code(constant specific heat ratio=4/3)
Mizuta et al. (2004,2006) + MPIThe photosphere separates from forward shockas time goes on.
If there is large beaming factor along the photonray, the location photosphere lay deep insidethe jet.
Post process calculation is also parallelized by MPI.

θ＝0
θ ＝5θ ＝10

●Another approach
Hydro – “spherical steady state”+
Monte Carlo simulation (photon transport)
Initial seed photon – around photosphere
Not necessary to assume T_gas~T_rad+IC effectPe'er (2008)

Beloborodov(2010)

Light curve
Dissipated region

Free expandingregionΓdissipated

BulletDuration of light curve ~ jet injection.
A few seconds time variability in early phasecaused by internal discontinuity in the jet.

Duration / initial half opening angle
θ0=10degrees
100s injectionΓCold Bullet
free expandion

θ0=10degrees
30s injectionΓθ0=5 degrees
30s injection

θ0=5degrees
100s injection

ΓCold Bullet
free expansion

ΓLight curves
OA10[0:100s]

OA10[0:30s]OA05 [0:100s]

OA5[0:30s]Spectrum by numerical hydrodynamics
Index~1(α=-1)

index∼2.5(α=0.5)

θ0=10degrees
100s injection

IC or another process
is necessary to explain
above the peak energy.

Cocoon baryon loading problem
log10(ρ/cm^3)

Backflow

log10(ρ/cm^3)progenitor
Expanding cocoon
Expanding envelopesΓΓjetinternal shocks
After shock break,? Ioka,Ohira,Kwanaka,
AM(2011) . High resolution calculation cananswer this problem.

Summary
Luminosity of photospheric thermal radiation is comparable toobserved one in GRBs.
A wide variety of light curves (a few seconds time valiability, flatstructure) are presented by changing jet parameters and observers
viewing angle.
Spectrum– close to Planckian (for observers θ<~2)– Band like spectrum (for observers θ>2)High resolution calculation is ongoing.
Hydrodynamic simulation + Monte Carlo simulation is planned.