1. Hyperon Suppression in Hadron- Quark Mixed Phase T. Maruyama (JAEA), S. Chiba (JAEA), H.-J. Schhulze (INFN-Catania), T. Tatsumi (Kyoto U.) 1 Property of nuclear matter in neutron stars. Non uniform “Pasta” structures at first-order phase transitions and the EOS of mixed phase. Structure and mass of neutron stars. Particle fraction in mixed phase -- hyperon suppression.

2. 2 Hulse-Taylor Observed Neutron Star Masses Most of them lie around 1.4 M sol Radius ~ 10 km Central density ~ several  0 —10  0 Mass ~ 1.4 M sol

3. 3 At 2-3    hyperons are expected to emerge in nuclear matter.  Large softening of the EOS  Maximum mass of neutron star becomes less than 1.4 solar mass.  Contradicts obs. >1.4 M sol Schulze et al, PRC73 (2006) 058801 With Y Without Y

4. 4 But the existence of mixed phase may soften the EOS again!  Bulk Gibbs calculation yields wide range of mixed phase and large softening [Glendenning, PRD46,1274]. Phase transition to quark matter may solve this problem. [Maieron et al, PRD70 (2004) 043010 etc]. Maxwell construction EOS of mixed phase is important !

5. 5 In the mixed phase with charged particles, non-uniform ``Pasta’’ structures are expected [Ravenhall et al, PRL 50 (1983) 2066]. Depending on the density, geometrical structure of mixed phase changes from droplet, rod, slab, tube and to bubble configuration. differentbulk picture Quite different from a bulk picture of mixed phase. We have to take into account the effect of the structure when we calculate EOS. Surface tension & Coulomb

6. 6 Hadron-Quark mixed-phase structure and EOS (T=0) Assume regularity in structure: divide whole space into equivalent and neutral cells with a geometrical symmetry (3D: sphere, 2D : cylinder, 1D: plate).  Wigner-Seitz cell approx. Divide a cell into hadron phase and quark phases. Give a geometry (Unif/Dropl/Rod/...) and a baryon density  B. Solve the field equations numerically. Optimize the cell size and H-Q boundary position (choose the energy-minimum). Choose an energy-minimum geometry among 7 cases (Unif H, droplet, rod, slab, tube, bubble, Unif Q). WS-cell

7. 7 Coupled equations to get density profile, energy, pressure, etc of the system Chemical equilibrium fully consistent with all the density distributions and potentials.

8. 8 Hadron EOS vs quark EOS --- Choice of parameters For quark phase, we choose  S =0 and B=100 MeV/fm 3. Quark threshold is above the hyperon threshold in uniform matter. For hadron phase, there is no adjustable parameter in the BHF model. Hyperon threshold 0.34 fm  Critical density

9. 9 Density profile in a cell Quark phase is negatively charged.  u quarks are attracted and d,s quarks repelled. Same thing happens to p in the hadron phase.  i (r) consistent with U i (r)

10. 10 EOS of matter Full calculation (with pasta) is close to the Maxwell construction (local charge neutral). Far from the bulk Gibbs calculation (neglects the surface and Coulomb).

11. 11 Density at r Mass inside r Total mass and Radius Pressure ( input of TOV eq.) Solve TOV eq. Structure of compact stars Bulk Gibbs Full calc  surf =40 MeV/fm 2 Maxwell const. Density profile of a compact star (M=1.4 solar mass)

12. 12 Mass-Radius relation of compact stars Full calc yields the neutron star mass very close to that of the Maxwell constr. The maximum mass are not very different for three cases.  surf =40

13.  u  s  2SC? 13 Important Side-effect of Pasta Structure Important Side-effect of Pasta Structure Although the EOS of matter and NS mass by the full calc is close to the Maxwell constr., the particle fraction is much different. Hyperon does not appear. Particle fraction Full calculation

14. Neutral hadron matter (positively) Charged hadron matter 14 Pasta  Local charge. Without charge-neutrality condition, hyperons appear at higher density. Neutral hadron   th =0.34 fm  Hyperon mixture is favoured to reduce electron and neutron Fermi energy. Charged hadron   th =1.15 fm  Heavy hyperons are not favoured. Hyperon suppression Mixed phase consists of negative Q and positive H phases.  Hyperon suppression particle fraction

15. 15 Summary We have studied ``Pasta’’ structures of hadron-quark mixed phase. Coulomb screening and stronger surface tension makes the EOS of mixed phase close to that of Maxwell construction instead of a bulk Gibbs calc. The mass-radius relation of a compact star is also close to the Maxwell construction case. But the particle fraction and the inner structure is quite different. Non uniform structure causes local charge and consequently the suppression of hyperons. All the strangeness in NS is in the quark phase. If the mixture of hyperons is suppressed in neutron stars  influence on thermal property and opacity (cooling process).

16. 16

17. 17 R and  dependence of E/A. Strong  surf  large R Weak Coulomb  large R

18. 18 Maxwell construction: Assumes local charge neutrality (violates the Gibbs cond.) Neglects surface tension. Bulk Gibbs calculation: Respects the balances of  i between 2 phases but neglects surface tension and the Coulomb interaction. Full calculation: includes everything. Strong  surf  Large R, charge-screening  effectively local charge neutral.  close to the Maxwell constrctn. Weak  surf  Small R  Coulomb ineffective  close to the bulk Gibbs calc.

19. 19 Energy density of Hadron phase YN scatt data, L -nuclear levels, and nuclear saturation are fitted. Brueckner Hartree Fock model

20. 20 Energy density of Quark phase Electron fraction is very small in quark matter. MIT bag model

21. 21 Phase transitions in nuclear matter Liquid-gas, neutron drip, meson condensation, hyperon, hadron-quark, color super-conductivity etc. EOS of mixed phase in first order phase transition Single component ( e.g. water) Maxwell const. satisfies Gibbs cond. T I =T II, P I =P II,  I =  II. Many components (e.g. water+ethanol) Gibbs cond. T I =T II, P i I =P i II,  i I =  i II. No Maxwell const ! Many charged components Gibbs cond. T I =T II,  i I =  i II. No Maxwell const ! No constant P !

22. 22

23. 23 Pure Hadron (Hyperon) Nicotra et al astro-ph/0506066 Hadron+Quark Maxwell constr. astro-h/0608021

24. 24