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Phase diagram of stellar matter and its impact on astrophysics

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

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Phase diagram of stellar matter and its impact on astrophysics

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  1. Phase diagram of stellar matter and its impact on astrophysics Francesca Gulminelli - LPC Caen, France Collaboration: Adriana RadutaIFIN Bucharest MicaelaOertelLUTH Meudon France PanagiotaPapakonstantinouIPNO France JerômeMargueronIPNO France

  2. A core crust Supernova remnant and neutron star in Puppis A (ROSAT x-ray) Time yp@ 1/2 T~1012K r~r0 A.Fantina, PhDthesis, 2011 yp@ 1/3 T~1011K r~r0 yp@ 1/5 T~6K r~r0 Dense matterisabundantly produced in a core-collapse supernova event leading to a neutron star (or black hole)

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

  4. 20 200 MeV Temperature 1 5? Density r/r0 Phases of dense matter in heavy-ion collisions RHIC FAIR Hadronic matter LHC QGP GANIL Liquid Gas

  5. 20 200 MeV Temperature 1 5? Density r/r0 Phases of dense matter in heavy-ion collisions Hadronic matter QGP Liquid Gas

  6. T rB This talk: Stellar matter versus nuclear matter phase diagram • The sub-saturation regime : • Coulomb effects and dishomogeneous phases • The super-saturation regime: • Hyperonicmatter & strangeness phase transition QGP? pasta ??

  7. T rB This talk: Stellarmatter versus nuclearmatter phase diagram • The sub-saturation regime : • Coulomb effects and dishomogeneous phases • The super-saturation regime: • Hyperonicmatter & strangeness phase transition QGP? pasta ?? G coex L

  8. r = 0.02 fm-3 r =0.04 fm-3 r =0.05 fm-3 r =0.08 fm-3 0.08 0.06 0.04 0.02 0 p n Densité / fm-3 e 0 5 10 0 5 10 0 5 0 5 10 Rayon / fm Coulomb effects • Nuclear matter is uncharged, while in stellar matter the proton charge is screened by a ~ uniform electron background Temperature T. Maruyama et al. PRC 72, 015802 (2005) Density r/r0

  9. Coulomb effects • Nuclearmatterisuncharged, while in stellarmatter the proton charge isscreened by a ~ uniformelectron background • The lowdensity phase is a Wigner cristal Temperature Density r/r0

  10. Coulomb effects • Nuclearmatterisuncharged, while in stellarmatter the proton charge isscreened by a ~ uniformelectron background • The lowdensity phase is a Wigner cristal • Phase coexistence i.e. macroscopicdensitydishomogeneities, wouldimply a macroscopic charge => a divergingenergydensity Temperature Density r/r0

  11. Coulomb effects • Nuclearmatterisuncharged, while in stellarmatter the proton charge isscreened by a ~ uniformelectron background • The lowdensity phase is a Wigner cristal • Phase coexistence i.e. macroscopicdensitydishomogeneities, wouldimply a macroscopic charge =>a divergingenergydensity • Dishomogeneitiesoccur on a microscopicscaleonly: a continuous transition through a cluster phase (innercrust) Temperature Density r/r0

  12. Coulomb effects • Nuclearmatterisuncharged, while in stellarmatter the proton charge isscreened by a ~ uniformelectron background • The lowdensity phase is a Wigner cristal • Phase coexistence i.e. macroscopicdensitydishomogeneities, wouldimply a macroscopic charge =>a divergingenergydensity • Dishomogeneitiesoccur on a microscopicscaleonly: a continuous transition through a cluster phase (innercrust) • Illustration via a phenomenological model Temperature Density r/r0

  13. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) • 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

  14. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) • No plateau in the EoS mI=1.6MeV T =1.6 MeV B

  15. The extended NSE model A.Raduta,F.G.,PRC 82:065801 (2010) PRC 85:025803 (2012) • No plateau in the EoS • Thermodynamicsverydifferentfrom a first order phase transition • Inaccessible in the standard grand-canonical NSE • Large distribution of cluster size mI=1.6MeV T =1.6 MeV B 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)………

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

  18. Towardsa quantitative EoS • The nuclear cluster energyfunctionalismodified by the externalnucleongas • Doesexcluded volume accountfor thiseffect? M.Hempel et al PRC 84, 055804 (2011) • In medium effectscalculatedfrom a HF calculation in the WS cell • Application to the NSE model in progress P.Papakonstantinou, et al., in preparation

  19. T rB This talk: Stellar matter versus nuclear matter phase diagram • The sub-saturation regime : • Coulomb effects and dishomogeneous phases • The super-saturation regime: • Hyperonicmatter & strangeness phase transition QGP? pasta ??

  20. Hyperons in dense stellarmatter • Hypernuclei: L potential attractive atlowdensity • Hyperond.o.f tend to soften the EoS • Still compatible with 2Mo NS if the hyperon-hyperoncouplingisstronglyrepulsiveat high density I.Vidana et al, Europhys.Lett.94:11002,2011 M.Oertel et al, http://arxiv.org/abs/1202.2679

  21. Strangeness phase transition • Attractive N-L and L-L interaction atlowrB , repulsiveathighrB • e(r) has a minimum =>dilute/dense PT ? • e(rL) has a minimum =>non-strange/strange PT ? • Illustration with a simple model: n-L equilibrium in the HF approximation; energyfunctionalfromBalberg & Gal YL= rn=0.45 fm-3 rn=0.3 fm-3 rn=0.15 fm-3 rS(fm-3) rr S.Balberg A.Gal NPA 625(1997)435

  22. n-L phase diagram • different first and second order phase transitions • I: L’s in neutron matter • II: n-Lliquid-gas • III: neutrons in Lmatter F.G.,A.Raduta and M.Oertel, in preparation

  23. n-L phase diagram • different first and second order phase transitions • I: L’s in neutron matter • II: n-Lliquid-gas • III: neutrons in Lmatter mS=0 F.G.,A.Raduta and M.Oertel, in preparation

  24. n-L phase diagram • different first and second order phase transitions • I: L’s in neutron matter • II: n-Lliquid-gas • III: neutrons in Lmatter => Coexistinghyperon-rich & hyperon-poorregionsalong the physicaltrajectorymS=0 mS=0 mS=0 F.G.,A.Raduta and M.Oertel, in preparation

  25. n-L phase diagram • different first and second order phase transitions • I: L’s in neutron matter • II: n-Lliquid-gas • III: neutrons in Lmatter => Coexistinghyperon-rich & hyperon-poorregionsalong the physicaltrajectorymS=0 => Explores a critical point at T>0: nopacity? mS=0 mS=0 critical point F.G.,A.Raduta and M.Oertel, in preparation J.Margueron et al, PRC70 (2004) 028801

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

  27. Tcr T dishomogeneous phase q Frustration and dishomogeneous phases P.ViotG.Tarjus PRE2001 • Frustrationis a genericphenomenon in physics • It occurswhenevermatterissubject to opposite interactions (here: nuclear & coulomb) on comparable lengthscales • Global variations of the orderparameter (here: density) are replaced by local variations =>Phase coexistence isquenched =>dishomogeneous phases arise =>Ensemble equivalenceisviolated

  28. Tcr T dishomogeneous phase q 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

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