Hybrid proto-neutron stars within a static approach. O. E. Nicotra Dipartimento di Fisica e Astronomia Università di Catania and INFN

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.

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)

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)

Microscopic EoS H-F

Microscopic EoS Three Body Forces:

Microscopic EoS  Pressure  Free energy M.Baldo, L.S.Ferreira PRC (1999)  Chemical potential & T c

Limiting Temperature  Nuclear matter Finite nuclei (S.Levit,P.Bonche, Nucl.Phys.A437,426 (1985) Liquid drop Corr.’s Coexistence equations

Limiting Temperature Natowitz et al. PRC (2002) M.Baldo, L.S. Ferreira, O.E. Nicotra, PRC (2004) & NPA c (2005) S.Fritsch, N.Kaiser, W.Weise, PLB (2002) B. Ter Haar & R. Malfliet Phys.Rep. 149, 207 (1987) H.Huber, F.Weber, M.K.Weigel PRC 57,3484,(1998)

 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).

Proto-neutron stars 1)Isothermal core (T core ) )Isentropic envelope (S env ) )Cold outer crust (BPS+FMT). LS220 NPA 535,331 (1997)

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/

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)

Quark phase G.F.Burgio et al. PRC (2002) Hadrons Quarks Phenomenological transition energy density. B fixed from phenomenological values of the transition energy density.

 Stellar matter (u,d,s,e -  ’s   free 1.Overall weak T-dependence. 2.e - and anti-quarks from thermal excitation. 3.Quark 33%. B 4.Quarks d decrease in favour of quarks s as  B increases.  trapped 1. Overall weak T-dependence. 2. Quark 42% and e 25%. 3. Quarks d and s lower  Quark phase Lepton number per baryon conserved.

 free  trapped Maxwell construction: QQ HH

Hybrid PNS O.E.Nicotra et al.astro-ph/ 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 

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.

Hybrid PNS