1. Francesca Gulminelli - LPC Caen, France Extended Nuclear Statistical Equilibrium and applications to (proto)neutron stars Extended Nuclear Statistical Equilibrium and applications to (proto)neutron stars Collaboration: LPC Caen, LNS Catania, LUTH Meudon, IFIN Bucarest

2. Dense matter in the universe F.S.Kitaura et al, A&A 450 (06) 345 Supernova explosion occurs via core-collapse in very massive stars (M>8M sun )

3. Dense matter in the universe Supernova explosion occurs via core-collapse in very massive stars (M>8M sun ) 10 6  10 15 g/cm 3 0.01<T<50 MeV in the core T.Fischer et al, 2011 ApJS 194 39 40 M sun progenitor

4. Dense matter in the universe Supernova explosion occurs via core-collapse in very massive stars (M>8M sun ) 10 6  10 15 g/cm 3 0.01<T<50 MeV in the core The density in the residual pulsar (neutron star) is of the same order    10 14 g/cm 3 => Matter with nucleonic or sub-nucleonic dof !

5. Matter below saturation Standard nuclear physics: theory very (?) well known Most of the supernova dynamics + NS crust SN: T>0, y p given by weak rates NS: T=0,  -equilibrium Same physical system but different thermo conditions => very different formalisms Cluster dof NSE Nucleon dof DFT

6. HF(B) or (E)TF in the WS cell Extended to finite temperature 6/27 I- DFT for neutron star matter J. W. Negele and D. Vautherin, NPA 207, 298 (1973)

7. HF(B) or (E)TF in the WS cell Extended to finite temperature Many applications: crust composition, pasta, cooling…. 7/27 I- DFT for neutron star matter, R.Wolf et al, PRL 110, 041101 (2013) M.Fortin et al., PRC 82 (2010), 065804 S.S.Avancini et al., PRC 79 (2009),035804 droplets rods slabs homogeneous

8. II- NSE for supernova matter R.I.Epstein W.D.Arnett APJ 201 (1975) 202

9. Finite temperature stellar matter Cluster distribution + consistency with DFT&correct T=0 limit 1.Elementary WS cell at T>0: volume associated to each (dressed) cluster 2.mapping microscopic WS cell cluster+gas (Skyrme functionals for both) 3.distribution of WS cells F.Gulminelli, A.Raduta, ArXiV:1504.04493 Free energy of the in-medium cluster Self-interacting nucleons Cluster distribution

10. Extended NSE: T=0 F.Gulminelli, A.Raduta, ArXiV:1504.04493 ° NV: Negele-Vautherin (HF) - BPS+BBP: Baym (cluster model) This work (Sly4) This work (SKM*) M.Fortin, C.Providencia, F.Gulminelli, et al., in preparation Can be applied at very low density like cluster models Gives the correct melting behavior of clusters at high density like microscopic calculations Unified EoS below and above   SkI4 mean field Pichon-Haensel (cluster model) This work (SkI4) (fm -3 )

11. Application: EoS dependence of the NS crust width M.Fortin, C.Providencia, F.Gulminelli, et al., in preparation EoS dependence of NS properties needs a unified EoS!

12. Extended NSE: T>0 The T>0 distribution cannot be reduced to the most probable cluster The presence of a distribution changes the relation  => Even the average quantites !  B =10 -3 fm -3 T=1.5 MeV F.Gulminelli, A.Raduta, ArXiV:1504.04493 WS cell free-energy surfaces Cluster distribution and zoom on light clusters Single Cluster Approximation

13. Core collapse 25 Mo - CoConuT Application: electron capture during core collapse F.Gulminelli, A.Raduta, M.Oertel, in preparation time

14. Inclusion of pairing in the T>0 BCS approximation Cao L.G., Lombardo U. and Schuck P., PRC74(2006) BHF in-medium surface tension modification in the LDA S.Burrello, F.Gulminelli, M.Colonna, in preparation Excluded volume

15. T=0 results T=0 results Neutron drip Crust-core transition BB Good agreement with full HFB

16. Temperature dependence of the proton fraction in  -equilibrium The temperature evolution of the proton fraction is important at low density Pairing is important close to the crust-core transition

17. Effect of the cluster distribution The cluster distribution becomes wider with increasing temperature At high temperature the clusters do not dissolve into a homogeneous gas, but in a gas of neutron-rich resonances Sizeable effects on the energy density close to the crust-core transition

18. Heat capacity Results consistent with HFB when heavy clusters dominate Temperature dependence of the proton fraction cannot be neglected Great sensitivity to the mass model Extra peaks corresponding to the emergence and dissolution of light resonances

19. Conclusions Unified theoretical modelling of T=0 (NS) and T>0 (SN) matter o T=0: a single WS cell variationally determined o T>0: a statistical distribution of WS cells=dressed clusters T=0: a unified EoS below and above saturation o Melting of clusters in the dense medium o No artificial discontinuity in the P(r) for TOV o => effect of the symmetry energy on the radius and crust thickness T>0: cluster distribution in hot NS o Inclusion of pairing in the local BCS approximation o Pairing gap from BHF o Different peaks in CV due to the presence of light resonances