1. Equation of State for Hadron-Quark Mixed Phase and Stellar Collapse
Ken’ichiro Nakazato （Waseda U）
Kohsuke Sumiyoshi （Numazu CT）
Shoichi Yamada （Waseda U）
Ref: Nakazato et al. （2007b） submitted to PRD.
2007, 12, 5, Hokkaido U

2. 1. Introduction 2. Setups 3. Results 4. Conclusion
Outline
1. Introduction 2. Setups 3. Results 4. Conclusion

3. 1. Introduction

4. Stellar Collapse & BH Formation
Results of our previous studies
Enough high r / T for QCD transition? 12
375M☉ （Pop III）
Nakazato et al. （2006）
100M☉ （Pop III）
Nakazato et al. （2007a） 11
Temperture　log（K） 10 9
40M☉
Sumiyoshi et al. （2006） Sumiyoshi et al. （2007） 8
Hayashi （1968） 4 6 8 10 12 14 16
Density　log（g / cm3）

5. Previous Studies Gentile et al. （1993） Drago & Tambini （1999）
Simulation of Core Collapse Supernova.
Following only 1 ms after bounce.
EOS of T = 0 and without neutrinos.
Mixed phase by Maxwell Construction.
Drago & Tambini （1999）
EOS with finite T and including neutrinos.
Mixed phase by Gibbs condition.
Dynamical simulations were not done.

6. Our Studies
Simulations of the stellar collapse and neutrino emission using EOS with finite T.
→ Can we probe hot / dense matter detecting neutrino signals? T
Quark Phase
accelerator
~150MeV
Early Universe
Mixed Phase
Hadronic Phase
Black Hole Formation
Stellar Collapse
Compact stars m

7. 2. Setups

8. Hydrodynamics & Neutrinos
Spherical, Fully GR Hydrodynamics （Yamada 1997）
metric：Misner-Sharp （1964） 　mesh：127 non uniform zones +
Neutrino Transport （Boltzmann eq.）
（Yamada et al ; Sumiyoshi et al. 2005）
Species : ne ,ne , nm （ = nt ） ,nm （ =nt ）
Energy mesh : 12 zones （0.1 – 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
for Hadronic phase

9. Equation of States EOS by Shen et al. （1998） for Hadronic phase
Based on the Relativistic Mean Field Theory
Adding thermal pion to original EOS table
MIT Bag model （Chodos et al. 1974） for Quark phase
Bag constant: B = 250 MeV/fm3
Gibbs conditions are satisfied in Mixed phase
mn = mu + 2md ・ mp = 2mu + md
PH = PQ
Neutrino Trapping in Mixed and Quark phase

10. 3. Results

11. Phase diagram of our EOS
Yℓ = 0.1
Quark
Mix
Quark
Hadron
Hadron
Mix
Quark
Quark
Mix
Hadron
Hadron
Mix
rtrans. and mB trans. are lower for high T
→ Consistent to well known properties!!

12. Maximum mass of Hybrid Star
1.8M☉ for our EOS with p and Quark
2.2M☉ for Shen EOS
Consistent to recent obser-vations of compact stars.
Shen EOS 2.2M☉
(original hadron)
only p, 2.0M☉
p + Quark
1.8M☉
only Quark
1.8M☉

13. Implication for Stellar Collapse
100M☉ Pop III
　（ test as 1st step! ）
EOS gets softer by p & Quark.
→ Duration of the neutrino emis-sion gets shorter.
→ Observational probe of EOS by neutrinos.
p + quark
335 ms
only p
only quark
350 ms
Shen EOS
（original hadron）
400 ms
n emission

14. Black Hole (Apparent Horizon)
Composition Profiles
neutron
proton
pion
u quark
d quark
s quark
In our model, quarks appear before black hole formation.
Black Hole (Apparent Horizon)

15. 4. Conclusion

16. Conclusion
We have constructed EOS for Hadron-Quark mixed matter with finite T.
Thermal pion is also included.
Maximum mass of the hybrid star is consistent with resent observations.
Pions and Quarks shorten the duration of neutrino emission because EOS gets softer.
Possibility to probe hot / dense matter.