Hyperon-Quark Mixed Phase in Compact Stars

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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
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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?

• No simple phase-separation is applied to the
  mixed phase !
• ? EOS of the mixed phase should be affected by
• the non-uniform structures.

We explore the properties of the
hadron(hyperon)-quark mixed phase with the
non-uniform structures.
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Quark phase
MIT bag model
Electron fraction is very small in quark matter.
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Hadron EOS vs quark EOS
Depending on B and aS , hadron and quark EOS
crosses at different density.
We use ?S 0, B100 MeV/fm3 ?Quark threshold
density is higher than that of hyperon in uniform
matter.
Hyperon threshold 0.34 fm??
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?We obtain density profile, energy, pressure,
etc.
Conditions Equations
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Density profile in a cell
Negatively charged Q (by u suppression) and
positive H (by p enhancement10)? ?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.
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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.
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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
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• 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

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Full calc
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.
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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 Msol
• Neutron star mass is close to that of Maxwell
  constr,
• while the internal structure is very different.

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Neutron Star mass-radius
Full calc yields NS mass close to that of Maxwell
constr. Maximum mass are almost the same for 3
cases.
?surf40
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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

• Multi components (waterethanol)?
• Gibbs cond. TITII, PiIPiII, ?iI?iII.
• Maxwell constr. Is not valid !

• Single component (water)?
• Maxwell constr satisfies Gibbs cond. TITII,
  PIPII, ?I?II .

• Multi charged components
• Gibbs cond. TITII, ?iI?iII.
• Maxwell constr. Is not valid.
• Pressure P is not uniform!

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Another quark EOS
rB-dependent effective Beff

• constant B ? MNSlt1.6Msol
• small B ?
• large MNS
• but H-Q transition at low rB
• ?
• We introduce phenomenological rB dependent B.

G.G.Burgio et al, PRC66(2002)025802, etc
Some density-dependent non-perturbative
interaction energy is effectively included into
bag constant.
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