1. Nuclear “Pasta” in Compact Stars Hidetaka Sonoda University of Tokyo Theoretical Astrophysics Group Collaborators (G. Watanabe, K. Sato, K. Yasuoka, T. Ebisuzaki)

2. Content Introduction Quantum Molecular Dynamics (QMD) Pasta Phases at zero and finite temperatures Neutrino opacity of Pasta phases Summary

3. Supernovae and Nuclear “Pasta” Core-collapse Supernova Explosion Neutrino transport in supernova cores EOS of dense matter No successful simulation with realistic settings Nonspherical nuclei --- “Pasta” phases Possible key element “Bounce” triggered by nuclear repulsive force Scenario Just before bounce (just before nuclear matter phase)

4. Neutron Stars and Nuclear “Pasta” Neutron Stars Pasta phases in the deep inside inner crust Core Outer Crust Inner crust Pasta Phases 10 km 1 km Solid of heavy nuclei Liquid of nuclear matter (quark matter, hyperons) Transition region from nuclei to nuclear matter

5. What is Nuclear “Pasta” ? (K.Oyamatsu, Nucl.Phys.A561,431(1993)) Nonspherical nuclei in dense matter ～ 10 14 g/cc Sphere→ Rod → Slab → Rod-like Bubbles → Spherical Bubbles →Uniform Nuclear Matter Meatball Spaghetti Lasagna Anti-spaghetti Cheese →”Pasta” Phases (Ravenhall et al. 1983,Hashimoto et al.1984)

6. Phase Diagram of Pasta Phases

7. Motivation How pasta phases appear in collapsing cores ? And in cooling neutron stars? How transition from sphere to uniform matter ? Pasta phases are dynamically formed as equilibrium-state of hot dense matter in supernovae ? as ground-state in neutron stars ?

8. Why QMD ? Quantum Molecular Dynamics (QMD) gives us a picture for How nuclei are deformed into uniform nuclear matter No assumptions on nuclear shapes. Nuclear system is treated in degrees of freedom of nucleons. Thermal fluctuations are included. QMD is suitable to answer the above question

9. Quantum Molecular Dynamics Model Hamiltonian 1 （ Chikazumi et al Phys.Rev.C 63 024602(2001)) Pauli PotentialNuclear ForceCoulomb EnergyKinetic Energy Nucleons obey Equation of Motion of QMD Saturation properties of symmetric nuclear matter Binding energy and rms radius of stable nuclei Hamiltonian is constructed to reproduce … Model Hamiltonian 2 （ Maruyama et al Phys.Rev.C 57 655(1998))

10. Simulation settings 2048 or 10976 nucleons in simulation box Periodic boundary condition Proton fraction x=0.3 Simulation Settings Ground state is obtained by cooling of hot matter Equilibrium state at finite temperature is obtained by Nose-Hoover thermostat for MD pot.

11. Pasta at zero temperature Sphere RodSlab Spherical Bubbles 0.100ρ 0 0.200ρ 0 0.393ρ 0 0.575ρ 0 0 0.490ρ Rod-like Bubbles Red : Protons Blue: Neutrons ρ =0.168 fm -3 （ Nuclear density ） 0 Cooling of hot nuclear matter (~10 MeV) below 0.1 MeV

12. Sponge-like Structure Between rod and slab, slab and rod-like bubbles Multiply connected “Sponge-like” structure appears 10976 nucleons at 0.3ρ 0 Between rod and slab 10976 nucleons at 0.45ρ 0 Between slab and rod bubbles These intermediate phases at least meta-stable

13. Phase diagram at zero temperature Model 1 Model 2 SP C C S SH S CH SP: sphere C: cylinder S: slab CH: cylindrical hole SH: spherical hole Uniform (C,S) SP&C coexist. (S,CH)CH,SH coexist. (C,S) SP&C 共存 (S,CH) 00.10.20.30.40.50.60.70.80.9 00.10.20.30.40.50.60.70.80.9 ρ/ρ ０ (a) (b) （密 度） (, ): intermediate Sphere →Rod → Slab → Rod-like bubbles → Spherical bubbles →Uniform matter

14. Pasta at finite temperatures 0.393ρ 0 (Slab nuclei at zero temperature) Evaporated Neutrons Connected Slab T= 2 MeV T= 1 MeV T= 0 MeV Slab Nuclei Increasing dripped neutrons Diffusive nuclear surface

15. Pasta at finite temperature Cannot identify nuclear surface Phase separation disappears Rodlike Bubble- like structure T=3MeVT=5MeV T=6MeV Phase transition, Melting surface, Dripped protons, Disappearance of phase separation

16. Phase diagram at finite temperatures SP 1 2 3 4 5 6 7 8 9 10 T (MeV) 0.1 0.20.3 0.4 0.50.60.70.8 0 ρ/ρ 0 SP ： Sphere C ： Cylinder S ： Slab CH ： C bubble SH ： S bubble (, ) ： Intermediate Phase separation line (T=6 ~ 10 MeV) Surface line (T=4 ~ 6 MeV) Thermal fluctuation increases volume fraction of nuclei Above T= 4 ~ 6 MeV, cannot identify surface At T= 6 ~ 10 MeV, Liquid-gas phase separation SH (C,S) C SCH (S,CH) Phase separation

17. Summary of Phase Diagram Performed simulation of nuclear matter at sub- nuclear densities with QMD Pasta Phases are obtained by QMD Ground-state by cooling hot matter Equilibrium-state of hot matter How structure of nuclear matter change in the density-temperature plane is examined

18. Neutrino Opacity of Pasta Phases

19. Motivation Neutrino transport --- a key element for success of supernovae How pasta phases change neutrino transport in collapsing cores ? Neutrinos are trapped in collapsing phase Lepton fraction affects EOS

20. Cross section of neutrino-Pasta Cross section of neutrino-nucleon system coherent scattering Neutrino-neutron cross section Amplification factor (Static structure factor) Total transport cross section →Amplification factor by structure

21. Method 1.Comparison cases with and without pasta phases using BBP liquid drop model 2. Show the results obtained by QMD as realistic model

22. Prediction by Liquid Drop Model Energy of neutrino (MeV) Red: with Pasta Black: without Pasta Peak at 30~40 MeV Peak monotonically decreases Below 25 MeV incoherent T=0 MeV ・ Y L =0.3 Amplification factor Existence of Pasta phases increases peak energy, and decreases opacity at lower energy

23. QMD results Y e =0.3, ρ=0.0660fm -3 (Slab at T=0) ・ Peak is lowered by increasing temp. ・ Transition from slab to rod-like bubbles dramatically changes peak energy and peak height T= 1 MeVT= 3 MeV Phase transitions can largely change neutrino opacity with low energy (~25-30 MeV)

24. Summary of neutrino opacity Pasta phases decrease neutrino opacity at low energy Phase transitions at finite temperatures complicate neutrino opacity

25. Summary Pasta phases appear with QMD simulation How nuclei are deformed into uniform nuclear matter has been examined Pasta phases decrease neutrino opacity at low energy side Phase transition at finite temperature complicate neutrino opacity