# Presentation: 687539

## 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.

-  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 ]

##  [Maieron et al, PRD70 (2004) 043010 etc].

-  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].

## “Pasta” structure is generally expected in the mixed phase of charged particles.

- “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.

## Numerical calculation

- WS-cell

## Hadron phase

- Reproduces YN scatt data, levels of -nucl,
- saturation properties of matter.

- Brueckner Hartree Fock  model

## Quark phase

- Electron fraction is very small in quark matter.

- MIT bag model

## Hadron EOS vs quark EOS

- We use  S =0,
*B*=100 MeV/fm3
-  Quark threshold density is higher than that of hyperon in uniform matter.

- Depending on *B* and aS , hadron and quark EOS crosses at different density.

- Hyperon threshold
- = 0.34 fm

## Conditions & Equations

- We obtain density profile, energy, pressure, etc.

## 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.

## 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.**

## Screening effects

- 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]

##  Maxwell constr.:

-  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

## 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

## Hyperon suppression

- 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.

- Mixed phase consists of negative Q and positive H phases.

## 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.

## Neutron star structure

- TOV eq.

- Neutron star density profile (*M*=1.4 *M*sol)‏

## 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**

## Phase transition in nuclear matter

- Liquid-gas, neutron drip, meson condensation, hyperon mixture, hadron-quark, color super cond, etc

- EOS of mixed phase in 1st 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*iI=*P*iII, iI=iII.
- Maxwell constr. Is not valid !

-  Multi charged components
- Gibbs cond. *T*I=*T*II,  iI=iII.
- Maxwell constr. Is not valid.
- Pressure *P * is not uniform!

## Another quark EOS

- Some density-dependent non-perturbative interaction energy is effectively included into bag constant.

- rB-dependent effective *B*eff

- constant *B*  *M*NS<1.6*M*sol
- small *B*   
-  large *M*NS
-  but H-Q transition at low rB
- 
- We introduce phenomenological rB dependent *B.*

- [G.G.Burgio et al, PRC66(2002)025802, etc]

## Another quark EOS  -- Results