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Hybrid proto-neutron stars within a static approach. O. E. Nicotra Dipartimento di Fisica e Astronomia Università di Catania and INFN
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Outline Introduction to proto-neutron stars (PNS). Microscopic nuclear Equation of State (EoS). A static model for PNS. Hadron-Quark phase transition. Structure and Stability. Conclusions.
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Proto-neutron stars t 50 sec (after bounce) T ~ 30 50 MeV S ~ 1 10 trapping (1 st stage) free (2 nd stage) Pons et al. ApJ, 513, 780 (1999) Prakash et al. Phys.Rep. 280,1 (1997)
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Microscopic EoS (main ingredients) Finite Temperature BHF (Brueckner-Hartree-Fock) 1.Two Body Correlations (Goldstone Matrix - Ladder summation) 2.Bloch-De Dominicis expansion of the grand-canonical potential. Realistic N-N interaction (Av18 and Bonn ) 1.Realistic: parameters adjusted to reproduce N-N scattering phase shifts. 2.Bonn: One Boson Exchange N-N potential Three Body Forces (TBF) 1.Urbana interaction. 2.Saturation improved Thermodynamic quantities 1.Pressure, Chemical potential, critical temperature… 2.Hugenholtz-Van Hove theorem. 3.Experimental constraint from HIC (limiting temperature)
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Microscopic EoS H-F
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Microscopic EoS Three Body Forces:
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Microscopic EoS Pressure Free energy M.Baldo, L.S.Ferreira PRC 59 682 (1999) Chemical potential & T c
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Limiting Temperature Nuclear matter Finite nuclei (S.Levit,P.Bonche, Nucl.Phys.A437,426 (1985) Liquid drop Corr.’s Coexistence equations
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Limiting Temperature Natowitz et al. PRC 65 034618 (2002) M.Baldo, L.S. Ferreira, O.E. Nicotra, PRC 69 034321 (2004) & NPA 749 118c (2005) S.Fritsch, N.Kaiser, W.Weise, PLB 545 73 (2002) B. Ter Haar & R. Malfliet Phys.Rep. 149, 207 (1987) H.Huber, F.Weber, M.K.Weigel PRC 57,3484,(1998)
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Stellar matter (n,p,e -, ’s) free trapped O.E.Nicotra et al. A&A 451,231(2006) 1.Overall strong T-dependence. 2.Increasing proton & leptons fractions (nucleonic). 3.Deleptonization and hyperons < 30%. 1. Overall weak T-dependence. 2. Proton rich matter ~30% (nucleonic case). 3. delayed (hyperonic case).
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Proto-neutron stars 1)Isothermal core (T core ) ----. 2)Isentropic envelope (S env ) ----. 3)Cold outer crust (BPS+FMT). LS220 NPA 535,331 (1997)
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Proto-neutron stars 1st stage: Isothermal and -rich core + Isentropic and -free envelope + Cold and -free crust = PNS in its early stage (t 1 5 sec) 2nd stage: Isothermal and -free core + Cold and -free crust = PNS in its final stage (t 40 50 sec) S env from matching conditions at ~ 0.01 fm -3, T core as a free parameter. O.E.Nicotra, nucl-th/0607055
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Structure 1. trapping reduce by ~0.1 M ๏ the maximum mass (nucleonic case). 2.Opposite behavior but with a maximum mass below 1.44 M ๏ quarks inclusion (hyperonic case). 1 ° stage. 2 ° stage. O.E.Nicotra et al. A&A 451,231(2006)
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Quark phase G.F.Burgio et al. PRC 66 025802 (2002) Hadrons Quarks Phenomenological transition energy density. B fixed from phenomenological values of the transition energy density.
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Stellar matter (u,d,s,e - ’s free 1.Overall weak T-dependence. 2.e - and anti-quarks from thermal excitation. 3.Quark u @ 33%. B 4.Quarks d decrease in favour of quarks s as B increases. trapped 1. Overall weak T-dependence. 2. Quark u @ 42% and e - @ 25%. 3. Quarks d and s lower Quark phase Lepton number per baryon conserved.
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free trapped Maxwell construction: QQ HH
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Hybrid PNS O.E.Nicotra et al.astro-ph/0608021 M max ~ 1.5 ÷ 1.56 M sun T core < 50 MeV M max weakly affected by trapped M max ~ 1.48 ÷ 1.55 M sun T core ~ 50 MeV M max affected by
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Conclusions 1.A temperature profile was assumed with T core as free parameter. 2.Within this model metastability does not occur for hybrid proto-neutron stars. 3.In conclusion, this work, in analogy with what has been done in the zero temperature case, suggests the possibility to study hot and compact objects with a microscopic finite temperature EoS properly checked by constraints coming from heavy ion collisions experiments.
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Hybrid PNS
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