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

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

1. Introduction

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）

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.

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

2. Setups

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

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

3. Results

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!!

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☉

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

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)

4. Conclusion

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.