Opening angle of GRB jet
θj~CxΓ0-1 (C~1/5)

Akira MIZUTA(KEK)collaboration with Kunihito IOKA(KEK)

Quarks to Universe in ComputationalScience(QUCS 2012)@NARA Prefectural New Public Hall
16.12.2012

Gamma-ray bursts (GRBs)~most energetic explosions in the Universe after Big Bang~
105cm

1010cm1012-13cm

1015-17cm

td:5sec

・GRBs are very bright events (can begood probe of ancient Universe)
・Some of GRBs originate from massive
star collapse, i.e., special type supernova.
・GRBs are collimated and highly
relativistic outflows (relativistic jets)

td:40sec

td:100sec

Opening angle of GRB jets

θj~ several degrees.
Opening angles are more than
10 degrees for some GRBs

Fong et al. (2012)

Relativistic beaming effect
GRBs are radiation from relativistic jets (Γ>100/ v>0.9999c)).
Fluid rest frame
isotropic emission

Observer frame
Lorentz transformation
Γc
Γ

=1/Γ

(for Φ'=π/2)

Angle Φ' in fluid rest fame is transformed to angle Φ.
Radiation/ fluid motion concentrates in half opening angle 1/Γ.
Relativistic beaming effect can be applied for relativistic isotopic
adiabatic expansion.

What determines opening angel of jets ?
Naive expectation

High density
Stellar envelopes

Γ0 ~θ0 -1

Our model
relativistic beaming
effectHigh density
Stellar envelopes

Γ0 ~θ0 -1

High density
stellar envelopes

For the jet from massive stars, the jet is influenced by the interaction withstellar envelopes.
Before jet breakout, the jet is not well accelerated (Γ~O(10)).
Numerical simulations by Zhang et al.,Mizuta et al., Lazzati et al.,Nagakura et al.
Analytic work by Bromberg et al. (2011)
How about after jet breakout ? There is large density jump atthe stellar surface. It is not trivial how the opening angle of jets evolves.

High resolution hydro. simulations(2D, axisymmetric)ρΓElongated:Aspect ratio is not correct

High resolution grid points are devoted
At least in the jet and cocoon.
Δzmin=Δr min=107cm or =5x106cm
Ej=5x1050erg/s, r=8x107cm
η=h0Γ0=533
Γ0=2.5, 5, 10
Progenitor : Woosley & Heger(2006)
M~14Msun, R*=4x1010cm

progenitor surfacepWhy is high resolution necessary ?
hΓ (=const along stream line, steady state :Bernoulli's principle)Along jet axishΓ is conserved tothe reverse shockbaryon loading
due to numerical
diffusionWhy is high resolution necessary ?

Γ0=20

thin layer

Collimation shock

ambient gas

Γ0=10

Γ0=5
θ0=1/Γ0Bromberg, Levinson (2009)Γ0=5mass density

Lorentz factor

Cocoon confinement (Before break)CocoonpressureΓ0θ0~1/Γ0jet injection

Bromberg + (2011)
collimation shock+Cylindrical jet (Γ~Γ0)
See also Komissarov & Falle 1998

Γ0=5

Γ0=2.5After collimation shock, jet is almost
cylindrical shape as Bromberg et al. predicted.
Some oblique shocks can be seen inside the jetProbe particles

ρt=2.3s

ρcocoonEvery 0.01s, 32 particle are injected with the jet

particle trace

xnew=xold+vr,zxΔt

t=4.6sParticle traces injected at t=5 sθjTime evolution of jet opening angles
break

10s after shock breakθj~Γ0-1 x1/5
~0.08=1/2.5X1/5~0.04=1/5X1/5~0.02=1/10X1/5

1D Pressure profile in the cocoon
Pc~ const Γ~Γ0Cocoon
confinement

Pc~ r-2 at breakacceleration Γ~5xΓ0Pc~ r-4 after reakStellar surfacdepDistribution of opening angle of GRB jets(t_d>2s))(t_d<2s))θj=1/5Γ0<0.2 rad~10grees
Constant luminosity and uniform jet
can not explain large opening angle jets==>Structured jet ?

Fong et al. (2012)

Conclusion●High resolution calculation of jet from collapsars
to reduce numerical baryon loading●Pressure drop in the cocoon just before the break
due to exponential drop of the progenitor's
mass density profile
Lorentz factor increases to about 5xΓ0 at the break.
●The opening angle after the break for first several seconds

θj~CxΓ0-1 (C~1/5)●Structured jet is proffered for large opening angle jets.
(ex. GRB120422A short duration, low luminosity)

Future works●Long-term evolution of jets with large computationaldomain.
●3D simulations to see the multidimensional effect