1. Hyperon-Quark Mixed Phase in Compact Stars T. Maruyama* (JAEA), T. Tatsumi (Kyoto U), H.-J. Schulze (INFN), S. Chiba (JAEA)‏ *supported by Tsukuba Univ. 1 Hadron (hyperon)-quark mixed phase in compact stars. Non-uniform matter structure and the EOS. Hyperon suppression mechanism. [ T.Maruyama et al, PRD76(2007)123015; PLB659(2008)192 ]

2. 2 Hyperon mixture at 2-3    softening of the EOS  max M NS < 1.4 M sol  contradiction: obs M NS > 1.4 M sol However, mixed phase can softens the EOS again. “Bulk Gibbs” calc （ neglecting the finite-size effects ） shows a wide range of the mixed phase [Glendenning, PRD46,1274]. Quark core resolves “max mass problem” ? [Maieron et al, PRD70 (2004) 043010 etc]. Schulze et al, PRC73 (2006) 058801 nucleon } incl. hyperons NSC97&NSC98

3. 3 “Pasta” structure is generally expected in the mixed phase of charged particles. Geometrical structure of the mixed phase changes with density. droplet  rod  slab  tube  bubble‏ We explore the properties of the hadron(hyperon)-quark mixed phase with the non-uniform structures. No simple phase-separation is applied to the mixed phase !  EOS of the mixed phase should be affected by the non-uniform structures.

4. 4 Numerical calculation Assume regularity in structure: divide whole space into equivalent and charge-neutral cells with a geometrical symmetry (3D: sphere, 2D : cylinder, 1D: plate).  Wigner-Seitz cell approx. Divide a cell into hadron phase and quark phase. Give a dimensionality and a baryon density. Solve the field equations numerically. Optimize the cell size and H-Q boundary position (choose the energy-minimum). Choose an energy-minimum configuration among 7 cases (Uniform H, droplet, rod, slab, tube, bubble, Uniform Q). WS-cell

5. 5 Hadron phase Reproduces YN scatt data, levels of  -nucl, saturation properties of matter. Brueckner Hartree Fock model

6. 6 Quark phase Electron fraction is very small in quark matter. MIT bag model

7. 7 Hadron EOS vs quark EOS We use  S =0, B=100 MeV/fm 3  Quark threshold density is higher than that of hyperon in uniform matter. Depending on B and  S, hadron and quark EOS crosses at different density. Hyperon threshold = 0.34 fm 

8. 8 Conditions & Equations  We obtain density profile, energy, pressure, etc.

9. 9 Density profile in a cell Negatively charged Q (by u suppression) and positive H (by p enhancement:10%)‏  Coulomb screening: 1. in Q-phase, u gather inside and d, s outside. 2. in H-phase, p are attracted by Q-phase. 3. most electrons exist in H-phase.

10. 10 EOS Our full calc yields EOS close to that of Maxwell construction (locally neutral). Far from Bulk Gibbs calc (without surface and Coulomb). Due to the strong surface tension and the Coulomb scr.

11. 11 Dependence of E/A on R and  surf. strong  surf and weak Coulomb  large R extreme case  no minimum. [Voskresensky et al, PLB541(2002)93; NPA723(2003)291] Screening effects

12. 12 Maxwell constr.: Assumes local charge neutrality (violates Gibbs cond.)‏ Neglects surface tension. Bulk Gibbs calc: Balance of  i between 2 phases. Neglects surface tension and the Coulomb interaction. Full calc: includes everything. Strong  surf  large R Coulomb scr  approx local charge neutral  close to the Maxwell constr. Weak  surf  small R  Coulomb ineffective  close to the bulk Gibbs

13. 13 Particle fraction Our full calc yields EOS close to that of Maxwell constr. But the particle fraction is completely different. No hyperon appears in the full calc. Full calc

14. 14 Approximately local charge neutral but not strictly. Without charge-neutrality condition for each phase, hyperon mixture is suppressed. Neutral matter   th =0.34 fm  Hyperon mixture is favoured to reduce electron and neutron Fermi energy. Charged matter   th =1.15 fm  Heavy hyperons are not favoured. Hyperon suppression Mixed phase consists of negative Q and positive H phases.  Hyperon suppression Neutral hadron matter (positively) Charged hadron matter

15. 15 Summary “Pasta structure” in hadron-quark mixed phase. Coulomb scr and strong surface tension enlarges the size of the structure. Then Maxwell constr is approximately valid for EOS. But the particle fraction in the full calc is completely different from Maxwell constr and bulk Gibbs calc. Especially hyperon mixture is suppressed. Neutron star mass is slightly above 1.4 M sol Neutron star mass is close to that of Maxwell constr, while the internal structure is very different.

16. 16 density at r mass inside r total mass and radius pressure (input of TOV eq.)‏ TOV eq. Neutron star structure Neutron star density profile (M=1.4 M sol )‏

17. 17 Neutron Star mass-radius Full calc yields NS mass close to that of Maxwell constr. Maximum mass are almost the same for 3 cases.  surf =40

18. 18 Phase transition in nuclear matter Liquid-gas, neutron drip, meson condensation, hyperon mixture, hadron-quark, color super cond, etc EOS of mixed phase in 1 st order phase transition Single component ( water )‏ Maxwell constr satisfies Gibbs cond. T I =T II, P I =P II,  I =  II. Multi components (water+ethanol)‏ Gibbs cond. T I =T II, P i I =P i II,  i I =  i II. Maxwell constr. Is not valid ! Multi charged components Gibbs cond. T I =T II,  i I =  i II. Maxwell constr. Is not valid. Pressure P is not uniform!

19. 19 Another quark EOS Some density-dependent non-perturbative interaction energy is effectively included into bag constant.  B -dependent effective B eff constant B  M NS <1.6M sol small B  large M NS but H-Q transition at low  B  We introduce phenomenological  B dependent B. [G.G.Burgio et al, PRC66(2002)025802, etc]

20. new EOS with B eff 20 Another quark EOS -- Results