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

2. 2 4.3km ・１００ｍ below ground ・ The LHC has started !!  STOP…!? Y. Nambu (1921 ～ now) ２００８ Nobel Prize “experiment”“experiment” “numerical experiment” “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 …

3. 3 Compact stars topics Supernova remnants Supernova remnants Non-spherical effects are fundamentally important for SN mechanism !! Non-spherical effects are fundamentally important for SN mechanism !!  “ rotation ” and “ magnetic field ” 3D simulation of SN (Iwakami et al. 2008) Magnetars (B ～ 10 14 G at surface) Magnetars (B ～ 10 14 G at surface) Origin ? Origin ? What kind of matter in the core ?  Structure ? What kind of matter in the core ?  Structure ? Our study is “ Magnetized Rotating compact stars w/wo exotic matter ”

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

5. 5 Pasta Structure In the mixed phase of 1st order phase transitions, non-uniform “Pasta” structure is expected. In the mixed phase of 1st order phase transitions, non-uniform “Pasta” structure is expected. These structures will appear at Liquid-gas : supernova matter 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  Today’s Talk

6. 6 U O U+ UO UO 2 UO 3 O- Quasi-chemical representation ( “ chemical picture ” ) Multi-molecular model (Liquid & Gas) U + O + O 2 + UO + UO 2 + UO 3 U + + UO + + UO 2 + + O − + UO 3 − + e − U + 2O  UO 2 2O  O 2 U + + e  U UO 3 + e  UO 3 –... “Strange” stars Non-ideal U– O plasma u, d, s, p, n, e  u,  d,  s,  p,  n,  e u + e  d d  s p + e  n n  u + 2d (p  2u + d)  U + 2  U =  UO2 2  O   O2  U+ +  e =  U  UO3 +  e =  UO3–.............  Iosilevskiy et al.

7. 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. 8 EOSs ② : Uncertainty for surface tension Theoretical estimation on the MIT bag model for strangelets (Farhi & Jaffe 1984; Berger & Jaffe 1987) 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) Lattice gauge simulations at finite temperature (Kajantie et al. 1991; Huang et al. 1990, 1991) σ= 10 – 100 MeV/fm 2 σ= 10 – 100 MeV/fm 2 However, for σ> 40 MeV/fm 2, EOSs are almost same as ones under Maxwell construction However, for σ> 40 MeV/fm 2, EOSs are almost same as ones under Maxwell construction (Maruyama et al. 2007). (Maruyama et al. 2007). We choose σ= 10, 40 MeV/fm 2

9. 9 EOSs ③ : Brueckner Hartree Fock (Baldo et al.(1999), w/wo hyperon) Qaurk-Hadron pasta EOSs “Droplet” does not appears. “Rod” does not appears. BHF(with hyperon) QH pasta (σ=10 MeV/fm 2 ) QH pasta (σ=40 MeV/fm 2 ) 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 1 st phase transition like (Maxwell condition-like). We expand them to “finite temperature” cases.

10. 10 EOS with Quark-Hadron pasta at finite temperature (T=30 MeV, Yl=0) 1.finite T  more Maxwel-like EOS 2.Softer EOS region in mixed phase HM QM Mixed

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

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

13. 13 Neutron Stars with hyperons Neutron Stars without hyperons M 0 =1.45Ms, Φ=5×10 29 G cm 2 M =1.31 Ms B max =7.1×10 17 G M =1.32 Ms B max =4.6×10 17 G ρ0ρ0 ρ0ρ0 BΦBΦ BΦBΦ

14. 14 Hybrid Star : B=100 MeV/fm 3, σ=1 ０ MeV/fm 2 Hybrid Star : B=100 MeV/fm 3, σ=4 ０ MeV/fm 2 M 0 =1.45Ms, Φ=5×10 29 G cm 2 M =1.30 Ms B max =6.2×10 17 G M =1.31 Ms B max =6.2×10 17 G BΦBΦ BΦBΦ ρ0ρ0 ρ0ρ0

15. 15 Density distributions for equatorial direction for equatorial direction Mixed Phase

16. 16 C. Chiral symmetry restoration in proto-neutron stars in proto-neutron starsC. Chiral symmetry restoration in proto-neutron stars 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 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. 17 3-flavor NJL model ① (only chiral phase transitions) vector Gv ・・・ vector coupling constant  parameter λ ・・・ Gelll-Mann matrix

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

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

20. 20 M-n BC relations Hadron (Shen et al.1998) Hybrid (bulk Gibbs) Hybrid (Maxwell) Ejection of leptons  The EOS becomes HARD !! Ejection of leptons Ejection of leptons  The EOSs become SOFT !!

21. 21 Summary & Discussion

22. 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.  EOS becomes harder than only hyperon case. ② Strong surface tension  EOS becomes Maxwell condition-like.  EOS becomes Maxwell condition-like. ③ Finite temperature cases.  EOS becomes more Maxwell condition-like.  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. Clearly, distributions of magnetic field are different between w/wo phase transition. Strong magnetic field may change EOSs ? Strong magnetic field may change EOSs ? Poloidal magnetic field? Other origins of magnetic field? Poloidal magnetic field? Other origins of magnetic field? Astrophysical phenomena? (SN, GRB, NS cooling curve/spin- down rate) Astrophysical phenomena? (SN, GRB, NS cooling curve/spin- down rate) 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.  EOS becomes harder than only hyperon case. ② Strong surface tension  EOS becomes Maxwell condition-like.  EOS becomes Maxwell condition-like. ③ Finite temperature cases.  EOS becomes more Maxwell condition-like.  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. Clearly, distributions of magnetic field are different between w/wo phase transition. Strong magnetic field may change EOSs ? Strong magnetic field may change EOSs ? Poloidal magnetic field? Other origins of magnetic field? Poloidal magnetic field? Other origins of magnetic field? Astrophysical phenomena? (SN, GRB, NS cooling curve/spin- down rate) Astrophysical phenomena? (SN, GRB, NS cooling curve/spin- down rate)

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