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

2. 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.

3. 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)

4. 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)

5. Microscopic EoS H-F

6. Microscopic EoS Three Body Forces:

7. Microscopic EoS  Pressure  Free energy M.Baldo, L.S.Ferreira PRC 59 682 (1999)  Chemical potential & T c

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

9. 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)

10.  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).

11. Proto-neutron stars 1)Isothermal core (T core ) ----. 2)Isentropic envelope (S env ) ----. 3)Cold outer crust (BPS+FMT). LS220 NPA 535,331 (1997)

12. 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

13. 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)

14. 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.

15.  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.

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

17. 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 

18. 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.

19. Hybrid PNS