Physical Ingredients in
Core-Collapse Supernova
Explosion Mechanismo)nationsctralgYudai SUWA

(YITP, Kyoto University)
Collaboration with

T. Takiwaki, K. Kotake (NAOJ), M. Liebendörfer, S.C. Whitehouse (U. Basel), T. Fischer (GSI),
S. Yamada (Waseda U.), K. Sato (NINS & U. Tokyo)

pt

ld a

Core-collapse supernovae
One of the most energetic explosion in the universe
Eexp〜1051 erg
Egrav〜1053 erg (〜0.1 M⦿ c2)
Eν〜1053 erg

Formation of neutron Star / Black hole
Formation of gamma-ray bursts?
✤ All known interactions are important•Macrophysics

Weak

Gravity
core collapse

Elecromagnetic
pulsar, magnetar,magnetorotational explosion

2012/12/15•Microphysics
neutrino physics

Strongequation of state of dense matter

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Standard scenario of core-collapse supernovae
Final phase ofstellar evolution

Fe
Si
O,Ne,Mg
C+O
HeH

Neutrinosphere formation（neutrino trapping）

Neutron star formation(core bounce）

Neutrinosphere

NeutronStarρc~1011 g cm-3

ρc~1014 g cm-3

ρc~109 g cm-3

shock stallshock revival

Supernova!

Fe
Si
O,Ne,Mg
C+O
He
H
2012/12/15

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Standard scenario of core-collapse supernovae
Final phase ofstellar evolution

Fe
Si
O,Ne,Mg
C+O
HeH

Neutrinosphere formation（neutrino trapping）

Neutron star formation(core bounce）

Neutrinosphere

NeutronStarρc~1011 g cm-3

ρc~1014 g cm-3

ρc~109 g cm-3

shock stallshock revival

Supernova!

Fe
Si
O,Ne,Mg
C+O
He
H
2012/12/15

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Systematics in supernova simulations
Our Goal: Produce Successful Explosion! of ~1051 erg
Dimensionality of hydrodynamics

Iwakami+ 08, Nordhaus+ 10, Hanke+ 11,
Takiwaki+ 12, Couch 12

General relativity

Liebendörfer+01, Müller+ 12, Kuroda+ 12

Neutrino physics
Scheme to solve Boltzmann equation

Ott+ 08, Shibata+ 11, Sumiyoshi & Yamada 12

Interaction rate

Langanke+ 03, Arcones+ 08, Lentz+ 12

Collective oscillation

Raffelt & Smirnov 07, Duan+ 10,
Dasgupta+ 10

Nuclear equation of state

Lattimer & Swesty 91, H. Shen+ 98, G.
Shen+ 10, Furusawa+ 11, Hempel+ 12

Initial condition

Nomoto & Hashimoto 88, Woosley &Weaver 95, Woosley+ 02, Limongi & Chieffi
06, Woosley & Heger 07, Yoshida+ 12

progenitor structure (mixing, wind...)rotation / magnetic ﬁeld
2012/12/15

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Systematics in supernova simulations
Our Goal: Produce Successful Explosion! of ~1051 erg
Dimensionality of hydrodynamics

Iwakami+ 08, Nordhaus+ 10, Hanke+ 11,
Takiwaki+ 12, Couch 12

General relativity

Liebendörfer+01, Müller+ 12, Kuroda+ 12

Neutrino physics
Scheme to solve Boltzmann equation

Ott+ 08, Shibata+ 11, Sumiyoshi & Yamada 12

Interaction rate

Langanke+ 03, Arcones+ 08, Lentz+ 12

Collective oscillation

Raffelt & Smirnov 07, Duan+ 10,
Dasgupta+ 10

Nuclear equation of state

Lattimer & Swesty 91, H. Shen+ 98, G.
Shen+ 10, Furusawa+ 11, Hempel+ 12

Initial condition

Nomoto & Hashimoto 88, Woosley &Weaver 95, Woosley+ 02, Limongi & Chieffi
06, Woosley & Heger 07, Yoshida+ 12

progenitor structure (mixing, wind...)rotation / magnetic ﬁeld
2012/12/15

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1D simulations: fail to explodeRammp & Janka 00

Liebendörfer+ 01

By including all available physics to simulations, weconcluded that the explosion cannot be obtained in 1D!
(The exception is an 8.8 M⦿ star; Kitaura+ 06)
Thompson+ 03

2012/12/15

Sumiyoshi+ 05

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Numerical simulation
YS+, PASJ, 62, L49 (2010); ApJ, 738, 165 (2011); ApJ in press (2012)

Spherically symmetric and axisymmetric simulation(ZEUS-2D; Stone & Norman 92)

Hydrodynamics + Neutrino transfer
df
f
+µ
+ µ
cdt
r
= j(1

d ln
3v
+
cdt
cr
f)

(1

µ2 )

E2
f+
(1
c(hc)3

f
+ µ2
µ
f)

d ln
3v
+
cdt
cr

Rf dµ

f

v
f
D
cr
E
R(1

f )dµ

(Lindquist 1966; Castor 1972; Mezzacappa & Bruenn 1993)

Isotropic Diﬀusion Source Approximation (Liebendörfer+ 09)
electron-type neutrino/antineutrino

2012/12/15

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Neutrino-driven explosion in multi-D simulation
Recently, we have successful exploding models driven by neutrino heating
YS, Kotake, Takiwaki, Whitehouse, Liebendörfer, Sato, PASJ, 62, L49 (2010)

Müller, Janka, Marek (2012)

comparison between 1D and 2D

2012/12/15

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The first 3D simulation with neutrino transfer
Takiwaki, Kotake, YS, ApJ, 749, 98 (2012)

K computer

T2K-Tsukuba

XT4@NAOJ

320(r)x64(θ)x128(φ)x20(Eν)

2012/12/15

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Systematics in supernova simulations
Our Goal: Produce Successful Explosion! of ~1051 erg
08, Nordhaus+ 10, Hanke+ 11,
Dimensionality of hydrodynamics Iwakami+
Takiwaki+ 12, Couch 12
General relativity

Liebendörfer+01, Müller+ 12, Kuroda+ 12

Neutrino physics
Scheme to solve Boltzmann equation

Ott+ 08, Shibata+ 11, Sumiyoshi & Yamada 12

Interaction rate

Langanke+ 03, Arcones+ 08, Lentz+ 12

Collective oscillation

Raffelt & Smirnov 07, Duan+ 10,
Dasgupta+ 10

Nuclear equation of state
Initial condition
progenitor structure (mixing, wind...)Lattimer & Swesty 91, H. Shen+ 98, G.
Shen+ 10, Furusawa+ 11, Hempel+ 12
Nomoto & Hashimoto 88, Woosley &Weaver 95, Woosley+ 02, Limongi & Chieffi
06, Woosley & Heger 07, Yoshida+ 12

rotation / magnetic ﬁeld
2012/12/15

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Problems of multi-D explosions
small explosion energy (~1049-1050 erg)
0100time [ms]

200

300

explosion simulation of an 11.2 M! progenitor star. Note that the mass-shell spacing outside of the redcomposition interface between the silicon layer and the oxygen-enriched Si shell) is reduced to steps of

2.5
2.0

1.5

1.5
1.0
1.0
0.5

0.5

explosion energy [1049 erg]

2.0

radius [103 km]

the panels for
12).
Therefore
Marek& Janka 09
for some time,
her abundances
he matter swept
nuclei and αh is constructed
a at each radius,
al appears to be(at post-bounce
penetration into
∼ 250 ms p.b.,ening effect on

Fig. 3. Snapshots of the density (left half) and the entropy (right half) for models M13-2D (left panel
shock reaches to 1000 km, corresponding to ! 470 ms after a bounce in both cases.

when we terminatedSuwa+
all of10
the models. F
speculate that they
the nextof
500Supern
ms by
No. 6]
Explosion Geometry
to unquestionably imodels, a losessential for an increased efficiency of the neutrino heatingin thesphericalphysics would be nein multi-D models.
! numericalis estiOur heatre
A more detailed analysis of the timescale is shown inresultsspecificbinof Marek
early pfigure 2. The right half shows !adv =!heat, which is the ratioa relatively
gravitationa more cleaof the advection to the neutrino-heating timescale. For theshows
neutrinos,
models do.

2D model (right panel), it can be shown that the condition of where rgai
and!adv =!heat & 1 is satisfied behind the aspherical shock, which4. Summary
By compa
time [ms]the conditions
2D modelFigure 11. Left panel: mean shock radius (arithmetical average over all is deformed predominantly by the SASI, while the ratio is Performingof the 11.2 M!
2D c
Fig.
4.
Time
evolutionofthediagnostic
energyversuspostbounce
lateral directions, dashed line) and maximum and minimum shock positions shown to be smaller than unity in the whole region behind the
This
is
also
layer increases
with spectral neutr
time for 2D models with and without rotation.
as functions of post-bounce time for our two-dimensional explosion simulation
MAREK
&
JANKA
Vol.
694
. At the same
sourceciently
approximati
in mof an 11.2 M! progenitor. Right panel: “explosion energy” of the 11.2 M! star,er between thedefined as the total energy (internal plus kinetic plus gravitational) of all mass
expansion
of
the
sh
We
now
1.40
in
the
gain
layer
with
positive
radialvelocity,asafunctionofpost-bouncetime.
ues to be wellthe 2D models with and without rotation. Although the diag- sion on the initialforby
ml, this suggests
outwardnostic energies depend on the numerical resolutions quantita- drivenBoth
he gain layer toeffects,suctively, they show a continuous increase for the rotating models. multi-D
model
M13
the absolute value of the total gas energy in the numerator ofm the continued
The diagnostic energies for the models without rotation, on the shownt a preponder
Equation (5) goes to zero.
1000
1000 and E
1.30
re 10). Shortly
withrotation.
We h
other
hand,
peak
at
around
180
ms
when
the
neutrino-driven
3.4. Explosion Energy
study
main
d a pronounced
explosion sets in (see also figure 1), and show a decrease later can become larger f
ms, it makes
In both our 11.2 M! and 15 M! explosions, the energy ofwhiThephase,conclusion
on. With values of order 1049 erg it is not yet clear whether
is decline is a
the matter in the gain layer with positive radial velocities
obtainedFor
in thisthese models will also eventually lead to an explosion.
thestuinosities at the(“explosion energy”) reaches ∼2.5 × 1049 erg at the end of(2009),
whosugg
The reason for the greater explosion energy for models with
deformationd the neutron100 the computed evolutions and rises with a very steep gradientrotation is due to the bigger mass of the exploding material. impact on the exp
steep negative(Figures 9 and 11). Therefore, reliable estimates of the final
althoughthwave onThis is because a north–south symmetric (` = 2) explosion can the shock
he composition
explosion energy cannot be given at this time. For that to be
the nonrotati
expel more material than a unipolar explosion can. In fact, whilewhen
the S
gen-enriched Si
possible, the simulations would have to be continued for many
the mass enclosed inside the gain radius is shown to be larger to the short simul
a bounce).
at the shock (athundred milliseconds more (which is numerically a challenging
for the rotating models (e.g., table 1). The explosion energies Therefore, because
ating timescalemation, thetask and currently impossible for us with the sophisticatedto an evolution 10 and computationally expensive neutrino transport and chosen
for the 2D
ound state, i.e.,
resolution). This is obvious from the neutrino-driven explosion
shown in fi
-100
0
100
200
300
geometry,time [ms]2012/12/15
10the
/23
for
2D
Quarksin Computational
Science @ Naras Figure 2 but for our two-dimensional explosion simulation of an 11.2
M! progenitorto
star. Universe
Note that the mass-shellspacing outside of the red
0.0
0

100

200

300

200

300

0.0

radius [km]continuous accretion <=> The remnant is NOT a NS

A possibility: the collective oscillationof neutrinos
46
a

Pvv

Duan+
b 10

ve' initialvµ' initialve' finalvµ' final

Burrows & Thompson 02

-2

1

ƒv

-2.2

Spectral swap

-2.4

Ω0

-2.6

Eν = + δm2ω

20

Figure 620

E (MeV)

40

60

Because of the mass of neutrinos,

-2.8

ω

0

∞

Eν = – δm
2ω

2

-3

Illustration of the stepwise spectral swap phenomenon in the two-flavor mixing case with !m2 < 0 (inverted
neutrino
mass hierarchy)
that was discoveredby Duan et al. (70). (a) The-3.2
stepwise swapping of νe and νµ
the ﬂavor
oscillates
in propagationenergy spectra about Es ! 9 MeV in a single-angle scheme. The spectra of ν̄e and ν̄µ are nearly fully
swapped in this calculation. (b) The corresponding survival probability Pνν , which is a step-like function ofThe
spectrumcandiﬀerent
at thestructure of-3.4Pνν (ω) is pushed rightward toω.
For thenormal neutrino
massbehierarchy
case, the step-like
2$0 > 0. Because Es = | !m| splits a neutrino spectrum into two parts with different flavors, this2$0emissionandabsorption
site.
-3.6
phenomenon is also sometimes termed spectral split. Reprinted with permission
from Reference 124.
Copyright 2009, American Institute of Physics.
Especially, νμ/τ→νe is important
-3.8

Just
as in the conventionalcase (Figure 2), in the adiaReaction
rate: σ adiabatic
E2 " MSW flavor transformation-4
5 changes
10
15 decreases.
20
25
30
35
as µ
batic precession solution P"ω follows H̃ ω , whose direction (and magnitude)" → (ω − $ ) B,
" whereThisAverage
induces neutrino
flavortransformation.
Specifically,
as
µ
→
0,
H̃
ω
0
energy: νμ/τ>νeFigure 9.
This figure shows the ν̄e (thin lines) and “νµ ” (thick lines) emergent
mode converts the initial$0 = $(µ = 0). This means that the adiabatic collective precession
luminosity spectra for the 11 M! progenitor evolution depicted in Fig. 8. The
luminosity
spectra(logarithm
base
ten)
are
in units of 1054 ergs s−1 MeV−1 and
into
the
mass
state
|ν
%
or
|ν
%,
dependingonwhetherωissmallerorlarger
than
$
(70).
ν
e
1
2
0
2012/12/15
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the neutrino energy (abscissa) is in units of MeV. There is no appreciable flux prior

Collective oscillation
YS, Kotake, Takiwaki, Liebendörfer, Sato, ApJ, 738, 165 (2011)
10000

3

Rν=30km, <εν>=12MeV
N13R30E12T100

2.5

Diagnostic Energy [10 erg]

2
Radius [km]

51

1000

100

10
100
10000

150

200
250
300
Time after boune [ms]

350

400

RN13R30E13T100
ν=30km, <εν>=13MeV

N13R30E12T100S
N13R30E13T100S
N13R30E15T100S
N13R30E15T200S

1.5
1
0.5
10-2
10-3
10-4
100

150

200
250
300
Time after bounce [ms]350

Radius [km]1000

critical heating rate
explosion energy~1051 erg

100

PNS (~1M⦿)
10100

2012/12/15

150

200
250
300
Time after boune [ms]

350

400

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Important note
Chakraborty+ 11 (1D, 10.8 M⦿)Dasgupta+ 12 (2D, 15 M⦿)

The matter density would suppress the collective oscillation
However, after the onset of the explosion the swapped spectrum mightenhance the heating rate and amplify the explosion stronger
Numerical simulations that include the neutrino collective oscillations in aself-consistent way are required to pin down this problem!
2012/12/15

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Systematics in supernova simulations
Our Goal: Produce Successful Explosion! of ~1051 erg
08, Nordhaus+ 10, Hanke+ 11,
Dimensionality of hydrodynamics Iwakami+
Takiwaki+ 12, Couch 12
General relativity

Liebendörfer+01, Müller+ 12, Kuroda+ 12

Neutrino physics
Scheme to solve Boltzmann equation

Ott+ 08, Shibata+ 11, Sumiyoshi & Yamada 12

Interaction rate

Langanke+ 03, Arcones+ 08, Lentz+ 12

Collective oscillation

Raffelt & Smirnov 07, Duan+ 10,
Dasgupta+ 10

Nuclear equation of state
Initial condition
progenitor structure (mixing, wind...)Lattimer & Swesty 91, H. Shen+ 98, G.
Shen+ 10, Furusawa+ 11, Hempel+ 12
Nomoto & Hashimoto 88, Woosley &Weaver 95, Woosley+ 02, Limongi & Chieffi
06, Woosley & Heger 07, Yoshida+ 12

rotation / magnetic ﬁeld
2012/12/15

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temperature can e.g. be found in Nadyozhin and Yudin
0+ξfRMF(T, nn /ξ, np /ξ) ,(2005); Potekhin et al. (2009); Potekhin and Chabrier(2010). However, we leave this for future studies as the
The first term in Eq. (6) is the summed ideal g
Coulomb energy becomes only important at low temperpression of the nuclei. The Coulomb free energy
atures so that the simplest expression is sufficient for our
nuclei appears in addition. The second line in Eq
purposes.
the direct contribution from the excluded volum(1985)
temperature leads to the population of Hillebrandt
excitedcause&of Wolﬀ
this term,
as long as nuclei are present, tLattimer states&FiniteSwesty(LS)(1991)of the nuclei. Here we use the temperature depenenergy density goes to infinity when approachingdent degeneracy function of Fái and Randrup (1982).Hartree-FockItration density,
because the free volume of nuclei gcalculation
based oncompressible
drop
model
is thesame analyticliquid
expression
as inthe original reference
zero, κ → 0. Thus, nuclei will always disappearof the HS model (Hempel and Schaffner-Bielich 2010),
saturation density is reached. The RMF contribu
G.Shenetal. (2010,2011)
0
nowK=180,
we consider
energies below thevariantsbut
with
220,only
andexcitation
375 MeV
the nucleons fRMF
is weighted with their filling fa
binding energy of the corresponding nucleus, in order toas the free energy is an extensive quantity. If nuc
representthat the2011)
excited states still have to be boundrelativistic
mean
(NL3,
FSUGold)
absent,ξ = ﬁeld
1, andtheory
we get theunmodified
RMF dH.Shen etal.
(1998,(see, e.g., Röpke (1984)). We note that the inclusion oftion, as it should be. The excluded volume correct
excited states up to infinite energies had only aHempel
minor
the al.
nucleirepresents a hard-core repulsion of theet(2012)
relativistic
meanonﬁeld
theory (TM1)
influencethe composition
but would lead to an unat large densities close to saturation density. Instephysically large contribution of the excited states to themodification of the free energy of the unbound nu
relativisticmean
ﬁeld theory
(TM1,
TMA,
energydensitycomponent
and entropy (~2011)at very large temperatures.
including
hyperonis purely
geometric
and just
describes
that the nu
We describe nuclear matter as a chemical mixtureFSUGold)offill only a fraction of the total volume. In this sen
the different nuclear species and nucleons. As we distintwo aforementioned model assumptions for the ex
guish
between nuclei andthe surroundingslope
interacting
nuvolume are essential, as they lead to the desired li
incompressibility
symmetry energy
of symmetry energy
cleons we still have to specify how the system is composed
behavior of the EOS.
K
[MeV]
J
(S)
[MeV]
L
[MeV]
of the different particles. Our thermodynamic model is
2.4. EOS characteristics & constraints
built on two main assumptions: First, we assume for unbound
not allowed to be situatedLS
180,nucleons
220, 375that they are
29.3--Table 2 lists some characteristic saturation pro
inside of nuclei, whereas nuclei are described as uniformof uniform bulk nuclear matter for the three di0
hard spheres at saturation density nB . Second, for nuRMF parameterizations. We also include the L
mass number A ≥36.9
2) we assume that they 111
mustwith the compressibility of K = 180 MeV in the
HShen clei (with281
not overlap with any other baryon in the system (nuclei
The quantities shown in Table 2 correspond to t
or unbound nucleons). Thus we take the volume whichefficients of the following power-series expansion
is available
to be the part of the totalbinding energy per baryon at T = 0 around the s
HW
263 for the nucleons32.9--volume of the system which is not excluded by nuclei.
tion point:
This is described by the filling factor of the nucleons271.5 (NL3)
37.29
(NL3)
118.2 (NL3)
1
1
2
!
GShen
E(x,
β)
=
−E
+
Kx
+
K ! x3 + ...
00
162
230.0 (FSU)ξ = 1 −32.59A (FSU)
60.5 (FSU)
nA,Z /nB ,
(3)
" 18
#
1
A,Z
318 (TMA)
30.7
(TMA)
90 (TMA)+β 2 J + Lx + ... + ... ,Hempel3
32.6we(FSU)
60 (FSU)(here230
and(FSU)in the following,mean A ≥ 2). The
freevolume in which a nucleus can move is the total volume
with x = nB /n0B − 1 denoting the relative deviatio
2012/12/15
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Finite temperature EOSs

Numerical simulation
400

EOS: LS180, (LS220,) LS375, and Shen
Axisymmetric simulation (ZEUS-2D; Stone & Norman 92)

Imcompressibility [MeV]

LS375

= j(1

d ln
3v
+
cdt
cr
f)

(1

f
µ2 )
+ µ2
µ

E2
f+
(1
c(hc)3

f)

f

Shen

250

LS220

200

LS180
20

25

30

35

40

Symmetry Energy [MeV]

d ln
3v
+
cdt
cr

Rf dµ

300

150

Hydrodynamics + Neutrino transfer
df
f
+µ
+ µ
cdt
r

350

v
f
D
cr
E
R(1

Note: Of course the other parameters
differ as well.

f )dµ(Lindquist 1966; Castor 1972; Mezzacappa & Bruenn 1993)

Isotropic Diﬀusion Source Approximation (Liebendörfer+ 09)
electron-type neutrino/antineutrino

progenitor: 15 M⦿ (Woosley & Weaver 95)
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Shock radius evolution depending on EOS
YS, Takiwaki, Kotake, Fischer, Liebendörfer, Sato, ApJ in press, arXiv:1206.6101

maximum
averageminimum

LS180 and LS375 succeed the explosion
Shen EOS fails
2012/12/15

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O’Connor & Ott 10
17/23

6

0

100

200

300

400

Radius of neutron
starTime after
Bounce [ms]

500

600

(b)YS,
Mass-weighted
entropy perin thegain region.
Takiwaki, Kotake,average
Fischer, Liebendörfer,
Sato,baryon
ApJ in press,
arXiv:1206.6101
Janka, arXiv:1206.2503

90

70
60
50

80

60

40

20

60

40

20

L&S
H&W
Shen

0
0

100

200

300

time [ms]

400

500

1500

L&S
H&W
Shen

FIG. 4: Two-dimensional SN simulations [121] of an 11.
show cross-sectional entropy distributions at 412 ms after(middle), and at
500 ms p.b. for the Hillebrandt & Wolff Eo
1000
contraction of the PNS (bottom left) and because of weak
L&S
does not yield an explosion within the simulated time as v
shock radius [km]80

Faster contraction isbetter for the
explosion!

80

neutron star radius [km]

LS180
LS375
Shen

neutron star radius [km]Radius of Neutron Star [km]

100

500

H&W
Shen

strong feedback between the EoS, weak interactions, n
In order to achieve a more elaborate treatment of t
0
100
200
300
400
500 trinospheric
600 densities after bounce and to connect sm
00
11 400 3 500
0
100
200
300
400
500
0
100
200ρ < 300
Garching
simulations
employat
10g/cm a Bo
Time after Bounce [ms]
time
[ms]
time [ms]species, and in the non-NSE regime at T ! 5 × 109 K−3(d) Protoneutron star radii, determined at ρ = 1011 g cm
now, a .small reaction network for nuclear burning.
FIG. 4: Two-dimensional SN simulations [121] of an 11.2
M!astar[22] forgravitational
three differentmass
nuclear
EoSs.
With
maximumof 1.83
M!The
forshow cross-sectional entropy distributions at 412 ms after bounce for the LS180-EoS (left), at 586 ms p.b. for thwith PSR J1614-2230. Moreover, an incompressibilit(middle),
and
at
500
ms
p.b.
for
the
Hillebrandt&
Wolff
EoS [122]. The last is the stiffest EoS of the set. It leads t
the models using the LS EOS have a larger anisotropic downflow,
favoredvalue ofheatingK ∼ 240for symmetricnuclearm
contraction of the PNS (bottom left) and because of weaker neutrino
andMeV
less vigoroushydrodynamic
nd2012/12/15
10 so that the downflow
is yieldratherclosewithinbespherical,
fulfills
both
constraints,of shock∼15 km
a 1
18for
/23
QuarkstoanUniverse
into
Computational
Science@inNaradoes
notexplosion
the simulated
time
asslightly
visibletheevolution ofitstheradiusaverageradius(bott

Systematics in supernova simulations
Our Goal: Produce Successful Explosion! of ~1051 erg
08, Nordhaus+ 10, Hanke+ 11,
Dimensionality of hydrodynamics Iwakami+
Takiwaki+ 12, Couch 12
General relativity

Liebendörfer+01, Müller+ 12, Kuroda+ 12

Neutrino physics
Scheme to solve Boltzmann equation

Ott+ 08, Shibata+ 11, Sumiyoshi & Yamada 12

Interaction rate

Langanke+ 03, Arcones+ 08, Lentz+ 12

Collective oscillation

Raffelt & Smirnov 07, Duan+ 10,
Dasgupta+ 10

Nuclear equation of state
Initial condition
progenitor structure (mixing, wind...)Lattimer & Swesty 91, H. Shen+ 98, G.
Shen+ 10, Furusawa+ 11, Hempel+ 12
Nomoto & Hashimoto 88, Woosley &Weaver 95, Woosley+ 02, Limongi & Chieffi
06, Woosley & Heger 07, Yoshida+ 12

rotation / magnetic ﬁeld
2012/12/15

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Progenitor dependence
YS, Kotake, Takiwaki, Liebendörfer, & Sato (2011)15

10

N13 (NH88)
N15 (NH88)
S15 (WW95)
H15 (WHW02)
H20 (WHW02)
H25 (WHW02)

1014

Density [g cm-3]

1013
1012
1011
1010
109
108
7

10

106

0

0.5

1
1.5
Enclosed Mass [M!]2

2.5

Density proﬁles 100 ms after the bounce
Almost same for M<0.8M⦿

Proﬁle for M>0.8M⦿ reﬂect the initial proﬁle2012/12/15

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Shock evolution in 2D simulation

Shock Radius [km]2D simulation using progenitors from Woosley & Heger (2007)
1000
WH07/s12
WH07/s15
WH07/s20
800
WH07/s30
WH07/s40
WH07/s55
600
WH07/s100
400
200
0

0

200

400

600

800

1000

1200

Time after Bounce [ms]Several progenitors lead to shock expansion
No monotonic trend is found
What determines the diﬀerence?
2012/12/15

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•

What makes difference?: M-Lν curve

Total Neutrino Luminosity [1052-1erg s ]

Burrows & Goshy 93
109explode

8
7
6

s12
s15
s20
s30
fail
s40
marginal s55
s100

5
4
3
2

0.1

0.2

0.3 0.4 0.5 0.6 0.7 0.8 0.9-1Mass accretion rate at 300 km [M! s ]1•

Low M and high Lν are achieved for several progenitors, which produce theexplosion
In order to unveil the relationship between the progenitor structure andtrajectories in this plane, more systematic study is necessary...
2012/12/15

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Summary
For supernova modeling, there are a lot of ingredients topin down the explosion mechanism
We performed multi-dimensional neutrino-radiationhydrodynamic simulations of core-collapse supernovae
The physical parts investigated are
Multi dimensionality [1D<2D<?3D] (YS+ 2010; Takiwaki, Kotake, YS 2012)
Eﬀect of neutrino oscillation [potentially strengthen the explosion] (YS+ 2011)
Impacts of nuclear equation of state [“softer” is better] (YS+ 2012)
Dependence of Progenitor structure [under investigation...] (YS+ 2013?)

There are still a lot of tasks to do to unveil the explosion
mechanism of core-collapse supernovae...
2012/12/15

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