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This research paper discusses the equation of state for hadron-quark mixed matter, including results on stellar collapse and black hole formation. It explores the impact of quarks and pions on neutron stars and the possibility of probing hot and dense matter. Maximum mass calculations and composition profiles are also examined, with implications for observational probes using neutrinos.
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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.