1. Stellar core collapse with QCD phase transition
Ken’ichiro Nakazato
（Tokyo University of Science）
with K. Sumiyoshi（Numazu CT）and S. Yamada（Waseda U）,
EOS project: T. Miyatsu （Soongsil U）and S. Yamamuro（TUS）
Compact Stars in the QCD Phase Diagram Prerow, Sep. 27, 2014

2. Fates of massive stars
Stars with > 10Msolar make a gravitational col- lapse and, possibly, a supernova explosion.
Stars with > 25Msolar are thought to form a black hole （BH）.
Observations show
2 branches.
Hypernovae
（Rapid rotation）
Faint or Failed
Supernovae
（Weak rotation）
Normal SN
Nomoto+ （2006）

3. Failed supernova neutrinos
Failed supernova progenitor makes bounce once and recollapse to the black hole.
In this process, temperature and density of central region gets a few times 10 MeV and a few times r 0 (saturation density of nuclear matter), and a lot of neutrinos are emitted.
Massive star
Proto-neutron star
Black hole n n n n
Core Collapse n
Bounce
Mass accretion

4. Motivation
Collapsing core would be enough hot and dense to undergo QCD transition. T
heavy ion collision
Quark Phase
~150MeV
Early Universe
Mixed Phase
Hadronic Phase
Black Hole Formation
Stellar Collapse
Supernova
Compact stars r r0

5. Aims of this study
Nakazato, Sumiyoshi and Yamada（2008a, 2010b, 2013b）.
We compute the dynamics and n emission for the black hole formation of 40Msolar （failed supernova） and supernova explosion of 15Msolar non-rotating progenitor involving equation of state （EOS） with QCD transition.
General relativistic n radiation hydrodynamics in spherical symmetry （Sumiyoshi+ 2005）.
QCD transition: Shen EOS + MIT bag
We investigate the impacts on the dynamics and n signal.

6. 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 : ne ,ne , nm （ = nt ） ,nm （ =nt ）
Energy mesh : 14 zones （0.9 – 350 MeV）　　
Reactions : e- + p ↔ n + ne, e+ + n ↔ p +ne, n + N ↔ n + N,
n + e ↔ n + e, ne + A ↔ A’ + e-, n + A ↔ n + A,
e- + e+ ↔ n +n, g* ↔ n +n, N + N’ ↔ N + N’ + n +n

7. Hadron-quark mixed EOS
Nakazato et al., PRD 77 （2008a）,
Shen EOS （1998） 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.
mn = mu + 2md , mp = 2mu + md
PH = PQ
b equilibrium （n trapping） is assumed in Mixed and Quark phase.
md = ms , mp + me = mn + mn

8. Results for 40M☉ star Evolution of the central density.
QCD transition fastens the BH formation.
At the bounce, the case with B = 90 MeV/fm3 has high density while others are similar.
B = 90 MeV/fm3
B = 150 MeV/fm3
B = 250 MeV/fm3
Without Quarks （Shen）

9. Compositions （B = 250 MeV/fm3）
Nakazato et al., Astrophys. J. 721 （2010b）, 1284
27 ms before BH formation
0.07 ms before BH formation
at BH formation u 1 d 1
fraction n s
0.5
0.5 p
1015
1015
density （g/cm3） AH
1013
1013 10 20 10 20 10 20
radius （km）
radius （km）
radius （km）
Quark transition occurs at the very late phase and trigger the black hole formation.

10. Compositions （B = 90 MeV/fm3）
Nakazato et al., Astron. Astrophys. 558 （2013b）, A50
100 ms after bounce
at bounce
at BH formation u 1 1
fraction n s d
0.5
0.5 p
1015
1015
density （g/cm3） AH
1013
1013 10 20 10 20 10 20
radius （km）
radius （km）
radius （km）
Quarks appear already at bounce.
→ the central density gets higher.

11. Neutrino Signal ne
ne
nm /nm / nt /nt 2
250
250
luminosity（1053erg/s）
150
150 2 90 90
250 90
150 1 1 40 40 20 20
energy（MeV）
0.5 1
1.5
0.5 1
1.5
0.5 1
1.5
time （s）
time （s）
time （s）
Apart from end points, there is no difference even for the model with B = 90 MeV/fm3.
Neutrinos emitted from the outer region.

12. Fate of 15M☉ star
For the cases with B = 250,150 MeV/fm3 , QCD transition does not occur at least 1 sec after the bounce.
　→ no SN explosion
mass trajectory
Phase diagram: B = 250 MeV/fm3
103
Hadron
Mix
Quark
Yℓ = 0.3
radius （km）
100 10
0.2
0.4
0.6
0.8 1
time after bounce （s）
（Sumiyoshi et al. 2005）
Central r and T of 1 s after bounce

13. 2nd bounce with B = 90 MeV/fm3
Confirming 2nd bounce and shock formation occurs for 15M☉ model. （Sagert+ 2009, Fischer+ 2011）
s = 4.0kB
Yℓ = 0.35
Mix → Quark
200.5 ms
Hadron → Mix

14. Our recent work and ADVERTISEMENT

15. Japanese proverb quark phase? hadron phase?
木に竹を接ぐ（Ki ni také wo tsugu）
Joining bamboo to a tree: disharmony
quark phase?
tree
bamboo
hadron phase?

16. New EOS for neutron star matter
Miyatsu, Yamamuro & Nakazato, ApJ 777 （2013）, 4
Chiral quark-meson coupling （CQMC） model
involving the coupling of scalar and vector fields to the quarks within nucleons
Relativistic Hartree-Fock
PI: Dr. Tsuyoshi Miyatsu

17. New EOS for neutron star matter
Miyatsu, Yamamuro & Nakazato, ApJ 777 （2013）, 4
Crust EOS with Thomas-Fermi model
consistent with atomic mass data

18. New EOS for neutron star matter
Miyatsu, Yamamuro & Nakazato, ApJ 777 （2013）, 4
Mmax = 1.95Msolar with hyperons

19. New EOS for neutron star matter
Miyatsu, Yamamuro & Nakazato, ApJ 777 （2013）, 4
On-line EOS tables!!

20. Thank you for your attention

21. Chiral quark-meson coupling model
一様核物質の状態方程式
ベクトル中間子のテンソル結合により、ハイペロンの生成が抑制される。
→　コア部分の状態方程式。
： Chiral quark-meson coupling model から
　s dependence を取り込む（非線形効果）

22. Coupling constant Thomas-Fermi 計算により、原子核の質量・核子分布を計算し、N との結合定数を決める。
gsN, gwN, grN : mass data
gsY : Hyperon potential
gwY, grY, fwB, frB : ESC model を gwN, grN で scale
（Oyamatsu & Iida 2003）

23. Thomas-Fermi 計算 バルクエネルギーに一様核物質 EOS を用いる。 n 結合エネルギーを最大化 表面 エネルギー クーロン r
Chiral quark-meson coupling model
結合エネルギーを最大化 n
幅 dr の領域では一様 表面
エネルギー
中性子 陽子
クーロン
エネルギー r

24. saturation パラメータ
n0 = fm－3 w0 = MeV K0 = 274 MeV Esym = 32.7 MeV L = 75.8 MeV
Li et al.
arXiv:
Esym (MeV)