中村 航 (Nakamura, Ko)	National Astronomical Observatory of Japan				Collaborators: T. Takiwaki、K. Kotake（NAOJ）			 N. Nishimura（Univ. of Basel／GSI）			 	新領域-HPCI研究会 @ 合歓の郷

December 3-5, 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	  – 2-­‐D	  simula9ons	  for	  15.0	  Msun	  model	  – using	  ZEUS-­‐MP	  code	  incl.	  nuclear	  reac9on	  network	  • Summary	  Neutrino-driven SN explosion mechanism	
• Gravitational binding energyof the collapsing core（>~1053 erg） >>Typical SN explosion energy（~1051 erg）!"#$%&'()*+*,-./()&('**0"123'&)4• Neutrinos carry away mostof the energy, but ..
• A small fraction of emitted
neutrinos can interact with
V,&,8'-/3..WX<7)1')(1.:;.%+#.
the matter behind a shock,0)(5#0%'5#7;.1$<<)&%#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

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

ν+(QCDtransition)

1D
(GR)

255

0.44(350)

Boltzmann
2, (GR)

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

Acoustic
Mechanism

2DDim.
(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)
0.440.01
(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])

13 M!
11.2
M!
(WHW02[72])(WHW02[72])(NH88[71])ν-drivenν-drivenν+(QCDν-driventransition)

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
MGFLD
1,1, (N)(N)

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

NAOJ+
ν-driven
3D
∼100
0.01
IDSA
15 M!
MPA[81]ν-driven
2D
∼600
0.025
Boltzmann[78](2011)
(N)
(300)
1, (N)(WW95[73])(2009)(PN)(∼700)
2,O(v/c)
ALLDO
NOT reachSN explosion
energy12M! resultsOakRidge+
ν-driven at the
2D typical
∼300
0.3
”RBR”
MGFLD !
(WHW02[72])Princeton+
Acoustic
2D
MGFLD
51
(WHW02[72])[79](2009)(PN)(1000)
1,1,O(v/c)[77] (Eexp < 1 Bethe(N) = 10 ergs)	
(-)
(N)
13 M!
(WHW02[72])(NH88[71])20 M!
(WHW02[72])
15
25 M
M!!
(WW95[73])(WHW02[72])(WHW02[72])Princeton+
OakRidge+[77](2007)[79](2009)
NAOJ+
Princeton+[80](2010)[77](2007)

Acoustic
ν-driven

2D
2D(N)
(PN)

"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

OakRidge+[79](2009)

∼600
"1200

∼ 0.7(-)(1200)
∼ 0.3
(600)

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)Various nuclear reactionsin CCSNe	Energy feedback tohydrodynamic motion 	
spallations	proton #	neutron #	

is used&θ)Norman
007).
vr (r,(Stoneθ) = vr (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 protoYneutronstar.
Thebasicevolution
equations2.1. Basic equations
δvr = 0.01 × rnum × vr0 (r, θ) ,Figure 1 shows the radialescribing accretion flows of matter attracted by a protoYneutron
We investigate
the timeemitted
evolutionfromof collapsing
coreflows.
where vr0 (r,theθ) isunperturbed
the unperturbed
radialThevelo
ar and irradiatedby neutrinos
the protoYneutron
accreting materials by solving the following basic
tionmulti-mode
flow througha standingis the random
perturbationwit
ar can beand
writtenasequations:
Basic equations (Murphy & Burrows ‘08)	
Neutrino
irradiation	number−1manner< rnum <as1.in Ohnishi et al.
d# dρ + ρ∇ · v = 0,electronfraction is less thanLνe = L0 exp(-t(1)Lνe =ð1Þpb/td)	
þ#:=v
¼0;
2.3. of
Neutrino
irradiation
regionnegativeentropy
dt dt
neutrino heating/cooling （Janka ’01）
We searcha marginalneutrino
rates
is formed
for luminosity
the neutdv
dv
52-1%1s )1.544e20×10(L52νfore /10erg
ρ p=	
%−∇p− ρ∇Φ,(2) H =ð2Þcay time scale
neutrino-induced
explosio#¼ %:P#:!
% : = Q;ergs
s. Thevalues
o-22dtdt
× (r / 100km)(Tburningνe / 4MeV)
effectof nuclear
is expected
to be opoints
at the outerboundary! "τ	× (YneForthis+ Ye)
purpose,weadoptmesha verypoints
simpleattr∂e d eontheghostQ	 (3)= −pv
ρ(H+ Q),# + ∇ · [(e +¼p)v]
ð3Þ
%P:= v ·þ∇ΦQρ+E(H%-Q
C−:+C:v;Q)	
neutrino irradiation
andtransportation
so th6
identicaltothoseon
theadjac∂t dt #C = 1.399e20(T / 2MeV)
putational× cost
is considerablly reduced. Neτ
radialvelocity, which
is fixe× (Yn +evolvesYe)
e exponentiallynositywith time
as L
GMrdYe[erg/g/s]
andouter)/tboundaries.
Φ =¼−Q(4) ð4Þ
YeNprescription/ Γe	;,
L
exp(−(t−tν0bounced ), where Lν0 is init
rdt
order
to bounce,induce andnonsp
ity, tbounce is In
timeof coretd
Q : Nuclear reactionenergyradialvelocity
perturbation,
where ρ, v, p, and e areGM
theinfluid mass density, vetime
scale.
Landtaretreated as freeν0d←Network
calculation incl. He-Ni	;
ð5Þ!
¼%
locity, pressure, and total energy
density, respectively.
symmetric
accordingwhile 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
constant
GandthemassM
en2.4.
Hydrodynamicsrpectively, and G isδvthe
gravitational
The self-gravity （Limongi0.01
rand
× vr0constant.
(r,θ)
M=15& Chieffi‘06）	
wherev1D
is the unpertur
closed in ther =radiusr× as
equation(4).	 We
adoptMsun、Z=Zsuna simr (r)thethreehydrodynamics
code
matter inplethe
accretionflow
is ignored.
the artificialWe developed
considertypes of pertu
treatment(Janka2001)
instead of HeresolvingQaiscomplex
ZEUS-MP (Hayes et al. 2006) code which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 = 0-5000km& 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 reactions
to 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+08

1e+50

5e+07
00
0.2

0.3

0.4
0.5
Time [sec]

0.6

0.7

0.2

0.3

0.4
0.5
Time [sec]

0.6

0.7

Summary	• Neutrino-driven model is one of the possible solution for Corecollapse SN explosion mechanism.
• However, it’s less powerful to reproduce the typical SN
explosion energy of 1051 erg (even with the aid of hydro.
instabilities or acoustic oscillation).
• We have demonstrated the 2-D simulations taking
account of the effects of nuclear reactions on hydr.
– nuclear network including 13 alpha-nuclei from He to Ni.
• We found that:– explosion is available even if Lν is low and/or td is short,– explosion energy is enhanced by the energy released via
nuclear reactions,– and we could reproduce the typical SN explosion energy.