Rigid strange lattices in Proto-Neutron Stars

1. Rigid strange lattices in Proto-Neutron Stars Juergen J. Zach Ohio State/UCSD 13 May, 2002 INT Nucleosynthesis workshop

2. Physical Environment: Core Collapse Supernovae • Protoneutron star: core at late stages of Kelvin-Helmholtz cooling phase • Times: t3s after bounce  mostly deleptonized • Densities: C~2-5nuclear • Temperature: T~10MeV •  conditions for which many studies (e.g. Heiselberg et al. 2000) indicate a 1st-order phase transition to matter with macroscopic strangeness

3. Forms of macroscopically strange matter • Deconfined quark matter (Pons et al. 2001), formation of strange quarks through weak reactions, e.g.: • Bose-Einstein condensate of mesons (K-) (Pons et al. 2000) • (-, --, … ) Hyperons (Balberg et al. 1999)

4. Formation of a Phase Transition Lattice • Gibbs conditions in mixed phase determine strange phase fraction : B,s=B,N ; e,s=e,N; Ps = PN ; Ts = TN ; global charge neutrality (Glendenning 1992). • Geometrical structure determined by minimum of E=Ecoulomb+Esurface+Ecurvature+…(Heiselberg et al. 1993, Glendenning 2001) • Spherical droplets of minority phase at =0/1. • Rods, platelets at ~0.5.

5. Liquid Lattice – Upper Layers

6. Crystallized Lattice – Upper Layers

7. Properties of the Phase Transition Lattice at Finite Temperature • Solution of the whole lattice: equivalent to general problem of solid state physics from first principles  intractable • OCP-model for the limit of small droplet sizes: - structure-less point charges - uniform charge distribution (no screening)

8. Solving the OCP Model • Displacement: • Degeneracy parameter:  intermediate range between classical and quantum limits • Solid-liquid coexistence curve: • Lindemann parameter : Monte Carlo simulations (Stringfellow 1990, Ceperley 1980):

9. Melting Curves – Charge Dependence • M=0.4fm-3; R=3fm; •  protoneutronstar cools through melting temperature during Kelvin-Helmholtz cooling phase

10. Melting Curves – Size Dependence • C=0.4fm-3; R=3fm; •  no crystallization below Rdroplet ~ 1fm •  lattice crystallizes first for deeper layers

11. Limits of OCP Model • Deformation (“wobble”) modes:  freeze-out around lattice crystallization for small droplets • Screening effects; Debye lengths (Heiselberg et al. 1993, Norsen et al. 2001):

12. Mechanical Stability of the Crystallized Lattice • Obtain Wl with Ewald’s method (Ewald 1921). • Shear constant of bcc - Coulomb lattice: • Critical shear stress:

13. Lattice Crystallization and Hydrodynamics • Lepton number gradient dominant driving force of convection (Epstein 1979) at late stages of PNS evolution: • Differential rotation(Goussard et al. 1998); min. period ~1ms •  convection and differential rotation can prevent crystallization •  convection can break up lattice formed during transient quiet period

14. Possible effects on neutrino transport ~3-20sec. post-bounce? • Reddy et al. 2000: coherent scattering off strange droplets  increase in -opacity of mixed phase by 1-2 orders of magnitude •  Knee in -luminosity after 1st-order phase transition? •  Rearrangements of solid lattice during PNS evolution  irregularities in -emission? •  Localized fractures of lattice by convection  asymmetric -transport?

15. Work in progress - other observational signatures? • Gravity wave signature of anisotropic neutrino transport pattern detectable for Galactic SN. • “Settling” of lattice defects might cause some pulsar glitches. • Interaction with magnetic field in PNS? • Phase transition lattice might be responsible for non-spherical features in core collapse supernovae?

16. Conclusions: • Crystallization of the lattice formed during a first order phase transition in protoneutronstars possible for temperatures T~1-10MeV. • Deformation modes of the lattice droplets freeze out around the same temperature. • Critical shear stress ~10-3MeV/fm3 complex interaction between lattice crystallization and hydrodynamics (convection and differential rotation). • Solid lattice could lead to spatial anisotropies and temporal irregularities in -transport.

17. (Heiselberg et al. 2000): H. Heiselberg, M. Hjorth-Jensen, Phys. Rep. 328 (2000) 237-327. (Glendenning 1992): N.K. Glendenning, Phys. Rev. D 46 (1992) 1274. (Heiselberg et al. 1993): H. Heiselberg, C.J. Pethick, E.F. Staubo, Phys. Rev. Lett. 70 (1993) 1355. (Glendenning 2001): N.K. Glendenning, Phys. Rep. 342 (2001) 393-447. (Pons et al. 2001): J.A. Pons, A.W. Steiner, M. Prakash, J.M. Lattimer, Phys. Rev. Lett. 86 (2001) 5223-5226. (Pons et al. 2000): J.A. Pons, S. Reddy, P.J. Ellis, M. Prakash, J.M. Lattimer, Phys. Rev. C 62 (2000) 035803. (Balberg et al. 1999): S. Balberg, I. Lichtenstadt, G.B. Cook, ApJS. 121 (1999) 515-531. (Chabrier 1993): G. Chabrier, ApJ. 414 (1993) 695-700. (Stringfellow 1990): G.S. Stringfellow, H.E. DeWitt, Phys. Rev. A 41 (1990) 1105. (Ceperley 1980): D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. (Norsen et al. 2001): T. Norsen, S. Reddy, Phys. Rev. C 63 (2001) 065804. (Ewald 1921): P.P. Ewald, Ann. Phys. 64 (1921) 253-287. (Epstein 1979): R.I. Epstein, Mon. Not. R. Astr. Soc. 188 (1979) 305-325. (Goussard et al. 1998): J.O. Goussard, P. Haensel, J.L. Zdunik, Astron. Astrophys. 330 (1997) 1005-1016. (Reddy et al. 2000): S. Reddy, G. Bertsch, M. Prakash, Phys. Lett. B 475 (2000) 1-8. References: