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【 May . 20th. 2009. CS QCD II】

【 May . 20th. 2009. CS QCD II】. The pasta structure of quark-hadron phase transition and the effects on magnetised compact objects. N. Yasutake (NAOJ) 安武 伸俊. ・ Introduction A. Finite size effects on the quark-hadron phase transition ( NY , Maruyama, Tatsumi in prep . )

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【 May . 20th. 2009. CS QCD II】

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  1. 【 May. 20th. 2009. CS QCD II】 The pasta structure of quark-hadron phase transition and the effects on magnetised compact objects N. Yasutake (NAOJ) 安武 伸俊 ・Introduction A. Finite size effects on the quark-hadron phase transition (NY, Maruyama, Tatsumi in prep.) B. Rotating compact stars w/wo magnetic field (NY, Hashimoto, Eriguchi, 2005 PTP; NY, Kiuchi, Kotake, 2009 MNRAS submitted, etc…) C. Chiral symmetry restoration in proto-neutron stars (NY & Kashiwa 2009 PRD) ・Summary

  2. “HOT TPICS IN QUARK NUCLEAR PHYSICS” 4.3km “numerical experiment” “experiment” Lattice QCD (KEK:IBM Blue Gene) “effective theory” Y. Nambu (1921～now) ２００８ Nobel Prize ・１００ｍ below ground ・The LHC has started !!  STOP…!? “Others” Ads/CFT correspondence …

  3. Compact stars topics • Supernova remnants • Non-spherical effects are fundamentally important for SN mechanism !!  “rotation” and “magnetic field” 3D simulation of SN (Iwakami et al. 2008) • Magnetars (B～1014G at surface) • Origin ? • What kind of matter in the core ?  Structure ? Our study is “ Magnetized Rotating compact stars w/wo exotic matter”

  4. A. Finite size effects on the quark-hadron phase transition cf. Maruyama et al., PRD 2007 (T=0) NY, Maruyama, Tatsumi, in prep. (T≠0)

  5. Pasta Structure • In the mixed phase of 1st order phase transitions, non-uniform “Pasta” structure is expected. These structures will appear at ① Liquid-gas : supernova matter ② Neutron drip: neutron star inner crust ③ Meson condensation: neutron star outer core ④ Quark-hadron: neutron star inner core (Hybrid star)  Today’s Talk

  6. Quasi-chemical representation(“chemical picture”) Iosilevskiy et al. Non-ideal U–O plasma “Strange” stars O UO3 U UO2 U+ u, d, s, p, n, e mu, md, ms, mp, mn, me UO O- u + e  d d  s p + e  n n  u + 2d (p  2u + d) Multi-molecular model (Liquid & Gas) U + O + O2 +UO +UO2 + UO3 U+ + UO+ +UO2+ + O− + UO3− + e− U + 2O  UO2 2O  O2 U+ + e  U UO3 + e  UO3– . . . . . . mU + 2mU= mUO2 2mO =mO2 mU+ + me= mU mUO3 + me= mUO3– . . . . . . . . . . . . . 

  7. EOSs ①: MIT bag model and BHF hadron EOS Maruyama et al. (2007)PRD 76, 123015 Hadron phase: Brueckner Hartree Fock (Baldo et al.(1999), with hyperons) + Quark phase: MIT model (Free fermions - bag constant) For mixed phase ・Balance of “Coulomb interaction” and “Surface tension” ・Electrical charge neutrality ・Baryon number conservation ・Phase equilibrium

  8. EOSs ②:Uncertainty for surface tension • Theoretical estimation on the MIT bag model for strangelets (Farhi & Jaffe 1984; Berger & Jaffe 1987) • Lattice gauge simulations at finite temperature (Kajantie et al. 1991; Huang et al. 1990, 1991) σ= 10 – 100 MeV/fm2 • However,for σ> 40 MeV/fm2, EOSs are almost same as ones under Maxwell construction (Maruyama et al. 2007). We choose σ= 10, 40 MeV/fm2

  9. EOSs ③: Brueckner Hartree Fock (Baldo et al.(1999), w/wo hyperon) BHF(with hyperon) QH pasta (σ=10 MeV/fm2) QH pasta (σ=40 MeV/fm2) BHF(without hyperon) HARD EOS • ①　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. Qaurk-Hadron pasta EOSs “Droplet” does not appears. “Rod” does not appears.

  10. EOS with Quark-Hadron pasta at finite temperature (T=30 MeV, Yl=0) QM QM Mixed HM Mixed HM • finite T  more Maxwel-like EOS • Softer EOS region in mixed phase

  11. B. Rotating compact stars w/wo magnetic field cf. NY, Hashimoto, Eriguchi, PTP 2005 NY, Kiuchi, Kotake, MNRAS 2009 submitted

  12. Magnetized rotating star equilibrium Unfortunately, there is not the formulation for 【　Full GR, toroidal + poloidal magnetic field, rotation　】　! ! 【　Full GR, rotation　】 + 　【　Quark Matter　】 NY, Hashimoto, Eriguchi (2005) 【　Full GR, toroidal magnetic field, rotation　】　+ 【　Quark Matter　】 NY, Kiuchi, Kotake (2009), submitted Assumptions 1. stationary, aximetric star 2. perfect fluid, infinite conductivity 3. no meridional flow 4. barotropic EOS

  13. Neutron Stars with hyperons ρ0 BΦ M =1.31 Ms Bmax=7.1×1017G Neutron Stars without hyperons M0=1.45Ms, Φ=5×1029G cm2 ρ0 BΦ M =1.32 Ms Bmax=4.6×1017G

  14. Hybrid Star : B=100 MeV/fm3, σ=1０ MeV/fm2 ρ0 BΦ M =1.30 Ms Bmax=6.2×1017G Hybrid Star : B=100 MeV/fm3, σ=4０ MeV/fm2 M0=1.45Ms, Φ=5×1029G cm2 ρ0 BΦ M =1.31 Ms Bmax=6.2×1017G

  15. Density distributions for equatorial direction Mixed Phase

  16. C. Chiral symmetry restoration in proto-neutron stars cf. “Lepton effects on the proto-neutron stars with the hadron-quark mixed phase in the Nambu-Jona-Lasinio model” NY, Kashiwa, PRD 2009

  17. 3-flavor NJL model ①(only chiral phase transitions) Gv・・・ vectorcoupling constant  parameter λ・・・ Gelll-Mann matrix

  18. EOS and Chiral symmetry restoration • High Yl  High Ye  low ns • chiral restoration of s-quark is suppressed • Hard EOS !! Quark (SU(3) NJL) • High Yl  High Ye  low nn • repulsive nuclear force is suppressed • Soft EOS !! Hadron (Shen et al.1998)

  19. Quark-Hadron phase transition bulk Gibbs construction Maxwell construction large surface tension small surface tension “finite size effects”

  20. Hybrid　(bulk Gibbs) M-nBC relations Hadron (Shen et al.1998) Hybrid　(Maxwell) <Without the phase transition> Ejection of leptons  The EOS becomes HARD !! • <With the phase transition> • Ejection of leptons • The EOSs become SOFT !!

  21. Summary & Discussion

  22. Summary & Discussion A: “Pasta structures on the quark-hadron phase transition” ①　Number of hyperons are suppressed by appearance of quark matter. • EOS becomes harder than only hyperon case. • ②　Strong surface tension • EOS becomes Maxwell condition-like. • ③　Finite temperaturecases. • EOS becomes more Maxwell condition-like. • B: “Structures of magnetars with QH pasta” • Clearly, distributions of magnetic field are different between w/wo phase transition. • Strong magnetic field may change EOSs ? • Poloidal magnetic field? Other origins of magnetic field? • Astrophysical phenomena? (SN, GRB, NS cooling curve/spin-down rate)

  23. C: “The Chiral restoration on the structures of proto-compact stars” • With PT ： small Yl  soft EOS • Without PT： small Yl  hard EOS • This will change dynamics of SN, GRB. • How about color super conductivity? D: “Other topics” • Gravitational wave ? [NY et al. 2007, etc. ] • NS+NS, NS+BH binaries • Neutrino emission ? [Fischer et al. 2008, etc.] 謝謝!

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