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Francesca Gulminelli & Adriana Raduta LPC Caen, FranceIFIN Bucharest, Romania Statistical description of PNS and supernova matter

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Microscopic phenomenology of dilute PNS and SN matter

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Nuclei in the outer crust Homogeneous matter in the core Neutron (proton) drip in the inner crust

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Nuclei in the outer crust Homogeneous matter in the core Neutron (proton) drip in the inner crust + electrons e p, Microscopic phenomenology of dilute PNS and SN matter

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An hybrid model for the crust- core transition Neutron (proton) drip in the inner crust Homogeneous matter in the core Finite temperature Hartree Fock with Skyrme interactions (SKM*, Sly230a) + electrons e p, Nuclei in the outer crust

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

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

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

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

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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… L>>L WS l ~L ws

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

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

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

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

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

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

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Outlooks 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) http://fr.arxiv.org/abs/1009.2226

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

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

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

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

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

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