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 IV @ Prerow, Sep. 27, 2014

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）

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

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

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.

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

Hadron-quark mixed EOS Nakazato et al., PRD 77 （2008a）, 103006 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

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）

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.

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.

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.

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

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

Our recent work and ADVERTISEMENT

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?

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

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

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

New EOS for neutron star matter Miyatsu, Yamamuro & Nakazato, ApJ 777 （2013）, 4 http://asphwww.ph.noda.tus.ac.jp/myn/ On-line EOS tables!!

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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）

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）

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

saturation パラメータ n0 = 0.155 fm－3 w0 = -16.1 MeV K0 = 274 MeV Esym = 32.7 MeV L = 75.8 MeV Li et al. arXiv:1211.1178 Esym (MeV)