Behaviour of Proton Component in Neutron Star Matter for Realistic Nuclear Models

1. Behaviour of Proton Componentin Neutron Star Matterfor Realistic Nuclear Models Adam Szmagliński, Marek Kutschera, Włodzimierz Wójcik • Realistic Nuclear Models Used in Calculations. • Symmetry Energy and Proton Localization. • Model of Proton Component in Neutron Matter. • Astrophysical Consequences. • Conclusions.

2. Neutron Star Structure • Atmosphere • Envelope • Crust • Outer Core • Inner Core

4. Realistic Nuclear Models: • Myers-Świątecki (MS) • Skyrme (Sk) • Friedman-Pandharipande-Ravenhall (FPR) • UV14+TNI (UV) • AV14+UVII (AV) • UV14+UVII (UVU) • A18 • A18+δv • A18+UIX • A18+δv+UIX*

5. Energy per particle of asymmetric nuclear matter: Kinetic Energy of Fermi gas: Energy density: where:

6. UV14+TNI Model

7. AV14+UVII Model

8. UV14+UVII Model

15. Equilibrium

18. Symmetry Energy of Nuclear Matter

21. Coexistence Conditions are Implemented by Constructing Isobars Protons do not diffuse into neutron matter The neutron matter coexists with proton clusters of nucleon density and proton fraction in a pressure range .

24. The most important izobar parameters

25. Model of Proton Impurities in Neutron Star Matter (M. Kutschera, W. Wójcik) We divide the system into spherical Wigner-Seitz cells, each of them enclosing a single proton: The volume of the cell: The energy of the cell of uniform phase:

26. where

27. Variational Method for single protonin neutron matter We minimize the energy difference with variational parameters - neutron density enhancement around the proton - neutron density reduction in the proton vicinity • the mean square radius of the localized proton • probability distribution

29. The self-consistent variational method We look for such functions and , that minimize functional: - Lagrange multipliers boundary conditions:

30. By differentiation with respect to and we obtain following Euler-Lagrange equations: - variational parameter

34. Comparison of simple variational method and self-consistent variational method

37. Mass and radii of neutron stars: • Tolman-Oppenheimer-Volkoff equation • Equation of state

42. J.M. Lattimer and M. Prakash, astro-ph/0405262

44. Conclusions • Symmetry energy – inhomogeneity of dense nuclear matter in neutron stars. • Proposal of self-consistent variational method – neutron background profile as a solution of variational equation with parameter (mean square radius of proton wave function). • Localization of protons as an universal state of dense nuclear matter in neutron stars. • Finding of neutron star regions with localized proton phase. • Astrophysical consequences of proton localization: • spontaneous polarization of localized protons as a source of strong magnetic fields of pulsars; • influence on neutron star cooling rate.

45. References: [1] M. Kutschera, Phys. Lett. B340, 1 (1994). [2] M. Kutschera, W. Wójcik, Phys. Lett. B223, 11 (1989). [3] M. Kutschera, W. Wójcik, Phys. Rev. C47, 1077 (1993). [4] M. Kutschera, S. Stachniewicz, A. Szmagliński, W. Wójcik, Acta Phys. Pol. B33, 743 (2002).