Equation of State for Hadron-Quark Mixed Phase and Stellar Collapse

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, OMEG07 @ Hokkaido U

2. 1. Introduction2. Setups3. Results4. Conclusion Outline

3. 1. Introduction

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

5. Previous Studies • Gentile et al. （1993） • 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 / densematter detecting neutrino signals? T Quark Phase accelerator Early Universe ~150MeV Mixed Phase Hadronic Phase Black Hole Formation Stellar Collapse Compact stars m 0

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. 1999 ; 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 • rtrans. and mB trans. are lower for high T → Consistent to well known properties!! Mix Quark Hadron Hadron Mix Quark Quark Mix Hadron Hadron Mix

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

13. Implication for Stellar Collapse p + quark 335 ms • 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. only p only quark 350 ms Shen EOS （original hadron） 400 ms n emission

14. 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.