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