中村 航 (Nakamura, Ko)	National Astronomical Observatory of Japan				Collaborators: T. Takiwaki, T. Kuroda, K. Kotake（NAOJ）			 N. Nishimura（Univ. of Basel／GSI）			 	SN11 @ YITP

December 26-28, 2011

Outline	• Core-­‐collapse	  supernova	  explosion	  – collapse,	  bounce,	  and	  stalled	  • Neutrino-­‐driven	  explosion	  model	  – neutrino	  hea9ng	  (and	  cooling)	  – Standing	  Accre9on-­‐Shock	  Instability	  (SASI)	  • Shock	  revival	  and	  enhancement	  of	  expl.	  energy	  by	  nuclear	  reac9ons	  – 1-­‐D	  and	  2-­‐D	  simula9ons	  for	  11.2/15.0	  Msun	  model	  – using	  ZEUS-­‐MP	  code	  incl.	  nuclear	  reac9on	  network	  • 3-­‐D	  simula9ons	  (primi9ve)	  – MPI-­‐AMR	  code	  w.o.	  network	  • Summary	  Neutrino-driven SN explosion mechanism	
• Gravitational binding energyof the collapsing core（>~1053 erg） >>Typical SN explosion energy（~1051 erg）!"#$%&'()*+*,-./()&('**0"123'&)4• Neutrinos carry away mostof the energy, but ..
• A small fraction of emitted
neutrinos can interact withV,&,8'-/3..WX<7)1')(1.:;.%+#.
the matter behind a shock,0)(5#0%'5#7;.1$<<)&%#8.(#$%&'()*
depositenergy, and revive+#,%'(-./#0+,('1/the stalled shock wave.

• Hydrodynamic instabilities (c) H.T. Janka	
enhance the neutrino heating.
!

Y1.Z.FSS.9/!"#$%&'()*+#,%'(-./#0+,('1/23.."#$%&'()1.4&#5'5#6.1%,77#8.1+)09.:;.#(#&-;.8#<)1'%')(.....
.................................................. =>)7-,%#.?.@+'%#.ABCCD.@'71)(.ABEFD.G#%+#.?.@'71)(.ABEHIJ

0-100015100time [ms]s[kB/ barr [ks[kB/ bar

15200300

10gure 10. Same as Figure
2 but for our two-dimensional explosion simulation
10 of an 11.2 M! progenitor star. Note that the mass-shell spacing outside of the redshed line at an enclosed mass of -500
1.25 M! (marking the composition interface between the silicon layer and the oxygen-enriched Si shell) is reduced to steps of0125 M! instead of 50.025 M! .
5

Previous studies of SASI+ν -induced explosion	

600 in the polar directions
500
0 the panels
500
ane 200
later400than(seefor
2.0
2.5km]
r[km]& Janka= 250 ms and 275• msMarek
after bounce
in Figure(2009)12). Therefore
30 around thewedgelike
regiontime,
1500equator remains for somet=275 ms
t=303 ms
2.0
here silicon and sulfur are still present with higher abundances
1.525
1000
etween the shock25and the oxygen
layer, while the matter swept
1.5
p by the shock 20
consists mostlyof iron-group nuclei and α20500
articles.
Themass-shellof Figure
10, whichis constructed
1.0
n of Model W00
for several
moments nearplot
the beginningof the nonlinear
phase (the displayedtimes have a separationd),
and
at
t=
1s.
WithineachSASI
oscillation
cycle
thepostshock
entropies
varystrongly
andsteep,
unstableentropy
015om
the laterally averaged
two-dimensional
data at each radius,15
1.0
ostshock flow. Finally, the Rayleigh-Taylor
growth timescale becomes smaller than the oscillation period and the charures
are able to grow.by
In thesubsequent
the low-mode
oscillations
saturate andappears
the model doesto
notbe
develop anmisleading
thefact evolutionthat thispreshockmaterial-500
re available in the online version.)10
cated behind the10angle-averaged shock radius (at post-bounce
0.5
0.5-1000
mes 270 ms ! t ! 300 ms). We note that the penetration into
55e oxygen-rich infallingshells, beginning at t ∼ 250 ms p.b.,-1500
0.00.0oes not have any obvious supportive or strengthening effect on
0500
1000
1500 1000 500
0500 1000 1500
0100200300 L. 200300
Scheck et al.: Multidimensional superno
ekm]
outgoing shock.
r [km]
time [ms]In Figure 13, we provide information about the conditions
our 11.2 M! explosion model at times t = 230 ms, 250 ms, 275 ms, and 303 ms after core bounce. The figures contain
Figure 11. Left panel: mean shock radius (arithmetical average over all
Schecketgainal.layer(2008)nd neutrino energy•depositionin theof the 11.2 M!
lateral directions, dashed line) and maximum and minimum shock positions
odel. As in the 15 M! case, the mass in the gain layer increases
as functions of post-bounce time for our two-dimensional explosion simulation
hen the shock begins its 10outward expansion. At the sameof an 11.2 M! progenitor. Right panel: “explosion energy” of the 11.2 M! star,me, the infall (advection) timescale of matter between thedefined as the total energy (internal plus kinetic plus gravitational) of all mass
8in the gain layer with positive radial velocity, as a function of post-bounce time.
hock and the gain radius increases, but continues to be wellefined. Again, as in the 15 M! explosion model, this suggests
6
e presence of ongoing accretion of gas through the gain layer tothe absolute value of the total gas energy in the numerator ofe neutron star (which can also
beconcluded
fromthecontinued
4Equation (5) goes to zero.
ontraction of mass shells in this region in Figure 10). Shortly
3.4. Explosion Energy
2ter the (net) neutrino-heating
rate has reached a pronounced
eak of about 7.5 × 1051 erg
s−1 at t ≈ 70 ms, it makes
In both our 11.2 M! and 15 M! explosions, the energy of051−1
200 decline
250
300is a0150 drop
200 250300
rapid
to around3 × 010 50 erg100s 150. This
the matter in the gain layer with positive radial velocities
time [ms]time [ms]onsequence of the decay of the neutrino luminosities at the(“explosion energy”) reaches ∼2.5 × 1049 erg at the end of100
me when the mass infall rate
onto the shock and the neutron
the computed evolutions and rises with a very steep gradient
nofModels
W12F-c(leftcolumn)
and
W12F(rightcolumn) whenfor several thetimes. steep
Model W12F-c
quickly develops
ar decreases. The decrease80 occurs
negative(Figures 9 and 11). Therefore, reliable estimates of the final

explosion energy [1049 erg]

radius [103 km]

s[kB/ baryon]

r [km]

heating rate [1051 erg/ s]s[kB/ baryon]

010 M!
(WHW02[72])Basel[75](2009)

ν+(QCDtransition)

1D
(GR)

255

0.44
(350)

Boltzmann
2, (GR)

11M!
Progenitor(WW95[73])Princeton+
Group[74](2006)(Year)
MPA[51]
MPA[76](2006)(2006)

Acoustic
Mechanism

2D
Dim.
(N)
(Hydro)
1D
2D
(PN)
(PN)

"550
texp
(ms)
∼200
∼100

E∼0.1*
exp (B)(1000)@tpb (ms)0.1∼ 0.005(∼800)(∼220)

Princeton+
Princeton+[74](2006)[77](2007)
Basel[75]NAOJ+(2009)[78](2011)ν-driven
Acoustic

2D
2D
(N)
(N)
1D
3D
(GR)
(N)

!125
"1100255∼1000.1∼0.1*(1000)
0.44
0.01
(350)
(300)

νMGFLDtransport
1, O(v/c))
(N)
(Dim,
Boltzmann”RBR”
Boltz2,O(v/c)
mann, 2, O(v/c)

8.8
11.2MM! !
(NH88[71])(WHW02[72])10 M!
(WHW02[72])
11
12 M
M!!
(WW95[73])(WHW02[72])ν-drivenν-drivenν+(QCDν-driven
transition)

MGFLD
MGFLD
1,1, (N)(N)

Boltzmann
IDSA
2,1,(GR)(N)

Princeton+
Oak
Ridge+[74](2006)[79](2009)
MPA[76]
Princeton+(2006)[77](2007)

Acoustic
ν-driven

2D
2D
(N)
(PN)

"550
∼300

∼0.1*0.3(1000)(1000)

ν-driven
Acoustic

∼100
"1100

∼∼0.3*
0.005(∼220)(1400)

Princeton+
NAOJ+
[77]
(2007)[80](2010)

Acoustic
ν-driven

2D
2D(PN)
(N)
2D
2D
(N)
(N)

"1100
∼200

∼0.1*
0.1
(1000)
(500)

MGFLD
IDSA
1,1, (N)(N)

15 M!
(WW95[73])12M!
(WHW02[72])(WHW02[72])NAOJ+
MPA[81][78](2011)(2009)
Oak
Ridge+
Princeton+[79](2009)[77]

ν-drivenν-driven

3D
2D(N)
(PN)
2D
2D(PN)
(N)

∼100
∼600

0.01
0.025
(300)
(∼700)
0.3(1000)
(-)

13 M!
(WHW02[72])Princeton+
OakRidge+[77](2007)[79](2009)
NAOJ+
Princeton+[80](2010)[77](2007)

Acoustic
ν-driven

2D
2D(N)
(PN)

IDSA
Boltzmann
1, (N)
2,O(v/c)
”RBR”
MGFLD
MGFLD
1,1,O(v/c)
(N)

"1100
∼300

∼0.3*
∼ 0.3(1400)(600)

ν-driven
Acoustic

∼200
"1200

MPA[81]
Princeton+(2009)[77](2007)
Princeton+
OakRidge+[77][79](2009)ν-driven
Acoustic

2D
2D(N)
(N)
2D
2D(PN)(N)

0.1∼0.7*(500)(1400)
0.025(∼700)(-)

Acoustic
ν-driven

2D
2D(N)
(PN)

∼300

ν-driven

2D(PN)∼300

13 M!
11.2M!
(WHW02[72])(WHW02[72])(NH88[71])(NH88[71])20 M!
(WHW02[72])
15
25 M
M!!
(WW95[73])(WHW02[72])(WHW02[72])OakRidge+[79](2009)ν-driven
Acoustic

∼300
-

∼600
"1200∼ 0.7(-)(1200)
∼ 0.3
(600)

MGFLD
”RBR”
MGFLD
1,(N)
1, O(v/c)”RBR”
BoltzMGFLD
mann,1,2,(N)O(v/c)

MGFLD
”RBR”
MGFLD
1,(N)
1,O(v/c)
IDSA
MGFLD
1,1, (N)(N)
Boltzmann
MGFLD
2,O(v/c)
1, (N)
MGFLD
”RBR”
MGFLD
1,(N)
1, O(v/c)”RBR” MGFLD
1,O(v/c)

is used&θ)Norman
007).
vr (r,(Stoneθ) = vr0 (r,+ δvr , 1
tificial viscosity to axisymm
We consider spherical2. coordinates(r; !; ") with the origin at
NUMERICAL SCHEME
andthe previous results (Ohnishe center of the protoYneutron star. The basic evolution equations
02.1. Basic equations
δv=0.01×
rnum×v(r, θ) ,rFigure 1 shows therradialescribing accretion flows of matter attracted by a protoYneutron
We investigate
the timeemitted
evolutionfromof collapsing
coreflows.
ar and irradiatedby neutrinos
the protoYneutron
where vr0 (r,theθ) isunperturbed
the unperturbed
radialThevelo
andaccreting
materials
bysolving
thefollowing
basic
tionmulti-mode
flow througha standingis the random
perturbationwit
ar can be written as
Basic equations (Murphy & Burrows ‘08)	
Neutrino irradiation	equations:
number −1manner< rnum <as1.in Ohnishi et al.
d# dρ + ρ∇ · v = 0,electronfraction is less thanLνe = L0 exp(-tpb/td)	
(1)Lνe =ð1Þ
þ
#:=v
¼0;
2.3. of
Neutrino
irradiation
regionnegative
entropydt dt
neutrino heating/cooling （Janka ’01）
rates
is formed
for luminosity
the neutWe searcha marginalneutrinodv
dv
52-1%1s )1.544e20×10(L52νfore /10erg
ρ p=	
%−∇p− ρ∇Φ,(2) H =ð2Þ
#
¼ %:P
#:!
% : = Q;
cay time scale
neutrino-induced
explosioergss. Thevalues
o-22dtdt
× (r / 100km)(Tburningνe / 4MeV)
effectof nuclear
is expected
to be opoints
at the outerboundary! "τ	× (YneFor
this+ Ye)purpose,adoptmesha verypoints
simpleattr∂e d eon the weghost# + ∇ · [(e +¼p)v]
ð3Þ
%P:= v ·þ∇ΦQρ+E(H%Q	 (3)-QC−:+C:v;Q)	
= −pv
ρ(H+ Q),
neutrino irradiation
andtransportation
so th6
identicaltothoseontheadjac∂t dt #C = 1.399e20 × (T / 2MeV)
putational radial
cost is considerablly reduced. Ne× (Yn + Ye) e-τ velocity, which is fixe
nosity evolves exponentially with time as LdYe
GMr
[erg/g/s]
andouter)/tboundaries.
YeNprescription/ Γe	;,
Φ =¼−Q(4) ð4Þ
Lexp(−(t−tν0bounce d ), where Lν0 is init
rdt
order
to bounce,induce andnonsp
Q : Nuclear
reactionenergyity, tbounce
is In
timeof coretdvelocity
perturbation,
where ρ, v, p, and e areGM
theinfluid mass density, ve- ←Networkcalculation
time scale.radialLν0 andtdincl.
are He-Ni	treated as free;
ð5Þ!
¼%
symmetric
accordinglocity, pressure, and total energy
density, respectively.
while tbounce
should be flow
determinedby numtr

Numerical scheme	

d/dt ≡ ∂/∂t + v · ∇ denotes the Lagrangian derivative.
lation for each model. We assume Tν = 4 M
assumethat theself-gravityof accreting
gas is internal
negliflavor and Lν0 = 0 for t < tbounce. !; ") ¼SASI	
Progenitor
model	 enhere #, v,Wee,P, Ye , and! arethe density,velocity,vr (r;gible andthe gravitational
potentialΦ is describedwithgy, pressure,electronfraction,andgravitational
potential,
re0
vr(r,θ) = vr (r,θ) + δvr	

derivedfrom
evolutionary
calculation
for a star with code
Newton’s
gravitational
constantG
andthemassM
en2.4.
Hydrodynamicsr
1D
pectively, and G isδvthe
gravitational
The self-gravity= 0.01× rand × vr0constant.
(r,θ)	 M=11.2-15.0
Msun、Z=Zsun	
wherevrr (r) is the unpertur
closed in the radius r as equation (4). We adopt a simthethreehydrodynamics
code
matter in the accretion flow is ignored. Here Q is the artificialWe developed
considertypes of pertu
ple treatment (Janka 2001) instead of solving a complex
ZEUS-MP (Hayes et al. 2006) code which1-D simulation	
7e+07

Li0=2.2, td=5.0
Li0=2.0, td=5.0
Li0=2.2, td=2.0
w.o. burning

Shock radius [cm]

6e+07
5e+07

速度分布v(r)の時間発展

4e+07
3e+07

衝撃波半径
Rsh(t)（核反応あり/なし）	

2e+07
1e+07
0
0.2

8e+50

0.60.81[sec]
Eexp (tTime
d=5.0)Enuc (td=5.0)
Eexp (td=5.0, w.o. burning)
Eexp (td=2.0)
Enuc (td=2.0)

7e+50
6e+50

Energy [erg]

0.4

5e+50
4e+50
3e+50
2e+50
1e+50
00

0.2

0.4

Time [sec]0.6

7e+07

Li0=2.2, td=5.0
Li0=2.0, td=5.0
Li0=2.2, td=2.0
w.o. burning

5e+07

Mass fractions

4e+07
3e+07

衝撃波半径
Rsh(t)（核反応あり/なし）	

2e+07
1e+07
0
0.2

8e+50

0.4

0.6

0.8

1(tTime=5.0) [sec]Eexp dEnuc (td=5.0)
Eexp (td=5.0, w.o. burning)
Eexp (td=2.0)
Enuc (td=2.0)

7e+50
6e+50

1.0

with burning
w.o. burning

0.0-1.0-2.0

300 ms

400 ms

O0.6OSi
0.4
0.2Fe+Ni

SiFe+NiSMg

NeAr+Ca

2.0
Velocity [109cm/s]

Shock radius [cm]

6e+07

1.0
0.0

Snapshots:-1.0

LC15 model-2.0

500 ms

550 ms

Ln_0 = 2.2[1052 Oerg/s]
Fe+Ni
t_d = 2.0[s]Si（左図の点破線）	

5e+50
4e+50

Mass fractions

Energy [erg]Velocity [109cm/s]

2.0

3e+50
2e+50
1e+50000.2

0.4Time [sec]

0.6

O

0.6
0.4

Fe+Ni

Si

0.2

1.4

1.5
1.6
Mr [Msun]

1.7

1.4

1.5
1.6
Mr [Msun]

1.7

Snap shots of entropy distributions from our simulations with (left) and without (right)
nuclear network calculation.
Example) Lνe = L0 exp(-tpb/td) ← L0 = 2.4×1052 erg/s, td = 1.1 s	
Time after core bounce:	
100 ms	

600 km	

200 ms	2000 km	

300 ms	3500 km	

-15Msun model-２-dimensional
axi-symmetriccoordinates

1000km(t<170ms)	

-300(r)*128(θ)
covering
r = 0-5000 km
θ = 0-π-ZEUS-MP codeequipped withnucl. network	
2500km(t>170ms)	

Entropy	

X_silicon	With/w.o. nucl. burning	• Si & O burning• “nuclear reaction-aided”
supernova explosion• corresponding parameterregion is narrow, but ..	

100ms(600km)	

200ms(2000km)	

52

Initial L! [10 erg/s]

4

LC15 model
3.5!"#$%&'%(3300ms!"#$%&'%()*'+,+)-.))(/0$,*1)-/1('(2)(3500km)	

2.5
2!"#$%&'"()"*
00.5

1

1.5

2

Decay time [sec]2.53Contribution of nuclear reactionsto explosion energy	
• Explosion energy– red: explosion energy = Σ(Ekin + Eint + Egrv)i for vri & Etoti > 0– green: net burning energy– blue-dotted: explosion energy in the case without nuclear burning	
Ln_0 = 2.1e52 [erg/s]
t_d = 2.0 [s]	4.5e+08

5e+50
Energy [erg]3.5e+08
3e+08
2.5e+08

Eexp
EnucEexp (no burning)

6e+50

averagemaximum
average (no burning)

4e+08
Shock radius [cm]7e+50

Shock radius	

2e+08

4e+50

Explosion energy	

3e+50
2e+50

1.5e+08
1e+081e+505e+07
000.2

0.3

0.40.5Time [sec]

0.6

0.7

0.2

0.3

0.40.5Time [sec]0.60.7

3-D simulation (primitive)	
- WW95 モデル(15 Msun)- 3-dimensional
Cartesiancoordinates- Ln_0 = 1.5e52[erg/s]- t_d = ∞	
- 核反応なし

200 km	Summary	• 重力崩壊型超新星においてニュートリノ爆発モデルは有力であるが、先行研究
では典型的な爆発エネルギー(1051erg)を再現できていない• ある種の流体不安定性や空間多次元効果がニュートリノ加熱の効率を上げるという報告はあるが、現時点では不十分• 核反応ネッワークを組み込んだ流体計算によって、反応エネルギーの流体運動への影響およびモデル/空間次元/ニュートリノ特性への依存性を調べた– 11.2 Msun (WHW02), & 15.0 Msun (WW95, WHW02, LC06) models– nuclear network including 13 alpha-nuclei from He to Ni.
– simple treatment of neutrino heating• 1,2次元計算の結果– 爆発しやすさ: WHW-11 > WW-15 > LC-15 > WHW-15、２次元>１次元– “核反応を入れることによって”爆発する ν パラメータ領域– すべてのモデルで核反応による爆発エネルギーの増加(1次元>2次元)• ３次元計算に向けて– AMR-MPI コード（12/27黒田さん）を用いて計算中– 核反応による加熱効率は上がる？