Stellar Core Collapseand Exotic Matter
Ken’ichiro Nakazato（Tokyo University of Science）

in collaboration with K. Sumiyoshi（Numazu CT）,
C. Ishizuka, H. Suzuki（Tokyo U of Sci.）, A. Ohnishi（Kyoto U）,
S. Furusawa and S. Yamada（Waseda U）
Quarks to Universe in Computational Science @ Nara, Dec. 16, 2012Outline
1. Introduction
Equation of state （EOS） of hot anddense matter and stellar core collapse

2. Hyperon appearance
Ishizuka+ 2008, Nakazato+ 2012

3. QCD transition
Nakazato+ 2008, 2010, in prep.

4. Conclusion

1. Introduction

Fates of massive stars• Stars with > 10Msolar make a gravitational collapse and, possibly, a supernova explosion.
• Stars with > 25Msolar are thought to form ablack hole （BH）.
• Observations show
2 branches.
– Hypernovae（Rapid rotation）– Faint or FailedSupernovae（Weak rotation）

NormalSN

Nomoto+ （2006）

Failed supernova neutrinos• Failed supernova progenitor makes bounce
once and recollapse to the black hole.
• In this process, temperature and density ofcentral region gets a few times 10 MeV anda few times ρ0 (saturation density of nuclearmatter), and a lot of neutrinos are emitted.
Proto-neutron star

Massive starνCoreCollapseBounceνννν
Mass accretion

Black holeMotivation• Collapsing core would be enough hot anddense to undergo exotic states, such as
hyperon appearance and QCD transition.

~150MeV

EarlyUniverseT0

heavy ion
collision

Quark Phase
Mixed Phase

HadronicPhase

Black HoleHyperons
Formation
espalloStellar C
Compact stars

ρ0ρ

Aims of this study• We compute the dynamics and ν emission
for the black hole formation of 40Msolar nonrotating progenitor （failed supernovae）
involving equation of state （EOS） withhyperon appearance and QCD transition.
– General relativistic ν radiation hydrodynamics inspherical symmetry （Sumiyoshi+ 2005）.
– Hyperon （Ishizuka+ 2008, Nakazato+ 2012）– QCD transition （Nakazato+ 2008, 2010, in prep.）• We investigate the impacts on the dynamicsand ν signal.

Hydrodynamics & Neutrinos
Yamada, Astrophys. J. 475 （1997）, 720
Yamada et al., Astron. Astrophys. 344 （1999）, 533
Sumiyoshi et al., Astrophys. J. 629 （2005）, 922

Spherical, Fully GR Hydrodynamics
metric：Misner-Sharp （1964）

mesh：255 non uniform zones+Neutrino Transport （Boltzmann eq.）
Species : νe ,⎯νe , νμ （ = ντ ） ,⎯νμ （ =⎯ντ ）Energy mesh : 14 zones （0.9 – 350 MeV）
Reactions : e- + p ↔ n + νe, e+ + n ↔ p +⎯νe, ν + N ↔ ν + N,
ν + e ↔ ν + e, νe + A ↔ A’ + e-, ν + A ↔ ν + A,e- + e+ ↔ ν +⎯ν, γ* ↔ ν +⎯ν, N + N’ ↔ N + N’ + ν +⎯νList of equations of state• Current status– Lattimer-Swesty (LS) EOS• Liquid drop model with Skyrme interactions （1991）– Shen EOS• Relativistic Mean Field theory （H. Shen et al. 1998）– Hyperon + pion EOS• Shen-EOS with hyperons （Ishizuka et al. 2008）– Quark + pion EOS• Shen-EOS with MIT Bag model （Nakazato et al. 2008a）• Notes– Kanzawa et al. （2009）, Hemple & Schaffner-Bielich （2010, NSE）,
G. Shen et al. （2011）, Furusawa et al. （2011, NSE）,
Steiner et al. （2012）, Togashi's talk in this symposium ...

2. Hyperon
appearanceHeperonic Equation of State
Ishizuka et al. J. Phys. G 35 （2008） 085201• Relativistic Mean Field Theory– extension of Shen EOS to the baryon octet• Potentials– UΛ = －30 MeV– UΣ = 30 MeV （repulsive）
or－30 MeV （attractive）– UΞ = －15 MeV• Data with thermal pions
is also prepared.

0Max. Mass of Neutron Stars• Maximum mass of neutron stars gets lower
due to softening by hyperons.
Ishizuka et al. （2008）• Difference between repulsive
2.17
and attractive
1.63 1.65
is ~5%.
1.55• Pions makes
subtle change.
without Hyperons
attractive
repulsive• Hyperonic EOS
repulsive + π
cannot accountfor 2Msolar.

Evolutions of Central density• Hyperons accelerate the collapse.
• Interval between
587 ms 682 ms
the bounce andBH formation
653 ms 1345 ms
gets shorter.
• The repulsive
case is ~15%
without Hyperons
attractive
longer than therepulsive
attractive case.
repulsive + π• Impact of pions
is tiny.

Key parameters （repulsive case）
tpb=0.68s
tpb=0.5s

tpb=0s• Roughly speaking, high ρ and low T at thecenter and low ρ and high T at r = 10 km.
→ Entropy is higher at r = 10 km due to shock heating.

Compositions （repulsive case）
tpb=0sn10010-11010-210-310-310-4

α10-210-4Λ-510010
radius [km]

n100

p-1

tpb=0.68s

tpb=0.5s

520x1020pn0

Λ

-110Λ

-210

α

Σ−

10-510-310

Ξ−
0-410
radius [km]20x1020Ξ−Σ−αΞ0105pΣ0-510010

520x1020

radius [km]• Hyperon fraction is tiny at the bounce.
• Hyperons appear for the late phase.
– Σ－ is suppressed for dense region （center）– Σ－ populates thermally for hot region （r = 10 km）

Compositions （tpb = tBH － 2 ms）
10

repulsive0

attractivenn

10-1

10-2ΛpΛ
Ξ−

Σ−
Σ0

Σ−
1010

Ξ−

-3

Ξ010-4Ξ0

Σ0-50p1020x10205radius [km]• More Σ－ for the center of the attractive case.
→ Collapse is more promoted due to EOS softening.

Compositions （tpb = 0.5 s）
repulsive
10

attractive

0nn

10-1

10-2pp

Λ

Λ
Σ−

Σ−

10-3
10-4

10-5

Σ0
Ξ−
Ξ−
010520x1020

radius [km]• For the attractive case, Σ－ appears earlier.
→ The influence is seen in the neutrino signal.

Neutrino Signal• Neutrinos aremainly emitted
till the blackhole formation.
• Difference due
to hyperons isseen earlier
for attractivecase.
→ Key for astrophysical probeνx

attractive

νewithoutHyperon
repulsive⎯νe3. QCD transition

Hadron-quark mixed EOS
Nakazato et al., PRD 77 （2008）, 103006• Shen EOS with pions for Hadronic phase• MIT Bag model （Chodos et al. 1974） for Quark phase– Bag constant: B = 90, 150 and 250 MeV/fm3• Gibbs conditions are satisfied in Mixed phase.
– μn = μu + 2μd ,– PH = PQz

μp = 2μu + μd

β equilibrium （ν trapping） is assumed in Mixedand Quark phase.
– μd = μs ,μp + μe = μn + μνEvolutions of Central density• QCD transition
also accelerates
the collapse.
• The case with
B = 90 MeV/fm3
has high density
already at thebounce.
• Others are
similar just until
BH formations.

B = 90 MeV/fm3
B = 150 MeV/fm3
B = 250 MeV/fm3
Without Quarks （Shen）

Compositions （B = 250 MeV/fm3）
Nakazato et al., Astrophys. J. 721 （2010）, 1284

density （g/cm3） fraction

27 ms before
BH formation
10.07 ms before
BH formation

dsn0.5at BH formation
u0.5

p001015

1015
AH

1013
01

10
radius （km）

20 010radius （km）

20 010radius （km）

1013
20

• Quark transition occurs at the very late phaseand trigger the black hole formation.

Compositions （B = 90 MeV/fm3）
Nakazato et al., in prep.
100 ms afterbounce

density （g/cm3） fraction

at bounce
1un0.5at BH formation

s1

d0.5

p0010151015
AH

1013
010radius （km）

20 0

10radius （km）

20 0

1013
10radius （km）

• Quarks appear already at bounce.
→ the central density gets higher.

20energy（MeV） luminosity（1053erg/s）

Neutrino Signal
νe
290

150

νμ /⎯νμ / ντ /⎯ντ

⎯νe
250
90

150

250

290

1150

250

10040

40

20

20

0000.5
1time （s）

1.5 0

1
0.5
time （s）

1.5 0

10.5
time （s）

1.5• Apart from end points, there is no difference
even for the model with B = 90 MeV/fm3.
• Neutrinos emitted from the outer region.

4. Conclusion

Summary• We have performed a series of black-holeforming core collapse simulations for nonrotating 40Msolar star with various EOS’s.
• We have found that EOS affects the emission
duration and luminosity of ν.
• For hyperons, impact is larger for attractive Σpotential case because Σ－ appears earlier
especially for the central region.
• For quarks, impact is larger for low bag const.
case because the transition is earlier and it isdrastic if the transition occurs at bounce.