【 【 MayMay. . 20th. 20th. 2009. 2009. CS QCD IICS QCD II 】】

N. Yasutake (NAOJ)N. Yasutake (NAOJ)

安武 伸俊安武 伸俊

The pasta structure of The pasta structure of quark-hadron phase transition andquark-hadron phase transition andthe effects on magnetised compact objectsthe effects on magnetised compact objects

・・ IntroductionIntroduction

A. Finite size effects on the quark-hadron phase transitionA. Finite size effects on the quark-hadron phase transition　　　　　　 ((NYNY, Maruyama, , Maruyama, TatsumiTatsumi in prep in prep..))B. Rotating compact stars w/wo magnetic fieldB. Rotating compact stars w/wo magnetic field　　　　　　 ((NYNY, Hashimoto, Eriguchi, 2005 PTP; , Hashimoto, Eriguchi, 2005 PTP; NYNY, Kiuchi, Kotake, 2009 MNRAS , Kiuchi, Kotake, 2009 MNRAS

submitted, etc…)submitted, etc…)C. Chiral symmetry restoration in proto-neutron starsC. Chiral symmetry restoration in proto-neutron stars　　　　　　 ((NYNY & Kashiwa 2009 PRD) & Kashiwa 2009 PRD)

・・ SummarySummary

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4.34.3kmkm

・１００ｍ below ground・ The LHC has started !! STOP…!?

Y. Nambu(1921 ～ now)２００８ Nobel Prize

““experiment”experiment” ““numerical experiment”numerical experiment”

““effective theory”effective theory”

Lattice QCD(KEK:IBM Blue Gene)

““HOT TPICS IN QUARK NUCLEAR PHYSICS”HOT TPICS IN QUARK NUCLEAR PHYSICS”

““Others”Others”Ads/CFT correspondence …

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Compact stars topicsCompact stars topics Supernova remnantsSupernova remnants

Non-spherical effects are Non-spherical effects are fundamentally important for SN fundamentally important for SN mechanism !! mechanism !!

““rotationrotation”” and and ““magnetic fieldmagnetic field””

3D simulation of SN3D simulation of SN(Iwakami et al. 2008)(Iwakami et al. 2008)

Magnetars (BMagnetars (B ～～ 10101414G at surface)G at surface) Origin ?Origin ? What kind of matter in the core ? What kind of matter in the core ? Structure ? Structure ?

Our study isOur study is““ Magnetized Rotating compact stars w/wo exotic Magnetized Rotating compact stars w/wo exotic

mattermatter””

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A.A.Finite size effects on the quark-hadron phase Finite size effects on the quark-hadron phase

transitiontransitioncf.cf.

Maruyama et al., PRD 2007 (T=0)Maruyama et al., PRD 2007 (T=0)

NYNY, Maruyama, Tatsumi, in prep. (T, Maruyama, Tatsumi, in prep. (T≠≠0)0)

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Pasta StructurePasta Structure

In the mixed phase of 1st order phase transitions, In the mixed phase of 1st order phase transitions, non-uniform “Pasta” structure is expected.non-uniform “Pasta” structure is expected.

These structures will appear atThese structures will appear at ① Liquid-gas : supernova matterLiquid-gas : supernova matter② ② Neutron drip: neutron star inner crustNeutron drip: neutron star inner crust③ ③ Meson condensation: neutron star outer coreMeson condensation: neutron star outer core④ ④ Quark-hadron: neutron star inner core (Hybrid Quark-hadron: neutron star inner core (Hybrid

star)star) Today’s TalkToday’s Talk

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UUOO

U+U+

UOUO

UOUO22

UOUO33

O-O-

Quasi-chemical representationQuasi-chemical representation((““chemical picturechemical picture””))

Multi-molecular modelMulti-molecular model((Liquid & GasLiquid & Gas))

U + O + OU + O + O2 2 ++ UO +UO + UOUO2 2 + UO+ UO33

UU+ + + UO+ UO+ + ++ UOUO22+ + ++ O O− − ++ UO UO33

−− + e + e−−

U + 2O UO2

2O O2

U+ + e U UO3 + e

UO3–

. . . . . .

““Strange” starsStrange” stars Non-ideal U–Non-ideal U– O plasmaO plasma

u, d, s, p, n, e

u, d, s, p, n, e

u + e dd s

p + e n n u + 2d(p 2u +

d)

U + 2U= UO2

2O O2

U+ + e= U

UO3 + e= UO3–. . . . . . . . . . . . .

Iosilevskiy et al.

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EOSs EOSs :①:①MIT bag model and BHF hadron EOSMIT bag model and BHF hadron EOSMaruyama et al. (2007)Maruyama et al. (2007) PRD 76, 123015PRD 76, 123015

Hadron phase: Brueckner Hartree FockHadron phase: Brueckner Hartree Fock((Baldo et al.(1999), with hyperons)Baldo et al.(1999), with hyperons)

++Quark phase: MIT modelQuark phase: MIT model

(Free fermions - bag constant)(Free fermions - bag constant)

For mixed phase・ Balance of “Coulomb interaction” and “Surface tension”・ Electrical charge neutrality・ Baryon number conservation・ Phase equilibrium

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EOSs :②EOSs :②Uncertainty for surface tensionUncertainty for surface tension

Theoretical estimation on the MIT bag model for Theoretical estimation on the MIT bag model for strangelets (Farhi & Jaffe 1984; Berger & Jaffe 1987)strangelets (Farhi & Jaffe 1984; Berger & Jaffe 1987)

Lattice gauge simulations at finite temperatureLattice gauge simulations at finite temperature ((Kajantie et al. 1991; Huang et al. 1990, 1991)Kajantie et al. 1991; Huang et al. 1990, 1991)

σ= 10 σ= 10 –– 100 MeV/fm 100 MeV/fm22

However,However, for σ> 40 MeV/fmfor σ> 40 MeV/fm22, EOSs are almost , EOSs are almost same as ones under Maxwell constructionsame as ones under Maxwell construction

(Maruyama et al. 2007).(Maruyama et al. 2007).We choose σ= We choose σ= 1010, , 4040 MeV/fm MeV/fm22

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EOSs ③EOSs ③::Brueckner Hartree Fock Brueckner Hartree Fock ((Baldo et al.(1999), w/wo hyperon)Baldo et al.(1999), w/wo hyperon)

Qaurk-Hadron pasta EOSsQaurk-Hadron pasta EOSs

““Droplet” does not appears. “Rod” does not appears.Droplet” does not appears. “Rod” does not appears.

BHF(with hyperon)BHF(with hyperon)QH pasta (σ=10 MeV/fmQH pasta (σ=10 MeV/fm22))QH pasta (σ=40 MeV/fmQH pasta (σ=40 MeV/fm22))BHF(without hyperon)BHF(without hyperon)

HARD EOS① Number of hyperons are suppressed by appearance of quark matter.EOS becomes harder than only hyperon case.② For strong surface tension EOS becomes 1st phase transition like (Maxwell condition-like).

We expand them to “finite temperature” cases.

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EOS with Quark-Hadron pasta EOS with Quark-Hadron pasta at finite temperature at finite temperature (T=30 MeV, Yl=0)(T=30 MeV, Yl=0)

1.1. finite T finite T more Maxwel-like EOS more Maxwel-like EOS2.2. Softer EOS region in mixed phaseSofter EOS region in mixed phase

HMHM

QM QM

MixedMixed

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B.B.Rotating compact stars w/wo magnetic fieldRotating compact stars w/wo magnetic field

cf.cf.

NYNY, Hashimoto, Eriguchi, PTP 2005, Hashimoto, Eriguchi, PTP 2005

NYNY, Kiuchi, Kotake, MNRAS 2009 submitted, Kiuchi, Kotake, MNRAS 2009 submitted

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Magnetized rotating star equilibriumMagnetized rotating star equilibrium

【 【 Full GR, rotationFull GR, rotation 】 】 + + 【 【 Quark MatterQuark Matter 】 】NY, Hashimoto, Eriguchi (2005)NY, Hashimoto, Eriguchi (2005)

【 【 Full GR, toroidal magnetic field, rotationFull GR, toroidal magnetic field, rotation 】 】 + + 【 【Quark MatterQuark Matter 】 】NY, Kiuchi, Kotake (2009), submittedNY, Kiuchi, Kotake (2009), submitted

Unfortunately, there is not the formulation forUnfortunately, there is not the formulation for 【 【 Full GR, toroidal + poloidal magnetic field, rotationFull GR, toroidal + poloidal magnetic field, rotation 】 】 ! !! !

AssumptionsAssumptions1. 1. stationary, aximetric starstationary, aximetric star2. 2. perfect fluid, infinite conductivity perfect fluid, infinite conductivity 3. 3. no meridional flowno meridional flow4. 4. barotropic EOSbarotropic EOS

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Neutron Stars with hyperonsNeutron Stars with hyperons

Neutron Stars without hyperonsNeutron Stars without hyperons M0=1.45Ms, Φ=5×1029 G cm2

M =1.31 MsBmax=7.1×1017G

M =1.32 MsBmax=4.6×1017G

ρ0

ρ0 BΦ

BΦ

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Hybrid Star : B=100 MeV/fmHybrid Star : B=100 MeV/fm33, σ=1, σ=1 ０ ０ MeV/fmMeV/fm22

Hybrid Star : B=100 MeV/fmHybrid Star : B=100 MeV/fm33, σ=4, σ=4 ０ ０ MeV/fmMeV/fm22 M0=1.45Ms, Φ=5×1029 G cm2

M =1.30 MsBmax=6.2×1017G

M =1.31 MsBmax=6.2×1017G

BΦ

BΦρ0

ρ0

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Density distributionsDensity distributions for equatorial directionfor equatorial direction

Mixed Phase

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C.C.Chiral symmetry restorationChiral symmetry restoration

in proto-neutron starsin proto-neutron starscf.cf.

““Lepton effects on the proto-neutron stars with the hadron-quark Lepton effects on the proto-neutron stars with the hadron-quark mixed phase in the Nambu-Jona-Lasinio modelmixed phase in the Nambu-Jona-Lasinio model””NYNY, Kashiwa, PRD 2009, Kashiwa, PRD 2009

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3-flavor NJL model ①3-flavor NJL model ①(only chiral phase transitions)(only chiral phase transitions)

Gv ・・・ vectorvector coupling constant parameter λ ・・・ Gelll-Mann matrix

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EOS and EOS and Chiral symmetry restorationChiral symmetry restoration

HadronHadron(Shen et al.1998)(Shen et al.1998)

QuarkQuark(SU(3) NJL)(SU(3) NJL)

High Yl High Ye low ns chiral restoration of s-quark is suppressedHard EOS !!

High Yl High Ye low nn repulsive nuclear force is suppressed Soft EOS !!

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Quark-Hadron phase transitionQuark-Hadron phase transition

Maxwell constructionMaxwell constructionbulk Gibbs constructionbulk Gibbs constructionlarge surface tensionlarge surface tensionsmall surface tension small surface tension

““finite size effects”finite size effects”

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M-nM-nBCBC relations relations

HadronHadron(Shen et al.1998)(Shen et al.1998)

HybridHybrid (bulk Gibbs(bulk Gibbs))

HybridHybrid (Maxwell)(Maxwell)

<Without the phase transition> <Without the phase transition> Ejection of leptons Ejection of leptons

The EOS becomes HARD !!The EOS becomes HARD !!

<With the phase transition><With the phase transition> Ejection of leptons Ejection of leptons

The EOSs become SOFT !!The EOSs become SOFT !!

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Summary & DiscussionSummary & Discussion

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Summary & DiscussionSummary & DiscussionA: A: “Pasta structures on the quark-hadron phase “Pasta structures on the quark-hadron phase

transition”transition”①① Number of hyperons are suppressed by appearance of Number of hyperons are suppressed by appearance of

quark matter.quark matter. EOS becomes harder than only hyperon case.EOS becomes harder than only hyperon case.②② Strong surface tension Strong surface tension EOS becomes Maxwell condition-likeEOS becomes Maxwell condition-like..③③ Finite temperatureFinite temperature cases.cases. EOS becomes more Maxwell condition-like.EOS becomes more Maxwell condition-like.

B: B: “Structures of magnetars with QH pasta”“Structures of magnetars with QH pasta” Clearly, distributions of magnetic field are different Clearly, distributions of magnetic field are different

between w/wo phase transition.between w/wo phase transition. Strong magnetic field may change EOSs ?Strong magnetic field may change EOSs ? Poloidal magnetic field? Poloidal magnetic field? Other origins of magnetic Other origins of magnetic

field?field? Astrophysical phenomena? (SN, GRB, NS cooling Astrophysical phenomena? (SN, GRB, NS cooling

curve/spin-down rate)curve/spin-down rate)

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C: “C: “The Chiral restoration on the structures of proto-The Chiral restoration on the structures of proto-compact stars”compact stars”

With PT With PT ： ： small Yl small Yl soft EOS soft EOS 　　 Without PTWithout PT ： ： small Yl small Yl hard EOShard EOS 　　　　　　　　　　 This will change dynamics of SN, GRBThis will change dynamics of SN, GRB.. How about color super conductivity?How about color super conductivity?

謝謝謝謝 !!

D: “D: “Other topics”Other topics” Gravitational wave ? [Gravitational wave ? [NYNY et al. 2007, etc. ] et al. 2007, etc. ] NS+NS, NS+BH binariesNS+NS, NS+BH binaries Neutrino emission ? [Fischer et al. 2008, etc.]Neutrino emission ? [Fischer et al. 2008, etc.]