Rigid strange lattices in Proto-Neutron StarsJuergen J. ZachOhio State/UCSD13 May, 2002INT Nucleosynthesis workshop
Physical Environment: Core Collapse SupernovaeProtoneutron star: core at late stages of Kelvin-Helmholtz cooling phaseTimes: t3s after bounce mostly deleptonizedDensities: C~2-5nuclearTemperature: T~10MeV conditions for which many studies (e.g. Heiselberg et al. 2000) indicate a 1st-order phase transition to matter with macroscopic strangeness
Forms of macroscopically strange matterDeconfined quark matter (Pons et al. 2001), formation of strange quarks through weak reactions, e.g.:
(-, --, ) Hyperons (Balberg et al. 1999)Bose-Einstein condensate of mesons (K-) (Pons et al. 2000)
Formation of a Phase Transition LatticeGibbs 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.
Liquid Lattice Upper Layers
Crystallized Lattice Upper Layers
Properties of the Phase Transition Lattice at Finite TemperatureSolution of the whole lattice: equivalent to general problem of solid state physics from first principles intractableOCP-model for the limit of small droplet sizes: - structure-less point charges - uniform charge distribution (no screening)
Solving the OCP ModelDisplacement:
Degeneracy parameter:Lindemann parameter : Monte Carlo simulations (Stringfellow 1990, Ceperley 1980): intermediate range between classical and quantum limitsSolid-liquid coexistence curve:
Melting Curves Charge DependenceM=0.4fm-3; R=3fm; protoneutronstar cools through melting temperature during Kelvin-Helmholtz cooling phase
Melting Curves Size DependenceC=0.4fm-3; R=3fm; no crystallization below Rdroplet ~ 1fm lattice crystallizes first for deeper layers
Limits of OCP ModelDeformation (wobble) modes: freeze-out around lattice crystallization for small dropletsScreening effects; Debye lengths (Heiselberg et al. 1993, Norsen et al. 2001):
Mechanical Stability of the Crystallized LatticeShear constant of bcc - Coulomb lattice:Obtain Wl with Ewalds method (Ewald 1921).Critical shear stress:
Lattice Crystallization and HydrodynamicsLepton 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 periodDifferential rotation (Goussard et al. 1998); min. period ~1ms
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?
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?
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.
References:(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.