The structure of a proto-neutron star

1. The structure of a proto-neutron star Chung-YeolRyu Hanyang University, Korea C.Y.Ryu, T.Maruyama,T.Kajino, M.K.Cheoun, PRC2011. C.Y.Ryu, T.Maruyama,T.Kajino, G.J.Mathews, M.K.Cheoun, PRC2012.

2. Outline 1. Introduction 2. Motivations 3. Models and conditions 4. Results 5. Summaries

3. 1. Introduction Vela pulsar

7. The structure of neutron star

8. The depiction of a Shapiro Delay

9. The masses of neutron stars

10. From A. Schwenk

11. 2. Motivations The depiction of a Shapiro Delay

12. Production of a proto-neutron star The structure of supernovae The production of proto-neutron star

13. Supernovae explosion and PNS A. Burrows(1995)

14. Motivation 1

15. Motivation 2 Isentropic process Burrows&Lattimer APJ (1981), APJ(1987) without convection with convection

16. Motivation 3 S. Reddy et al. PRD(1998)

17. Motivation 4 S. Reddy et al. PRD(1998) A. Burrows’ simulation

18. Idea Beta equilibrium n + νe p + e- : • Trapped ratio may depend on densities and temperature.

19. 3. Models and conditions

20. Many body theory in isolated system Thermodynamic potential Ω - Minimum condition Microscopic model: Hamiltonian or Lagangian Grand partition function Z • Chemical potential • Chemical equilibrium for given reaction • - Minimum of Gibbs free energy • Equation of state • - Energy density, Pressure, Temperature • Observables (mass and radius for neutron star) from EoS

21. Constraints from experiment Neutron star

22. Nuclear matter properties at saturation density • Saturation density • 0 = 0.15 - 0.17fm-3 • Binding energy • B/A =-(ε/ρ – m N)= 16MeV • Effective mass of a nucleon • m N*/m N = 0.7 - 0.8 (이론) • Compression modulus • K-1= 200 - 300MeV • Symmetry energy • asym= 30 - 35MeV

23. Equation of state from heavy ion collision

24. Symmetry energy from HIC and finite nuclei Symmetry energy Energy per nucleon in symmetric matter Energy per nucleon in asymmetric matter

25. Relativistic mean field model Nucleons (Dirac equation) + meson fields (Klein-Gordon equation) Meson fields  mean fields (notransition)

26. N N Mean fields theory : σ-ω-ρmodel Long range attraction(σ meson) + Short range repulsion(ω meson) + Isospin force : ρ meson Other mesons are neglected !! pion : (-) parity, other mesons : small effects, simplicity

27. σ, ω, ρ QHD and QMC models Hadronic degrees of freedom : Quantum Hadrodynamics (QHD) Quark degrees of freedom : Quark-meson coupling (QMC) model σ, ω, ρ

28. σ, ω, ρ The Lagrangian of QMC model

29. Eq. of state and entropy Isentropic process : S = 2 (S : entropy per a baryon)

30. The conditions in neutron star • Baryon number conservation : • Charge neutrality : • chemical equilibrium (Λ, Σ, Ξ) • Fixed YL =? or other condition - μνe where x is trapped ratio.

31. TOV equation(Mass and radius) • Macroscopic part – General relativity • Microscopic part – Strong interaction model • Einstein field equation : Static and spherical symmetric neutron star (Schwarzschild metric) Static perfect fluid Diag Tμν = (ε, p, p, p) • TOV equation : • equation of state (pressure, energy density)

32. The moment of inertia • Metric tensor • Kepler frequency • The moment of inertia in slow rotating approx.

33. Our picture Conditions Models QHD & QMC models -Eq. of motion • Baryon number conservation • Charge neutrality • Beta equilibrium with neutrinos • Trapped ratio depends on densities • Equation of state • - Energy density, Pressure, Temperature • Mass, radius and the moment of inertia

34. 4. Results

35. Cold neutron star (QMC)

36. Populations

37. Populations of neutrinos(S=2) • Our result A. Burrows’simulation

38. Temperature

39. Equation of state

40. Mass and radius Cold NS(T=0) Proto-NS(S=2)

41. The moment of inertia

42. Summaries 1. Proto-neutron star : After supernovae explosion, the initial state of NS is called PNS. 2. YL = 0.4 condition is not enough to explain trapped neutrino ratio. 3. So, we introduce that the trapped ratio may depend on the baryon densities. - The results agree with simulation. 4. The moment of inertia : PNS  CNS - Pulsar rotation may depend on the mass.