1. Francesca Gulminelli - LPC Caen, France Collaboration: Adriana Raduta IFIN Bucharest Micaela Oertel LUTH Meudon France Panagiota Papakonstantinou IPNO France Jerôme Margueron IPNO France Phase diagram of stellar matter and its impact on astrophysics

2. 2/27 A y p       Supernova remnant and neutron star in Puppis A (ROSAT x-ray) y p     core crust y p       Dense matter is abundantly produced in a core-collapse supernova event leading to a neutron star (or black hole) Time A.Fantina, PhD thesis, 2011

3. 3/27 Phases of dense matter in neutron stars Baryon density G.Watanabe et al, PRL 2009 pasta QGP?

4. 4/27 20200 MeV 15? Density   Temperature QGP Gas Liquid Hadronic matter Phases of dense matter in heavy-ion collisions LHC RHIC FAIR GANIL

5. 5/27 20200 MeV 15? Density   Temperature QGP Gas Liquid Hadronic matter Phases of dense matter in heavy-ion collisions

6. This talk: Stellar matter versus nuclear matter phase diagram  The sub-saturation regime : Coulomb effects and dishomogeneous phases  The super-saturation regime: Hyperonic matter & strangeness phase transition T B B pasta QGP ? 

7. This talk: Stellar matter versus nuclear matter phase diagram  The sub-saturation regime : Coulomb effects and dishomogeneous phases  The super-saturation regime: Hyperonic matter & strangeness phase transition T B B pasta QGP ?  G Lcoex

8. Coulomb effects  Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background T. Maruyama et al. PRC 72, 015802 (2005) Densité / fm -3 0.08 0.06 0.04 0.02 0  0.04 fm -3  0.08 fm -3  0.05 fm -3  = 0.02 fm -3 p n e 0 5 10 Rayon / fm 0 50 5 10 Density   Temperature

9.  Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background  The low density phase is a Wigner cristal Density   Temperature Coulomb effects

10.  Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background  The low density phase is a Wigner cristal  Phase coexistence i.e. macroscopic density dishomogeneities, would imply a macroscopic charge => a diverging energy density Coulomb effects Density   Temperature

11.  Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background  The low density phase is a Wigner cristal  Phase coexistence i.e. macroscopic density dishomogeneities, would imply a macroscopic charge =>a diverging energy density  Dishomogeneities occur on a microscopic scale only: a continuous transition through a cluster phase (inner crust) Coulomb effects Density   Temperature

12.  Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background  The low density phase is a Wigner cristal  Phase coexistence i.e. macroscopic density dishomogeneities, would imply a macroscopic charge =>a diverging energy density  Dishomogeneities occur on a microscopic scale only: a continuous transition through a cluster phase (inner crust)  Illustration via a phenomenological model Coulomb effects Density   Temperature

13. The extended NSE model  Mixture of nucleons, clusters of all sizes, photons, electrons, positrons, neutrinos  Nucleons treated in the Skyrme-HF approximation with realistic effective interactions  Nuclei form a statistical ensemble of excited clusters interacting via Coulomb and excluded volume  Thermodynamic consistency between the different components A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012)

14. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012)  No plateau in the EoS     1.6MeV  1.6 MeV

15. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012)  No plateau in the EoS  Thermodynamics very different from a first order phase transition  Inaccessible in the standard grand- canonical NSE  Large distribution of cluster size  S. R. Souza, et al,, Astrophys. J. 707, 1495 (2009), M. Hempel and J. Schaffner-Bielich, Nucl. Phys. A 837, 210 (2010) S. I. Blinnikov, et al, Astronomy & Astrophysics 535, A37 (2011). …………(among others)………    1.6MeV  1.6 MeV

16. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012)  No plateau in the EoS  Thermodynamics very different from a first order phase transition  Inaccessible in the standard grand- canonical NSE  Large distribution of cluster size

17. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012)  No plateau in the EoS  Thermodynamics very different from a first order phase transition  Inaccessible in the standard grand- canonical NSE  Large distribution of cluster size  Important for e-capture and -dynamics

18. Towards a quantitative EoS  The nuclear cluster energy functional is modified by the external nucleon gas  Does excluded volume account for this effect ? M.Hempel et al PRC 84, 055804 (2011)  In medium effects calculated from a HF calculation in the WS cell  Application to the NSE model in progress P.Papakonstantinou, et al., in preparation

19. This talk: Stellar matter versus nuclear matter phase diagram  The sub-saturation regime : Coulomb effects and dishomogeneous phases  The super-saturation regime: Hyperonic matter & strangeness phase transition T B B pasta QGP ? 

20. Hyperons in dense stellar matter  Hypernuclei:  potential attractive at low density  Hyperon d.o.f tend to soften the EoS  Still compatible with 2Mo NS if the hyperon-hyperon coupling is strongly repulsive at high density M.Oertel et al, http://arxiv.org/abs/1202.2679 I.Vidana et al, Europhys.Lett.94:11002,2011

21. Strangeness phase transition  Attractive and interaction at low  B , repulsive at high B  e() has a minimum =>dilute/dense PT ?  e  has a minimum =>non-strange/strange PT ?  Illustration with a simple model: n-equilibrium in the HF approximation; energy functional from Balberg & Gal S.Balberg A.Gal NPA 625(1997)435 YY  n =0.45 fm -3  n =0.3 fm -3  n =0.15 fm -3 rr  S (fm -3 )

22. n-phase diagram  different first and second order phase transitions  I: ’s in neutron matter  II: n- liquid-gas  III: neutrons in  matter F.G.,A.Raduta and M.Oertel, in preparation

23. n-phase diagram  different first and second order phase transitions  I: ’s in neutron matter  II: n- liquid-gas  III: neutrons in  matter F.G.,A.Raduta and M.Oertel, in preparation  S =0

24. n-phase diagram  different first and second order phase transitions  I: ’s in neutron matter  II: n- liquid-gas  III: neutrons in  matter => Coexisting hyperon-rich & hyperon-poor regions along the physical trajectory  S =0 F.G.,A.Raduta and M.Oertel, in preparation  S =0

25. n-phase diagram  different first and second order phase transitions  I: ’s in neutron matter  II: n- liquid-gas  III: neutrons in  matter => Coexisting hyperon-rich & hyperon-poor regions along the physical trajectory  S =0 => Explores a critical point at T>0: opacity? F.G.,A.Raduta and M.Oertel, in preparation  S =0 critical point J.Margueron et al, PRC70 (2004) 028801  S =0

26. Conclusion: Stellar matter phase diagram  The sub-saturation regime : Coulomb effects and phase transition quenching A specific thermodynamics Wide distribution of clusters Important for e-capture and -interaction  The super-saturation regime: A possible strangeness phase transition Consequences on EoS, NS mass, - transport ? Constraints on Y-N and Y-Y interaction needed

28. 28/27 Frustration and dishomogeneous phases  Frustration is a generic phenomenon in physics  It occurs whenever matter is subject to opposite interactions (here: nuclear & coulomb) on comparable length scales  Global variations of the order parameter (here: density) are replaced by local variations =>Phase coexistence is quenched =>dishomogeneous phases arise =>Ensemble equivalence is violated q T T cr dishomogeneous phase P.Viot G.Tarjus PRE2001

29. Example: frustrated Ising ferromagnets P.Viot G.Tarjus PRE2001 Frustration in soft-matter: diblock copolymer melts, cross linked copolymer mixtures, interpenetrating networks, oil-water surfactant mixtures Frustration in magnetism: ultrathin magnetic films Frustration in glasses: doped Mott insulator, supercooled liquids q T T cr dishomogeneous phase