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

Microscopic phenomenology of dilute PNS and SN matter

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

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

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

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)

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

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, 

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

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

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

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

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

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

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

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

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)

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

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

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 )

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 )

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 )