Hydrodynamical models fora successfull/failed jet from a massive starand implications to low-luminosity GRBs

Akihiro Suzuki
Center for Computational Astrophysics, NAOJ

GRB-SNe, YITP Nov. 201313年11月14日木曜日

Outline
Brief introduction of low-luminosity GRBs
Jet models
Implications to emission from low-luminosity GRBs
Summary

13年11月14日木曜日

Low-luminosity GRBs
less energetic and less luminous subgroup of long GRBs
They are found in the nearby universe. The event rate is highe.g., 230+490-190 Gpc-3 yr-1 (Soderberg+ 2006 ), 100-1800 Gpc-3 yr-1 (Guetta&Della Valle 2007)

They are accompanied by broad-lined Ic supernovaeEx.) GRB 980425/SN 1998bw, GRB 060218/SN 2006aj, GRB100316D/ SN2010bh

GRB 980425

long GRBs
long GRBs

ll GRBs
GRB 060218
Kaneko+ (2006)
13年11月14日木曜日

Levan+ (2013)

Low-luminosity GRBs
less energetic and less luminous subgroup of long GRBs
They are found in the nearby universe. The event rate is highe.g., 230+490-190 Gpc-3 yr-1 (Soderberg+ 2006 ), 100-1800 Gpc-3 yr-1 (Guetta&Della Valle 2007)

They are accompanied by broad-lined Ic supernovaeEx.) GRB 980425/SN 1998bw, GRB 060218/SN 2006aj, GRB100316D/ SN2010bh
Luminosity Lγ,iso

Isotropic energy Eiso

Duration T90

peak energy Ep

GRB 980425
SN 1998bw

6×1046 erg/s

9×1047 erg

35 s

122 keVGRB 060218
SN 2006aj

2×1046 erg/s

4×1049 erg

2100 s

4.7 keVGRB 100316D
SN 2010bh

5×1046 erg/s

6×1049 erg

1300 s18 keV
from Hjorth (2011)13年11月14日木曜日

Low-luminosity GRBs
less energetic and less luminous subgroup of long GRBs
They are found in the nearby universe. The event rate is highe.g., 230+490-190 Gpc-3 yr-1 (Soderberg+ 2006 ), 100-1800 Gpc-3 yr-1 (Guetta&Della Valle 2007)

They are accompanied by broad-lined Ic supernovaeEx.) GRB 980425/SN 1998bw, GRB 060218/SN 2006aj, GRB100316D/ SN2010bh
Luminosity Lγ,iso

Isotropic energy Eiso

Duration T90

peak energy Ep

GRB 980425
SN 1998bw

6×1046 erg/s

9×1047 erg

35 s

122 keVGRB 060218
SN 2006aj

2×1046 erg/s

4×1049 erg

2100 s

4.7 keVGRB 100316D
SN 2010bh

5×1046 erg/s

6×1049 erg

1300 s18 keV
from Hjorth (2011)

Question to answer: What is their origin?
What mechanism is responsible for X- and γ- ray emission
13年11月14日木曜日

Connection to HNe, engine-driven SNe
Optical observations: kinetic energy of non-relativistic ejecta is found by light.

curve modeling and spectroscopy : vph ~ 0.1c, Ekin ~ 1052-1053 erg
Radio observations: kinetic energy of the blast wave is found by usingsynchrotron emission model : Γv =(1-2) c, Ekin ~ 1049 erg
A&A 539, A76 (2012)12

Soderberg et al.
14

Olivares+ (2012)

Fig. 7. Quasi-bolometric light curve ofSN 2010bh produced by using GROND
g! r! i! z! JH filters (black open circles) in
the rest frame. For clarity, the uncertainties in the host-galaxy extinction are notincluded in the error bars. A single blackcontinuous line represents the best-fit
model (see Sect. 5.1). Early and latecomponents of the model are smoothly
joined at t0 + 30 d. SE and other GRBSNe quasi-bolometric light curves havebeen plotted as a comparison sample:
SN 2003lw (GRB 031203; Malesani
et al. 2004), SN 1998bw (GRB 980425;
Galama et al. 1998b), SN 2006aj(GRB 060218; Pian et al. 2006), thebroad-lined Ic SN 2009bb (Pignata et al.
2011), the type-Ic SN 1994I (Richmond
et al. 1996), the type Ibc SN 2008D(XRO 080109; Modjaz et al. 2009;
Soderberg et al. 2008), and the type-Ic
SN 2002ap (Gal-Yam et al. 2002; Foley
et al. 2003; Yoshii et al. 2003).

Soderberg et al.

Soderberg+ (2010)

Figure 2.

The analysis of the quasi-bolometric light-curve morphology
yields a peak luminosity of 4.3 × 1042 erg s−1 at about 8 d after
the trigger (equivalent to Mbol ≈ −17.87), i.e., approximately
two times fainter and six days sooner than for SN 1998bw. Our
luminosity is 16% higher than that computed by Cano et al.
(2011b), although consistent to within our 11% of uncertainty.
13年11月14日木曜日
Whilst the early peak of SN 2010bh correlates with its narrow-nebular, i.e., optically thin, and the emitted luminosity is powered by the energy deposition of: (1) γ-rays from 56 Co decay,(2) γ-rays from electron-positron annihilation, and (3) the kinetic
energy of the positrons (see appendix A in Valenti et al. 2008).
However, Maeda et al. (2003) noted that the two-component
configuration leads to inconsistencies between the parameters
derived from fitting the early and late light curves of SNe Ic,

Figure 4.

Connection to HNe, engine-driven SNe
Optical observations: kinetic energy of non-relativistic ejecta is found by light.

curve modeling and spectroscopy : vph ~ 0.1c, Ekin ~ 1052-1053 erg
Radio observations: kinetic energy of the blast wave is found by usingsynchrotron emission model : Γv =(1-2) c, Ekin ~ 1049 erg

Margutti+ (2013)13年11月14日木曜日

Failed jet hypothesis
Ekin for relativistic ejecta << Ekin for nonrelativistic ejecta ➡ It is suggested that failed
jet model produce such events.

Ultra-relativistic jet:
Ekin for rel. ejecta ~ Ekin for non-rel. ejecta

13年11月14日木曜日

Failed jet:
Ekin for rel. ejecta <<Ekin for non-rel. ejecta

Failed jet hypothesis
Ekin for relativistic ejecta << Ekin for nonrelativistic ejecta ➡ It is suggested that failed
jet model produce such events.
Many works to reveal whether or not an ultrarelativistic jet succeed in penetrating a
massive star (e.g., Bromberg+2011a,b, Lazzati+2011)

Lazzati+ (2011)13年11月14日木曜日

Bromberg+ (2011a,b)

Failed jet hypothesis
Ekin for relativistic ejecta << Ekin for nonrelativistic ejecta ➡ It is suggested that failed
jet model produce such events.
Many works to reveal whether or not an ultrarelativistic jet succeed in penetrating aThis study
Bromberg+ (2011a,b)
star (e.g., Bromberg+2011a,b, Lazzati
1. massive
carry out
a series simulations of jet propagation in a massive star
+2011)
andidentify a model corresponding to low-luminosity GRBs.
2. carry out further calculations to reveal the properties of themodel, including nucleosynthesis calculations and CSM interaction.

Lazzati+ (2011)13年11月14日木曜日

Outline
Brief introduction of low-luminosity GRBs
Jet models
Implications to emission from low-luminosity GRBs
Summary

13年11月14日木曜日

medium (ISM),
a uniform
mediumwiththe root
numberden
deceleration
radiusIisassume
inversely
proportional
to thecubicof thedthe ambient
mediumis given byfunctiothedensity
case of⇢ext
the ofsteadywind withthe mass-loss
ratetheṀfollowing
and the velocit⇢w of the ambient medium is inversely proportional to the square of t
GRB jet simulation⇢ext = ⇢w (r) + ⇢ISM ,mesh
Ṁ JET
3.4.4096×512
HYDRODYNAMICALSIMULATION OF THE,⇢w =2
4⇡r vw
Woosley&Heger(2006) 16TI model
3 , where
Here,
the
mass
density
of
the
ISM
is
⇢
=
100m
g
cm
u
ISM
WR starthe mass of the matter swept by the forward shock should be evaluate
theﬁnalatomicmass◉ unit. The profiles of the density and the mass fracti
mass~14M
Z rdec10cm
progenitor
model
are shown in Figures 3.9 and 3.10.2
Ṁ
Radius ~ 3×10
Msw =⇢w 4⇡r dr =rdec ,vw
0

The deceleration
radius is inversely proportional to the mass-loss rate
3.4.2
Jet injection

interaction
betweenthe ejecta
movingat relativistic
speedsan
The Theinjectionof the jet
is realized
in the samemanneras Ref. [91].
I imp
under
assumptionof atspherical
symmetry
by Reffor thefirstinnt
onthe thephysicalvariables
the inner
boundary.
The[12]
radiusof thesolution
the atflow.
theirareresult,the time
Rofin self-similar= 3 ⇥ 108 cm.
The ofvaluesthe From
boundary
determinedby depspe
quantities, e.g.,
the density
and thepressure,
shockedmediummparameters,
the energy
deposition
rate
Ė, the ofjettheopeningangle✓j , the2 (hereafter,in thehomologous
described
the previousI section.
thespecificinternalexpansion
energy ✏ phasenormalizedby cinadopt thI

13年11月14日木曜日

vj = 1 − 2 ,(2)at the inner boundary isΓgivenby,j!
s are set to be zero. Using the jet opening
angle θj and the radius1
vj = 1 − 2 ,e area SJet
which the jet is injectedΓj can be expressed as,
j throughinjection
injection2 radius:

Rin = 3×108cm(2)

Sj = 2πR− cos
θj ). Using the jet opening angle θj(3)er components
are setbe zero.
and the radiusj (1 to52 ergtotalarea
energy:E =5×10r core Rin , theSj through which
the jetis injected can be expressed as,
given by51
energy deposition rate:
2 dE/dt=200, 100, 50, 20, 10, 5, 2, 0.5×10 erg/s
Sj = 2πRj (1 − cos θj ).
(3)Ėhalf openingĖangle:
θj =10°
=
.
(4)
2
2πRby
nergy flux Sisj givenj (1 − cos θj )initial jet
factor: Γj = 5– 5Lorentz–
with the energy flux along
the radial
given in EquationĖ energy:Ė0/cdirection
2=20
speciﬁc internalε= inner.
(4)
2 boundary,obtain the density ρ0 attheSj
2πRj (1 − cos θj )boundary is CSM:
given by,
Mdot=10-7 M◉/yr, vw=1000km/s
1 along the radial direction given in Equation
is expressionĖwith!the energy flux
ρ20 =
,
(5)
1
2
2
2πR
(1vobtain−cos θ1jthe)−
vj [(1
Γj ] inner boundary,− D)vwe
density,+ γ%0ρ)Γ
(2)
j , in0 jat−thej =2Γjquation of state for an idealĖgas with the adiabatic
1 index of γ(= 4/3).
ρ0 zero.
=innerUsing(5)
sssureare setthe jetopening
angle2 θj and, the radius
2
p0 to
at be
the
boundaryiseasilyderived,
2πRin (1 − cos θj ) vj [(1 + γ%0 )Γj − Γj ]area Sj through which the jet is injected can be expressed as,
p0 = (γ2 −. an ideal gas with the adiabatic index(6) of γ(= 4/3).
ve used the equationof 1)ρ
state
0 %0forSj = 2πRj (1 − cos θj ).
(3)
ion of the pressure p0 at the inner boundary is easily derived,

13年11月14日木曜日
meters,Ė, θ , Γ , % , and τ are crucial for the evolution of the jet.

Jet models
ultra-relativistic jet is formed successfully (jet break time < jet injection time)
low dE/dt (=0.5 1051erg/s).
left: Lorentz factor right: density
long tinj (=50s)logΓ

z in clogρ

x in c
13年11月14日木曜日

Jet models
ultra-relativistic jet is formed successfully (jet break time < jet injection time)
low dE/dt (=0.5 1051erg/s).
left: Lorentz factor right: density
long tinj (=50s)logΓ

z in clogρ

x in c
13年11月14日木曜日

Jet models
ultra-relativistic jet is not formed (jet break time > jet injection time).
high dE/dt (=50 1051erg/s)
left: Lorentz factor right: density
short tinj (=0.5s)

logΓ

z in clogρ

x in c
13年11月14日木曜日

Jet models
ultra-relativistic jet is not formed (jet break time > jet injection time).
high dE/dt (=50 1051erg/s)
left: Lorentz factor right: density
short tinj (=0.5s)

logΓ

z in clogρ

x in c
13年11月14日木曜日

2.2.2Models with !"failed jet !""

()*+

'"
%"
#!
2.2.3 Kinetic energyof the ejecta!" distribution
!"
#%
'
!"
%
-'9!
#$ of the dynamical
For qualitative discussion
evolutionof the ejecta resulting from
(
)
8*,-.
!"
!"

"

Kinetic energy distribution()*+,-.

&
models, I calculate the !"kinetic
energy of the ejecta with the/4-velocity
higher than012343%"3516711
kinetic energy distribution of the ejecta at ~200 sec after the jet injection
$
!
.
!"
%
!"
Ek (> Γβ) = Γ(Γ − 1)ρdV,

!"

!
"

!"
Models with ultra-relativistic
jet show ﬂat distributions

where the integration run#! over the ejecta with the 4-velocity higher than Γβ. Thi!"#%
energydistributionoftheejecta. [Tanet al.(2001)]
performed
a atseriesofahydrodyn!"
For models with nearly spherical
blast waves,the distribution
falls
Γβ<

-'9!

()8*,-.
!" from a compact
relativistic
shock
breakout
progenitor star in spherical symmetry a
49
few
#$

in 10 erg

/012
012343$"3516711
343!"3516711!"!"&/
energy distribution of thespherical ejecta is proportional to a power of the 4-veloc$!"!"$()*+,-.
()*+,-.

&

%

!"!"%
!
!"!"!

.

−5.1
%""
E
(>
Γβ)
∝
(Γβ)
,
k
!""
"
'"
!"!""
%"
#! #!
when a star with a radiativeenvelope
is assumed. In Figure 3, I show the resultant
!"!"
!"
#% #%
'
!"
!"
for each model. The distribution %for spherical model
derived by [Tan et al.(2001)] is
-'9!
-'9!
#$ #$
8*,-.
(())8*,-.
!"!" ◦For models with θjet = 10"9"!
, the distribution
the models
with !"
Ė51 = 200 !""and 100 a"9!
!
&/012343%"3516711!",the spherical case. On theother hand, in the models with Ė51 = 10, 5 and 2, mo$!"by the ejecta moving !"at %highly relativistic speeds. The models with Ė51 = 50 and
13年11月14日木曜日

2.2.2Models with !"failed jet !""

()*+

'"
%"
#!
2.2.3 Kinetic energyof the ejecta!" distribution
!"
#%
'
!"
%
-'9!
#$ of the dynamical
For qualitative discussion
evolutionof the ejecta resulting from
(
)
8*,-.
!"
Lazzati+ (2011)!""

Kinetic energy distribution()*+,-.

&
models, I calculate the !"kinetic
energy of the ejecta with the/4-velocity
higher than012343%"3516711
kinetic energy distribution of the ejecta at ~200 sec after the jet injection
$
!
.
!"
%
!"
Ek (> Γβ) = Γ(Γ − 1)ρdV,

!"

!
"

!"
Models with ultra-relativistic
jet show ﬂat distributions

where the integration run#! over the ejecta with the 4-velocity higher than Γβ. Thi!"#%
energydistributionoftheejecta. [Tanet al.(2001)]
performed
a atseriesofahydrodyn!"
For models with nearly spherical
blast waves,the distribution
falls
Γβ<

-'9!

()8*,-.
!" from a compact
relativistic
shock
breakout
progenitor star in spherical symmetry a
49
few
#$

in 10 erg

/012
012343$"3516711
343!"3516711!"!"&/
energy distribution of thespherical ejecta is proportional to a power of the 4-veloc$!"!"$()*+,-.
()*+,-.

&

%

!"!"%
!
!"!"!

.

−5.1
%""
E
(>
Γβ)
∝
(Γβ)
,
k
!""
"
'"
!"!""
%"
#! #!
when a star with a radiativeenvelope
is assumed. In Figure 3, I show the resultant
!"!"
!"
#% #%
'
!"
!"
for each model. The distribution %for spherical model
derived by [Tan et al.(2001)] is
-'9!
-'9!
#$ #$
8*,-.
(())8*,-.
!"!" ◦For models with θjet = 10"9"!
, the distribution
the models
with !"
Ė51 = 200 !""and 100 a"9!
!
&/012343%"3516711!",the spherical case. On theother hand, in the models with Ė51 = 10, 5 and 2, mo$!"by the ejecta moving !"at %highly relativistic speeds. The models with Ė51 = 50 and
13年11月14日木曜日

!"""
2.2.3 Kinetic energy
distributionof the ejecta
'"
!"
%"
#!
!"
!"
For qualitative discussionof' the dynamical evolution of the ejecta resulting
#%
!"
%
-'9!
#$
()8*,-.
models, I calculate!"the kinetic energyof theejecta with the 4-velocity higher

()*+

!"

Kinetic energy distribution()*+,-.

&!/012343%"3516711!"
kinetic energy distribution of the ejecta at ~200 sec after the jet injection

!"

$

!"

%

!"

!

.

Ek (> Γβ) =Γ(Γ − 1)ρdV,

where the integration
run over the ejecta with the 4-velocity higher than Γβ.
"!"Models with ultra-relativistic
jet show ﬂat distributions

energy distributionof#! the ejecta. [Tan et al.(2001)] performed a series of hydr!"#%
relativistic
shock
breakout
fromcompactin Γβ<
spherical!"
For models with nearly spherical
blasta waves,theprogenitor
distributionstar
falls ata symme#$()8*,-.

-'9!

!"of the spherical ejecta is proportional to a power of the 4energy
distribution
few
in 1049erg&()*+,-.
()*+,-.

!"!"&
$
!"!"$
%

!"!"%
!
!"!"!

/012
012343$"3516711
343!"3516711/

Ek (> Γβ) ∝ (Γβ)−5.1 ,%""long GRBs?
!"""radiative'"envelope is assumed. In Figure 3, I show the resu"
when a star with!"
a!"
%"
#! #!
ll GRBs?
!"!" distribution!"
for each model. The
for spherical model derived
by [Tan et al.(200
#% #%
'
!"!"
◦
For models with θjet
= 10 ,%the distribution-'9!
-'9! the models with Ė51 = 200 and
#$ #$
8*,-.
(())8*,-.
!"!"
the spherical case. On
hand,in themodels with
"9"!the otherSNe"9!
!" Ė51 = 10,!""5 and 2
with
no!GRB?
&/012343%"3516711!",by the ejecta moving
at highly relativistic speeds. The models with Ė51 = 50$!"%
The kinetic energyof the ejecta moving at non-relativistic speeds can be m!".

13年11月14日木曜日

Outline
Brief introduction of low-luminosity GRBs
Jet models
Implications to emission from low-luminosity GRBs
Summary

13年11月14日木曜日

larger explosion energies. The aspherical explosion causes a
region of higher entropy along the z-axis, which o†ers better
conditions for the a-rich freezeout (Fig. 1). The high entropy
inhibits the production of 56Ni. Much 4He is left after thefreezeout, so the elements produced through 4He capture
are very abundant in the deepest region along the z-axis(Fig. 2). This results in the enhancement of the elements
synthesized in the deepest region, such as 44Ca (produced as
44Ti), 48Ti (as 48Cr), and elements heavier than A D 58.

Nucleosynthesis

Maeda+ (2002)

Post-process nucleosynthesis calculations

more ext
al. 2001b
40Ca, 52
reduction
duction o

The mments prenhancedburning
usually d

4

In ordaxisymm[Fe II] bl
were obt.

Many earlier works in the context of bipolar
explosion in SNe (e.g., Nagataki+1997,2003,2005,

ABUN

Ni

OxygenMaeda+2002,Tominaga+2007)
56Ni mass: (e.g.,Nagataki+2003,Tominaga+2007)

slow energy deposition ➡ M(56Ni)<<0.1M◉

FIG. 3.ÈTwo-dimensional distribution of 56Ni (open circles) and 16O(dots) of model C in the homologous expansion phase. Open circles anddots denote test particles in which the mass fractions of 56Ni and 16O,
respectively, exceeds 0.1. Lines are density contours at the level of 0.5 (solidlines), 0.3 (dashed lines), 0.1 (dash-dotted lines), and 0.01 (dotted lines) of the
maximum density.

instantaneous energy injection ➡ M(56Ni)~0.1M◉
56Ni distribution:

region with high X(56Ni) is formed around the jet
and a region with unburned 16O is surrounding
the region➡ consistent with optical spectra of some HNe

13年11月14日木曜日

Nagataki+ (2003)

Species

12C . . . . . . .
14N . . . . . .
16O . . . . . .
19F . . . . . . .
20Ne . . . . .
23Na . . . . .
24Mg . . . . .
27Al . . . . . .
28Si . . . . . .
31P . . . . . . .
32S . . . . . . .
35Cl . . . . . .
36Ar . . . . . .
39K . . . . . .

a [A/B]Nucleosynthesis
Post-process nucleosynthesis calculations.

Many earlier works in the context of bipolar
explosion in SNe (e.g., Nagataki+1997,2003,2005, Maeda+2002,Tominaga+2007)
Tracer particle method is employed
t=2.0

13年11月14日木曜日

t=5.0

t=100.0

Nucleosynthesis

Distributions of elements are similar to earlier
works in the context of HNe.

12C . . . . . . . .
17O . . . . . . . .
22Ne . . . . . .
26Al . . . . . . .
31P . . . . . . . .
35Cl . . . . . . .
39K . . . . . . . .
43Ca . . . . . .
47Ti . . . . . . .
51V . . . . . . . .
55Mn . . . . . .
59Co . . . . . .
64Ni . . . . . . .
67Zn . . . . . .

1.35E[011.11E[075.51E[026.28E[05
7.09E[033.92E[043.31E[041.25E[055.57E[059.91E[053.00E[036.56E[044.29E[126.53E[0713C . . . . . . .
18O . . . . . . .
23Na . . . . . .
27Al . . . . . .
32S . . . . . . . .
37Cl . . . . . .
40K . . . . . . .
44Ca . . . . . .
48Ti . . . . . . .
50Cr . . . . . .
54Fe . . . . . .
58Ni . . . . . .
63Cu . . . . . .
68Zn . . . . . .

1.84E[081.77E[061.87E[027.06E[022.37E[018.90E[057.56E[081.62E[032.02E[034.39E[043.87E[022.71E[021.80E[051.23E[0714N . . . . . . .
19F . . . . . . . .
24Mg . . . . . .
28Si . . . . . . .
33S . . . . . . . .
36Ar . . . . . . .
41K . . . . . . .
46Ca . . . . . .
49Ti . . . . . . .
52Cr . . . . . . .
56Fe . . . . . . .
60Ni . . . . . . .
65Cu . . . . . .
69Ga . . . . . .

values for model C (in Table 2, [A/B] 4 log (A/B)
10[ log (A/B) , where A and B are nuclear mass fractions).
10_
The main characteristics can be summarized as follows (seealso Nomoto et al. 2001b) :.

Particles that contains 56Ni have velocities <0.3c
Ni mass ~ 0.13 M◉, smaller by a factor of 2-3
than observed values

1. The complete Si-burning region is more extended forlarger explosion energies. The aspherical explosion causes a
region of higher entropy along the z-axis, which o†ers better
conditions for the a-rich freezeout (Fig. 1). The high entropy
inhibits the production of 56Ni. Much 4He is left after thefreezeout, so the elements produced through 4He capture
are very abundant in the deepest region along the z-axis(Fig. 2). This results in the enhancement of the elements
synthesized in the deepest region, such as 44Ca (produced as
44Ti), 48Ti (as 48Cr), and elements heavier than A D 58.

 


Because ofsimultaneo
elements regreatly enhe†ect of a-r
2. Incommore exten
al. 2001b).
40Ca, 52C
reduction
duction of t

The mos
ments prod
enhanced rburning pr
usually dom
4.

Maeda+ (2002)

In orderaxisymmet[Fe II] blen
were obtai

8.13E[051.45E[093.35E[015.27E[019.40E[044.01E[022.30E[051.23E[093.90E[058.25E[033.95E[011.20E[021.12E[059.72E[10ABUNDANSpecies●: X(56Ni) >0.1●: X(28Si) >0.1








13年11月14日木曜日







●: X(16O ) > 0.1
FIG. 3.ÈTwo-dimensional distribution of 56Ni (open circles) and 16O(dots) of model C in the homologous expansion phase. Open circles anddots denote test particles in which the mass fractions of 56Ni and 16O,
respectively, exceeds 0.1. Lines are density contours at the level of 0.5 (solidlines), 0.3 (dashed lines), 0.1 (dash-dotted lines), and 0.01 (dotted lines) of the
maximum density.

12C . . . . . . . .
14N . . . . . . .
16O . . . . . . .
19F . . . . . . . .
20Ne . . . . . .
23Na . . . . . .
24Mg . . . . . .
27Al . . . . . . .
28Si . . . . . . .
31P . . . . . . . .
32S . . . . . . . .
35Cl . . . . . . .
36Ar . . . . . . .
39K . . . . . . .

a [A/B] 4

Nucleosynthesis

Distributions of elements are similar to earlier
works in the context of HNe.

12C . . . . . . . .
17O . . . . . . . .
22Ne . . . . . .
26Al . . . . . . .
31P . . . . . . . .
35Cl . . . . . . .
39K . . . . . . . .
43Ca . . . . . .
47Ti . . . . . . .
51V . . . . . . . .
55Mn . . . . . .
59Co . . . . . .
64Ni . . . . . . .
67Zn . . . . . .

1.35E[011.11E[075.51E[026.28E[05
7.09E[033.92E[043.31E[041.25E[055.57E[059.91E[053.00E[036.56E[044.29E[126.53E[0713C . . . . . . .
18O . . . . . . .
23Na . . . . . .
27Al . . . . . .
32S . . . . . . . .
37Cl . . . . . .
40K . . . . . . .
44Ca . . . . . .
48Ti . . . . . . .
50Cr . . . . . .
54Fe . . . . . .
58Ni . . . . . .
63Cu . . . . . .
68Zn . . . . . .

1.84E[081.77E[061.87E[027.06E[022.37E[018.90E[057.56E[081.62E[032.02E[034.39E[043.87E[022.71E[021.80E[051.23E[0714N . . . . . . .
19F . . . . . . . .
24Mg . . . . . .
28Si . . . . . . .
33S . . . . . . . .
36Ar . . . . . . .
41K . . . . . . .
46Ca . . . . . .
49Ti . . . . . . .
52Cr . . . . . . .
56Fe . . . . . . .
60Ni . . . . . . .
65Cu . . . . . .
69Ga . . . . . .

values for model C (in Table 2, [A/B] 4 log (A/B)
10[ log (A/B) , where A and B are nuclear mass fractions).
10_
The main characteristics can be summarized as follows (seealso Nomoto et al. 2001b) :.

Particles that contains 56Ni have velocities <0.3c
Ni mass ~ 0.13 M◉, smaller by a factor of 2-3
than observed values

1. The complete Si-burning region is more extended forlarger explosion energies. The aspherical explosion causes a
region of higher entropy along the z-axis, which o†ers better
conditions for the a-rich freezeout (Fig. 1). The high entropy
inhibits the production of 56Ni. Much 4He is left after thefreezeout, so the elements produced through 4He capture
are very abundant in the deepest region along the z-axis(Fig. 2). This results in the enhancement of the elements
synthesized in the deepest region, such as 44Ca (produced as
44Ti), 48Ti (as 48Cr), and elements heavier than A D 58.

 




8.13E[051.45E[093.35E[015.27E[019.40E[044.01E[022.30E[051.23E[093.90E[058.25E[033.95E[011.20E[021.12E[059.72E[10Because ofsimultaneo
elements regreatly enhe†ect of a-r
2. Incommore exten
al. 2001b).
40Ca, 52C
reduction
duction of t

The mos
ments prod
enhanced rburning pr
usually dom
4.

Maeda+ (2002)

SN component
resulting from failed jet are similar to how typical
HNespectra look likeIn orderaxisymmet[Fe II] blen
were obtai

ABUNDANSpecies●: X(56Ni) >0.1●: X(28Si) >0.1








13年11月14日木曜日







●: X(16O ) > 0.1
FIG. 3.ÈTwo-dimensional distribution of 56Ni (open circles) and 16O(dots) of model C in the homologous expansion phase. Open circles anddots denote test particles in which the mass fractions of 56Ni and 16O,
respectively, exceeds 0.1. Lines are density contours at the level of 0.5 (solidlines), 0.3 (dashed lines), 0.1 (dash-dotted lines), and 0.01 (dotted lines) of the
maximum density.

12C . . . . . . . .
14N . . . . . . .
16O . . . . . . .
19F . . . . . . . .
20Ne . . . . . .
23Na . . . . . .
24Mg . . . . . .
27Al . . . . . . .
28Si . . . . . . .
31P . . . . . . . .
32S . . . . . . . .
35Cl . . . . . . .
36Ar . . . . . . .
39K . . . . . . .

a [A/B] 4

CSM interactionDense circumstellar medium is expected around the progenitor star.
.

ejecta-CSM interaction eﬃciently convert the kinetic energy of the ejecta into
the internal energy and thus might give rise to bright emission in X-ray andgamma-ray.
Some earlier works for the collision of mildly relativistic ejecta with CSM (e.g., Tan+2001).

η Carinae

13年11月14日木曜日©NASAvj = 1 − 2 ,(2)at the inner boundary isΓgivenby,j!
s are set to be zero. Using the jet opening
angle θj and the radius1
vj = 1 − 2 ,e area SJet
which the jet is injectedΓj can be expressed as,
j throughinjection
injection2 radius:

Rin = 3×108cm(2)

Sj = 2πR− cos
θj ). Using the jet opening angle θj(3)er components
are setbe zero.
and the radiusj (1 to52 ergtotalarea
energy:E =5×10r core Rin , theSj through which
the jetis injected can be expressed as,
given by51
energy deposition rate:
2 dE/dt=50×10 erg/s
Sj = 2πRj (1 − cos θj ).
(3)Ėhalf openingĖangle:
θj =10°
=
.
(4)
2
2πRby
nergy flux Sisj givenj (1 − cos θj )initial jet
factor: Γj = 5– 5Lorentz–
with the energy flux along
the radial
given in EquationĖ energy:Ė0/cdirection
2=20
speciﬁc internalε= inner.
(4)
2 boundary,obtain the density ρ0 attheSj
2πRj (1 − cos θj )boundary is CSM
given: by,
Mdot=10-3, 10-4, 10-5, 10-6, 10-7 M◉/yr, vw=1000km/s
1 along the radial direction given in Equation
is expressionĖwith!the energy flux
ρ20 =
,
(5)
1
2
2
2πR
(1vobtain−cos θ1jthe)−
vj [(1
Γj ] inner boundary,− D)vwe
density,+ γ%0ρ)Γ
(2)
j , in0 jat−thej =2Γjquation of state for an idealĖgas with the adiabatic
1 index of γ(= 4/3).
ρ0 zero.
=innerUsing(5)
sssureare setthe jetopening
angle2 θj and, the radius
2
p0 to
at be
the
boundaryiseasilyderived,
2πRin (1 − cos θj ) vj [(1 + γ%0 )Γj − Γj ]area Sj through which the jet is injected can be expressed as,
p0 = (γ2 −. an ideal gas with the adiabatic index(6) of γ(= 4/3).
ve used the equationof 1)ρ
state
0 %0forSj = 2πRj (1 − cos θj ).
(3)
ion of the pressure p0 at the inner boundary is easily derived,

13年11月14日木曜日
meters,Ė, θ , Γ , % , and τ are crucial for the evolution of the jet.

CSM interaction
Models with dense CSM lead to “forward shock - reverse shock” system.

Models with dilute CSM lead to “forward shock - rarefaction wave” system

dM/dt=10-7 M◉/yr



dM/dt=10-3 M◉/yr 
 
 
 
 




















 
 
 
 
 





 



13年11月14日木曜日

 





CSM interaction
The internal energy ﬂux F in the shocked region is of the order of 1020-1021 erg/s/.

cm2 for models with Mdot=10-3, 10-4, 10-5 M◉/yr

ﬂux : F = P/(γ-1)×Γ2vr

assume the internal energy is dominated by photons and some fraction ofphotons can decouple from the shocked region,τsc~3 for dM/dt=10-3M◉/yr-8

3

Density [g/cm ]

10
-9
10
-10
10
-11
10
-12
10
-13
10
-14
10
-15
10
-16
10

ε: fraction of the energy emitted as photons

L~4πR2Fε~4×1046 ε erg/s
×(R/6×1012cm)2(F/1020 erg s-1cm - 2)

Mdot=1e-3
Mdot=1e-4
Mdot=1e-5
Mdot=1e-6
Mdot=1e-7

22

CSM interaction has a potential toproduce emission with L ~ 1046-47 erg/s

21

10

2

[erg/s/cm ]However, thermal equilibrium between
radiation and gas is not achieved!

Internal energy flux

10

20

10

19

10

18

10

Mdot=1e-3
Mdot=1e-4
Mdot=1e-5
Mdot=1e-6
Mdot=1e-7

17

10

150

160

170

180

Radius in c

13年11月14日木曜日

190

200

210

Summary
Failed jet is promising to explain low-luminosity GRBs.
.

Ultra-relativistic jet is failed to be created➡ kinetic energy of the relativistic ejecta is much smaller than the kinetic energyof the non-relativistic one
Explosive nucleosynthesis in the failed jet model➡ similar result to HNe cases
The interaction of the ejecta with dense CSM is investigated➡ CSM interaction has a possibility in producing highly energetic emission withLγ,iso ~ 1046 - 1047 erg/s

13年11月14日木曜日

.

13年11月14日木曜日

Mapping proceduredynamical range is huge➡

jet ~ 1013-14 cm ⇄ Fe core ~ 108-9 cm

Courant condition limits the time stepΔt < cΔx
The numerical domain doubles as the ejecta expand. The resolution isz
halved.

z

×2x
13年11月14日木曜日

×2

xResults
Ultra-relativistic jet

Mildly relativistic
blast wave

13年11月14日木曜日.