Nuclear “Pasta” in Compact Stars

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

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

5. What is Nuclear “Pasta” ? Nonspherical nuclei in dense matter ～1014g/cc Sphere→ Rod → Slab → Rod-likeBubbles → SphericalBubbles →Uniform Nuclear Matter (Ravenhall et al. 1983,Hashimoto et al.1984) Meatball Spaghetti Lasagna Anti-spaghetti Cheese →”Pasta” Phases (K.Oyamatsu, Nucl.Phys.A561,431(1993))

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 QMD is suitable to answer the above question No assumptions on nuclear shapes. Nuclear system is treated in degrees of freedom of nucleons. Thermal fluctuations are included.

9. Quantum Molecular Dynamics （Chikazumi etalPhys.Rev.C 63 024602(2001)) Model Hamiltonian 1 Kinetic Energy Pauli Potential Nuclear Force Coulomb Energy （Maruyama etalPhys.Rev.C 57 655(1998)) Model Hamiltonian 2 Nucleons obey Equation of Motion of QMD Hamiltonian is constructed to reproduce … Saturation properties of symmetric nuclear matter Binding energy and rms radius of stable nuclei

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

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

12. Sponge-like Structure Between rod and slab, slab and rod-like bubbles Multiply connected “Sponge-like” structure appears 10976 nucleons at 0.3ρ0 10976 nucleons at 0.45ρ0 Between rod and slab Between slab and rod bubbles These intermediate phases at least meta-stable

13. Phase diagram at zero temperature (a) (S,CH) CH,SH coexist. SP&C coexist. S Model 1 SP C (C,S) CH SH Uniform ρ/ρ０ （密度） 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (b) SP&C共存 (S,CH) (C,S) CH SH Uniform SP C S Model 2 ρ/ρ０ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 （密度） SP: sphere S: slab SH: spherical hole C: cylinder ( , ): intermediate CH: cylindrical hole Sphere →Rod → Slab → Rod-like bubbles → Spherical bubbles →Uniform matter

14. Pasta at finite temperatures 0.393ρ0 (Slab nuclei at zero temperature) T= 1 MeV T= 0 MeV T= 2 MeV Evaporated Neutrons Slab Nuclei Connected Slab Increasing dripped neutrons Diffusive nuclear surface

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

16. Phase diagram at finite temperatures T (MeV) SP ： Sphere C ： Cylinder S ： Slab CH ： C bubble SH ： S bubble ( , ) ： Intermediate Phase separation line (T=6 ~ 10 MeV) 10 9 8 7 Phase separation 6 Surface line (T=4 ~ 6 MeV) 5 4 (S,CH) (C,S) 3 SP 2 SH C 1 S CH ρ/ρ0 0 0.1 0.4 0.2 0.3 0.5 0.6 0.7 0.8 Thermal fluctuation increases volume fraction of nuclei Above T= 4 ~ 6 MeV, cannot identify surface At T= 6 ~ 10 MeV, Liquid-gas 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 Neutrinos are trapped in collapsing phase Lepton fraction affects EOS How pasta phases change neutrino transport in collapsing cores ?

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

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

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

23. QMD results Ye=0.3, ρ=0.0660fm-3 (Slab at T=0) T= 1 MeV T= 3 MeV ・Peak is lowered by increasing temp. ・Transition from slab to rod-like bubbles dramatically changes peak energy and peak height 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