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

3. 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

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

5. Formation of a Phase Transition Lattice  Gibbs conditions in mixed phase determine strange phase fraction  :  B,s =  B,N ;  e,s =  e,N ; P s = P N ; T s = T N ; global charge neutrality (Glendenning 1992).  Geometrical structure determined by minimum of E=E coulomb +E surface +E curvature +… (Heiselberg et al. 1993, Glendenning 2001)  Spherical droplets of minority phase at  =0/1.  Rods, platelets at  ~0.5.

6. Liquid Lattice – Upper Layers

7. Crystallized Lattice – Upper Layers

8. 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)

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

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

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

12. 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):

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

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

15. 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 1 st -order phase transition?  Rearrangements of solid lattice during PNS evolution  irregularities in -emission?  Localized fractures of lattice by convection  asymmetric -transport?

16. 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?

17. 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 -3 MeV/fm 3  complex interaction between lattice crystallization and hydrodynamics (convection and differential rotation). Solid lattice could lead to spatial anisotropies and temporal irregularities in -transport.

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