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Statistical description of PNS and supernova matter

Statistical description of PNS and supernova matter. Francesca Gulminelli & Adriana Raduta LPC Caen, France IFIN Bucharest, Romania. Microscopic phenomenology of dilute PNS and SN matter. Microscopic phenomenology of dilute PNS and SN matter. Nuclei in the outer crust. Neutron (proton)

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Statistical description of PNS and supernova matter

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  1. Statistical description of PNS and supernova matter Francesca Gulminelli & Adriana Raduta LPC Caen, France IFIN Bucharest, Romania

  2. Microscopic phenomenology of dilute PNS and SN matter

  3. Microscopic phenomenology of dilute PNS and SN matter Nuclei in the outer crust Neutron (proton) drip in the inner crust Homogeneous matter in the core

  4. Nuclei in the outer crust Neutron (proton) drip in the inner crust Homogeneous matter in the core Microscopic phenomenology of dilute PNS and SN matter + electrons re=rp, g,n

  5. An hybrid model for the crust-core transition Nuclei in the outer crust Finite temperature Hartree Fock with Skyrme interactions (SKM*, Sly230a) Neutron (proton) drip in the inner crust Homogeneous matter in the core + electrons re=rp, g,n

  6. An hybrid model for the crust-core transition Nuclei in the outer crust Statistical ensemble of interacting excited clusters Neutron (proton) drip in the inner crust Homogeneous matter in the core Finite temperature Hartree Fock with Skyrme interactions (SKM*, Sly230a) + electrons re=rp, g,n

  7. Statistical ensemble of interacting excited clusters • Standard NSE • Analytical calculations • Non-interacting • This work • Coulomb interaction + excluded volume • Expensive MC calculations

  8. An hybrid model for the crust-core transition Neutron (proton) drip in the inner crust the two components together Homogeneous matter in the core Finite temperature Hartree Fock with Skyrme interactions (Sly230a) Statistical ensemble of interacting excited clusters Nuclei in the outer crust + electrons re=rp, g,n

  9. Mixture (ex:atmosphere) Coexistence (ex: Solid-Liquid) LI>>LWS L>>LWS LII>>LWS l~Lws Phase mixture versus phase coexistence A system composed of heterogenous components I=HM, II=clus • dishomogeneities on a • macroscopic scale • dishomogeneities on a • microscopic scale (Gibbs construction) • =>Continuous EOS • => jump in observables

  10. l~Lws L>>LWS The case of dilute stellar matter • Fluctuations occur on a microscopic scale (much smaller than the thermo limit characteristic length) • Mixture equilibrium rules • No phase coexistence • No first order crust-core transition at any T – even T=0! • Yet first order equilibrium rules are often supposed in the literature e.g.Lattimer-Swesty, Shen…

  11. Matter composition: cluster contribution Lines: LS EOS Symbols: this work T=1.6 MeV • No discontinuities • Decreasing cluster size • with increasing • temperature • Clusters still important • at T=10 MeV T=5 T=10

  12. Entropy density Symbols: this work Thin lines: clusters excluded T=1.6 MeV • Clusters are important • for the total energetics • The composition • of matter affects even integrated thermo quantities (here: S total) T=5 T=10

  13. Entropy density Symbols: this work Thick Lines: LS + virial EOS T=1.6 MeV • Clusters are important • for the total energetics • The composition • of matter affects even • integrated thermo • quantities! • Differences with LS • at high temperature T=5 T=10

  14. Pressure Thin lines: clusters excluded Symbols: this work T=1.6 MeV • Clusters cure the • homogeneous matter • instability T=5 T=10

  15. Pressure Thin lines: clusters excluded Thick lines: LS+virial EOS Symbols: this work T=1.6 MeV • Clusters cure the • homogeneous matter • instability • Differences with LS • at high density, • due to the absence of a • first order transition T=5 T=10

  16. Density at the crust-core transition Lines: LS + virial EOS Symbols: this work T=1.6 MeV • Crust-core transition naturally occurs T=5 T=10

  17. Outlooks http://fr.arxiv.org/abs/1009.2226 • More realistic cluster energy functional: temperature dependent effective mass, medium modifications to the self-energies of light fragments, shell and pairing corrections, deformation degree of freedom • More realistic matter energy functional: superfluidity at the BCS level • Coulomb interaction beyond the WS approximation • Consistent matching with high density EOS => Work in progress ! (ANR NS2SN with IPNO Orsay)

  18. Energy density Symbols: this work Lines: clusters excluded T=1.6 • Clusters are important • for the total energetics T=5 T=10

  19. Energy density Symbols: this work Lines: LS EOS virial EOS T=1.6 • Clusters are important • for the total energetics • Differences with LS • at high temperature T=5 T=10

  20. No first order transition in dilute stellar matter A first order crust-core transition (e.g. Lattimer-Swesty, Shen, etc.) • Does not correspond to the physical structure of the crust (microscopic fluctuations) • Gives no entropy gain G/V rp(fm-3)

  21. with electrons No first order transition in dilute stellar matter A first order crust-core transition (e.g. Lattimer-Swesty, Shen, etc.) • Does not correspond to the physical structure of the crust (microscopic fluctuations) • Ignores electron incompressibility!!! (transition quenched because => concave entropy) G/V rp(fm-3)

  22. No first order transition in dilute stellar matter A first order crust-core transition (e.g. Lattimer-Swesty, Shen, etc.) • Does not correspond to the physical structure of the crust (microscopic fluctuations) • Gives no entropy gain G/V rp(fm-3)

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