hadron quark crossover and neutron star observations
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Hadron-Quark Crossover and Neutron Star Observations Kota Masuda - PowerPoint PPT Presentation

Hadron-Quark Crossover and Neutron Star Observations Kota Masuda (Univ. of Tokyo / RIKEN) with Tetsuo Hatsuda (RIKEN) and Tatsuyuki Takatsuka (RIKEN) Hadron in nucleus, 31th Oct., 2013 Introduction: NS observations 1/16 NS observations QCD


  1. Hadron-Quark Crossover and Neutron Star Observations Kota Masuda (Univ. of Tokyo / RIKEN) with Tetsuo Hatsuda (RIKEN) and Tatsuyuki Takatsuka (RIKEN) Hadron in nucleus, 31th Oct., 2013

  2. Introduction: NS observations 1/16 NS observations QCD phase diagram Fukushima, Hatsuda (2010) EOS Mass (1 . 97 ± 0 . 04) M � Relation to stiffness of EOS and the existence of Demorest et al. (2010) the exotic components ? (2 . 01 ± 0 . 04) M � Antoniadis et al. (2013) Superfluid / Superconducting phase Cooling Cooling of CAS-A Relation to nucleon and quark superfluidity inside NSs ? Heinke et al. (2010)

  3. Neutron Star Radius 2/16 Guillot et. al. (2013) Steiner et. al. (2012) Ozel et. al. (2009) • Radius can make constraints on EOS at low density region • However, there are some different estimations.

  4. Hadronic EOSs 3/16 (1) (2) (3) ��� AV18+TBF TNI2 SCL3 ΛΣ ������������ �������������� ��� � Method BHF BHF Hyperons RMF RMF ����������� ��� 2NF AV18 Reid M/M �������� ���� ΛΣ � ���� 3NF Yes Yes No ��� Hyperons Yes Yes Yes � � � � �� �� �� �� �� (1) Baldo et al. (2000), Schulze et al. (2010) ������ (2) Nishizaki et al. (2001,2002) (3) Tsubakihara et al. (2010) • Hyperons soften EOS Maximum mass is less than 1 . 44 M �

  5. Hadronic EOSs 4/16 ��� ������������ TNI2 TNI2u �������������� ��� � ����� ����������� ��� ``NNN” Yes Yes M/M �������� ���� ΛΣ � ���� ``NNY” ``NYY” No Yes ��� ``YYY” � � � � �� �� �� �� �� ������ • Universal 3-body force stiffens EOS Maximum mass is larger than 1 . 44 M � • However maximum mass cannot exceed 2 M �

  6. Baryon density (ρ) Hadron-Quark Crossover 5/16 Pressure (P) BEC-BCS Crossover hadron crossover quark We seek the possibility of crossover Ref.) Baym (1979) Celik, Karsch and Satz (1980) Fukushima (2004) Hatsuda, Tachibana, Yamamoto and Baym (2006)

  7. Baryon density (ρ) Method of Interpolation 6/16 Phenomenological interpolation: P ( ρ ) f ± = 1 ± tanh( ρ − ¯ Γ ) ρ P = p H × f − + p Q × f + 2 P = ρ 2 ∂ ( ε / ρ ) ρ Pressure (P) hadron crossover quark Γ ¯ ρ ρ 0 Condition for : at f + < 0 . 1 ρ > ρ 0 + 2 Γ ¯ ¯ ρ 0 ρ

  8. EOS at ρ � ¯ 7/16 ρ (2+1)-flavor NJL Lagrangian (u,d,s, ) e − , µ − 8 + G s − g v [( q λ a q ) 2 + ( qi γ 5 λ a q ) 2 ] q γ µ q ) 2 X 2 (¯ L NJL = q ( i ∂ − m ) q + G D [det q (1 + γ 5 ) q + h . c . ] 2 a =0 M i = m i � 2 G s h ¯ q i q i i � 2 G D h ¯ q j q j ih ¯ q k q k i Ω = − T V ln Z h q † X µ i ! µ e ff ⌘ µ i � g v i q i i i i ! 2 X q i q i i 2 + 4 G D h ¯ � 1 X = Ω q ( M, µ e ff ) + Ω l + G s h q † h ¯ q i q i ih ¯ q j q j ih ¯ q k q k i i q i i 2 g v i ✓ 1 d 3 p ◆ Z X X ( i ω l , − → Ω q ( µ e ff ) = − T T S − 1 (2 π ) 3 Trln p ) , i i l = p − µ e ff γ 0 − M i , p 0 = i ω l = (2 l + 1) π T S − 1 i ∂ Ω Gap equations: q i q i i = 0 ∂ h ¯ Parameter sets Conditions: G s Λ 2 G D Λ 5 cutoff (MeV) m s ( MeV ) 0 ≤ g v ≤ 1 . 5 G s m u,d ( MeV ) 1. beta-equilibrium 631.4 3.67 9.29 5.5 135.7 (Fierz: ) 2. charge neutrality G V = 0 . 5 G S Hatsuda and Kunihiro (1994) Bratovic et al . (2012)

  9. EOS at ρ � ¯ 8/16 ρ Constituent mass Number fraction • s quark starts to appear above 4 Chiral restoration ρ 0 • SU(3) flavor symmetric matter at high densities • u,d quark : low densities • muon does not appear due to s quark • s quark : 4 ρ 0 charge neutrality • figures do not depend on the magnitude of vector interaction

  10. Results (1): Effects of Q-EOS 9/16 M-R relation (¯ ρ , Γ ) = (3 ρ 0 , ρ 0 ) g v = G S ��� ��� ���������������� ������������ ����� �������������� �������������� � � ���� ����� ����������� ����������� ��� ��� ���� ΛΣ M/M M/M �������� ���� ΛΣ � � ���� ��� �������� ��� ��� � � � � � �� �� �� �� �� � � � �� �� �� �� �� ������ ������ • Maximum mass exceeds 2 solar mass, no matter what kind of H-EOS is taken

  11. Results (1): Effects of Q-EOS 9/16 M-R relation (¯ ρ , Γ ) = (3 ρ 0 , ρ 0 ) g v = G S ��� ��� ���������������� ������������ ����� �������������� �������������� � � ���� ����� ����������� ����������� ��� ��� ���� ΛΣ M/M M/M �������� ���� ΛΣ � � ���� ��� �������� ��� ��� Guillot et. al. (2013) Steiner et. al. (2012) � � � � � �� �� �� �� �� � � � �� �� �� �� �� ������ ������ • Maximum mass exceeds 2 solar mass, no matter what kind of H-EOS is taken • Radius is essentially controlled by hadronic EOS.

  12. Results (2): Sound Velocity 10/16 M-R relation (¯ ρ , Γ ) = (3 ρ 0 , ρ 0 ) g v = G S ��� � ��������������������������� � � ������� � � � ������� � �������������� � ��� � � ���� � � ���������������� ����� ��� ��� � � ���� � ����������� M/M � � �� � � ���� � ��� ��� ��� ����� � � � � � � � � � � � � � �� �� �� �� �� ��� � ������ • The emergence of strangeness softens EOS • Due to the interpolation, the sound velocity increases rapidly in the crossover region

  13. Results (3): Strangeness Core 11/16 ρ − r relation (¯ ρ , Γ ) = (3 ρ 0 , ρ 0 ) g v = G S 2 M � 1 . 44 M � g V = G S 2 M � M � 1 . 44 M � Typical NSs with universal 3-body force do not include strangeness inside themselves possibility of solving cooling problem

  14. Color Superconductivity (CSC) 12/16 • Chiral Condensate • Diquark Condensate µ E Fermi Sea p Dirac Sea Alford • NJL model L CSC = L NJL + H H = 3 q T )( q T Ci γ 5 τ A λ A 0 q ) X X (¯ qi γ 5 τ A λ A 0 C ¯ 4 G s 2 A =2 , 5 , 7 A 0 =2 , 5 , 7 (Fierz)

  15. H = 3 Results (4): Case 1 4 G s 13/16 g v = 0 ��� �� � � �� � ������� ��� � � �� � ������������������������ ��� �� ��������� �� ��� �� ��� �� ��� �� ������� ������� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ������������������������������ ������������������������������

  16. Results (5): Case 2 14/16 H = G s g v = 0 ��� ��� � � ������� ��� � � � ������������������������ � ��� ��� ��������� ��� ��� �� ��� ������� ������� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ������������������������������ ������������������������������ 2SC phase u d u d u d

  17. Results (6): Effects of CSC 15/16 J P = 0 + Diquark condensation with L CSC = L NJL + H q T )( q T Ci γ 5 τ A λ A 0 q ) X X (¯ qi γ 5 τ A λ A 0 C ¯ 2 A =2 , 5 , 7 A 0 =2 , 5 , 7 H = 3 4 G s M-R relation (¯ ρ , Γ ) = (3 ρ 0 , ρ 0 ) g v = G S ��� ��� � � �� � � �� � � �������������� �������������� � � ����� ����� ��� ��� ����������� ����������� M/M M/M � � ��� ��� without CSC with CSC � � � � �� �� �� �� �� � � �� �� �� �� �� ������ ������ • CSC softens EOS, but the effects of CSC is very small

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