1. Neutron star core-quakes caused by a transition to the mixed-phase EOS mixed-phase linear response theory stellar models M. Bejger, collaboration with P. Haensel, L. Zdunik 1 st Astro-PF Workshop at CAMK, Warsaw, 13-15 Oct. 2004

2. Mixed-phase First-order phase transition – mixed-phase appears via nucleation 2 phases in equilibrium for a set of pressures Preferred, if more than one conserved charge (i.e. baryon and electric), and if Coulomb and surface energy terms are small Global (not local) electric charge neutrality (Glendenning 1992, Glendenning & Schaffner-Bielich, 1998)

3. Mixed-phase

5. Influence of the phase transition on the star structure

6. TOV equation: Linear response theory (Haensel et al. 1986, Zdunik et al. 1987) Linearization of the equation to compare the density profiles of stars with and without the dense core.

7. Transition from meta-stable core configuration C to stable mixed-phase core configuration C * Global number of baryons is conserved, but other global parameters (M, R, I) are not. From meta- to stable matter

8. Linear response theory – density jump Core mass excess (density jump) Stellar response on the appearence of the new phase (r s – radius of the newly-born core)

9. Linear response theory – mixed-phase Core mass excess (transition to a mixed-phase) Stellar response on the appearence of the new phase exponent l = 5 (R, I), 7 (M) Q = radius R, moment of inertia I, mass-energy M

10. Linear response theory Size of new core and critical density of the meta-stable core Transition to the mixed-phase and density-jump similarity:

11. Response coefficients – polytropes Relativistic polytrope EOS: Approximate formulae for the response:

12. Adiabatic index: Response coefficients – realistic EOS SLy (Douchin & Haensel 2001)

13. Response coefficients – realistic EOS

14. Core-size: r m = 1 km ΔR = 4 cm, ΔΩ/Ω = -ΔI/I 0 = 10 -5, ΔE = 10 45 erg r m = 4 km ΔR = 42 m, ΔΩ/Ω = -ΔI/I 0 = 10 -2, ΔE = 10 49 erg Comparison: Normal „glitch”: ΔΩ/Ω = 10 -8, SGR: 10 44 -10 45 erg, X-ray bursters: 10 37 -10 43 erg Realistic EOS SLy (Douchin & Haensel 2001): Reference configuration - M = 1.4 M sun, R = 11.73 km, I 0 = 1.37·10 45 g cm 2 Transition to a mixed-phase -  m =1.5 polytrope Realistic EOS - results

15. Astrophysical scenarios proto-neutron star slow-down of a solitary pulsar accretion in a binary system

16. More realistic case of rotating stars: spin-up coefficient and the Ω influence on the results Non-spherical stars Comparison of two independent conserved numbers: baryon number and angular momentum Plans & prospects