Hadron-Quark Crossover and Neutron Star Observations

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1 Hadron-Quark Crossover and Neutron Star Observations Kota Masuda (Univ. of Tokyo / RIKEN) with Tetsuo Hatsuda (RIKEN) and Tatsuyuki Takatsuka (RIKEN) Neutron star matter in view of nuclear experiments and astronomical observations, 25th Oct., 2013

2 Introduction: NS observations 1/13 NS observations QCD phase diagram Fukushima, Hatsuda (2010) Mass (1.97 ± 0.04)M (2.01 ± 0.04)M Cooling Cooling of CAS-A Demorest et al. (2010) Antoniadis et al. (2013) Heinke et al. (2010) EOS Are there any EOS which can explain 2M NS The fate of the quark matter inside a heavy NS Superfluid / Superconducting phase Relation to nucleon and quark superfluidity inside NSs

3 Hadronic EOSs 2/13 (1) (2) (3) AV18+TBF TNI2 SCL3 Hyperons Method BHF BHF RMF M/M ΛΣ 2NF AV18 Reid 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 1.44M

4 Hadronic EOSs 2/13 TNI2 TNI2u M/M ΛΣ ``NNN Yes Yes ``NNY ``NYY ``YYY No Yes Universal 3-body force stiffens EOS Maximum mass is larger than 1.44M However maximum mass cannot exceed 2M

5 Hadron-Quark Crossover 3/13 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)

6 Method of Interpolation 4/13 Phenomenological interpolation: P ( ) P = p H f + p Q f + P = ) f ± = 1 ± tanh( ) 2 Pressure (P) hadron crossover quark 0 Condition for : f + < 0.1 at 0 > 0 +2

7 EOS at 5/13 (2+1)-flavor NJL Lagrangian (u,d,s, e,µ ) g v L NJL = q(i@ m)q+ G 8X s [(q a q) 2 +(qi a 5 q) 2 ] 2 +G D [detq(1 + 5 )q +h.c.] Parameter set cutoff (MeV) a=0 G s 2 G D 5 m u,d (MeV) m s (MeV) 0 apple g v apple 1.5G s Conditions: Hatsuda and Kunihiro (1994) 2 ( q µ q) 2 1. beta-equilibrium 2. charge neutrality Recent estimate of g V apple = T c d 2 T c (µ) dµ 2 µ 2 =0 g V G S g V 0 : repulsive g V /G S Bratovic et al., Phys. Lett. B719 (2013)

8 Results (1): Effects of Q-EOS 6/13 M-R relation (, )=(3 0, 0 ) g v = G S M/M ΛΣ M/M ΛΣ Maximum mass exceeds 2 solar mass, no matter what kind of H-EOS is taken

9 Results (2): Radius 7/13 Hadronic EOSs M-R relation (, )=(3 0, 0 ) g v = G S ΛΣ M/M km Guillot et. al. (2013) We use WFF EOS as hadronic EOS (Wiringa et. al., 1988) Radius is essentially controlled by hadronic EOS.

10 Results (3): Strangeness Core 8/13 r relation (, )=(3 0, 0 ) g v = G S 1.44M 2M g V = G S 2M 1.44M Typical NSs with universal 3-body force do not include strangeness inside themselves possibility of solving cooling problem

11 Color Superconductivity (CSC) 9/13 Chiral Condensate Diquark Condensate µ E Fermi Sea p Dirac Sea NJL model L CSC = L NJL + H 2 X X ( qi 5 A A 0C q T )(q T Ci 5 A A 0q) A=2,5,7 A 0 =2,5,7 Alford H = 3 4 G s (Fierz)

12 Results (4): Case 1 H = 3 4 G s 10/13 g v =0

13 Results (5): Case 2 H = G s 11/13 g v =0 2SC phase u d u u d d

14 Results (6): Effects of CSC 12/13 Diquark condensation with L CSC = L NJL + H X 2 J P =0 + A=2,5,7 A 0 =2,5,7 X ( qi 5 A A 0C q T )(q T Ci 5 A A 0q) M-R relation (, )=(3 0, 0 ) g v = G S H = 3 4 G s M/M M/M without CSC with CSC CSC softens EOS, but the effects of CSC is very small

15 Summary 13/13 Summary (1) Crossover occurs at relatively low densities (2) Quarks are strongly interacting at and above the crossover region EOS at T=0 (A) Interpolated EOS can become stiffer due to the presence of quark matter Observation of very massive neutron star cannot exclude the existence of the quark matter core (B) CSC phase does not have effects on the maximum mass However, CSC may have large effect on phenomena related to transport. Other Characteristics: 1. Radius is essentially controlled by hadronic EOS 2. Interpolated EOS with the repulsive 3-body force among nucleons and hyperons have a impact on the cooling problem of neutron star with hyperon core Perspective 1. Cooling with 2SC+X phase by using our hadron-quark crossover model. 2. Constraints on the EOS from other observables such as neutron star radius. Thank you!

16 Back Up Slide

17 Introduction: Massive Neutron Star Typical value of the observed mass for double NS binaries 1.4M 1.44M In 2010, NS (PSR J , NS-WD binary) with was found M =(1.97 ± 0.04)M Shapiro delay 1.97M Timing residual (μs) Orbital phase (turns) Demorest et al. (2010) Ozel et al. (2012) Key Questions: Any EOS which can explain 2 M NS The fate of the quark matter inside a heavy NS

18 Introduction: Hadronic EOSs APR Method Variational M/M 2NF AV18 3NF Yes Hyperons No Akmal et al. (1998)

19 EOS at (2+1)-flavor NJL Lagrangian (u,d,s, e,µ ) g v L NJL = q(i@ m)q+ G 8X s [(q a q) 2 +(qi a 5 q) 2 ] 2 +G D [detq(1 + 5 )q +h.c.] a=0 2 ( q µ q) 2 = T V lnz = q (M,µ e )+ l + G s X h qi q i i 2 +4G D h q i q i ih q j q j ih q k q k i q (µ e )= T X i M i = m i 2G s h q i q i i 2G D h q j q j ih q k q k i X µ i! µ e i µ i g v hq i q ii X Z l d 3 p 1 (2 ) 3 Trln T S i 1 (i! l,! p ), i 1 2 g v X hq i q ii i! 2 S 1 i = p µ e 0 M i, p 0 = i! l =(2l +1) T Gap equations: Parameter sets q i q i i =0 G s 2 G D 5 m u,d (MeV) m s (MeV) Conditions: Hatsuda and Kunihiro (1994) 0 apple g v apple 1.5G s (Fierz: G V =0.5G S ) Bratovic et al. (2012) 1. beta-equilibrium 2. charge neutrality

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

21 EOS at 13/29 Pressure P EOS becomes stiffer as g v increases due to the universal repulsion

22 Crossover at finite temperature Phenomenological Interpolation: s(t) s: entropy density, T: temperature Asakawa, Hatsuda (1995) s(t )=s h (T )w h (T )+s q (T )w q (T ) w q (T )= n 1+tanh T m 1 tanh T T c + n 1+tanh T T c T c "/T 4 (" 3P )/T 4 P/T 4 Phenomenological Interpolation lattice QCD Karsch (1995)

23 Interpolated EOS H-EOS: TNI2u, Q-EOS: NJL g v = G S (, )=(3 0, 0 ) In the crossover region, interpolated EOS is larger than H-EOS. Rapid stiffening of the EOS in the crossover region

24 Results (2): Effects of parameters How maximum mass depends on, 3 0 g v = G s / 0 =1 / 0 =2 g v =1.5G s g v = G s g v =1.5G s Crossover occurs at relatively low densities and quarks are strongly interacting 2M

25 Results (2): Effects of Crossover Density ( ) M-R relation = 0 g v = G S M/M =6 0 =3 0 Crossover occurs at relatively low densities 2M

26 Results (3): Effects of Vector Int. ( ) g V M-R relation (, )=(3 0, 0 ) M/M The maximum mass exceeds 2M as strong as the scalar interaction only if the vector type repulsion is Radius: about 11km

27 Results (3): Sound Velocity M-R relation (, )=(3 0, 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

28 CSC Lagrangian L CSC = L NJL + H 2 X X A=2,5,7 A 0 =2,5,7 ( qi 5 A A 0C q T )(q T Ci 5 A A 0q) q C = C q T = 1 p 2 q q C H = 3 4 G s by Fierz 1 = Hs 55, 2 = Hs 77, 3 = Hs 22 (T,µ u,d,s )= T 2 X ` Z d 3 p S 1 (2 ) 3 Trln (i!`, p) T + G S X i 2 i S 1 = S S0 1 +4G D u d s 1 2 g V ( ) ab = X color " c " abc c 5, X i n i! H X color + = 0 ( ) 0 c 2 S 1 0± = p M ± µ 0 µ = µ 1 2 µ p 3 µ 8

29 CSC Lagrangian (2) p = X i=1,36 Z 0 dpp 2 " i +2T ln Buballa (2004) 1+e " i/t G s X i 2 i Gap i 4G D u d s g V X i n 2 i! 2 1 2H X color c 2 0 µ r d + M d p 0 3 p µ r d M d µ g u + M u p 1 C A 0 µ r d M d p 0 3 B p µ r + M d µ g u M u p 1 C A 0 µ r s + M s p 0 2 p µ r s M s µ b u + M u p 1 C A 3 0 p µ g u M u 3 0 p µ g u + M u 2 0 p µ b u M u 0 µ r s M s p 0 2 B p µ r s + M s µ b u M u p 1 C A 0 µ g s + M s p 0 1 p µ g s M s µ b d + M u p 1 C A 0 µ g s M s p 0 1 B p µ g s + M s µ b d M u p 1 C A 2 0 p µ b u + M u 1 0 p µ b d M d 1 0 p µ b d + M d

30 Results (5): Case 1 H = 3 4 G s g v =0 Gap Parameters [MeV] Δ 3 Δ 2 Δ M 2 S /μ [MeV] CFL gcfl Ms 2 /(µ ) Alford (2004)

31 Results (5): Gap parameter g v =0 Dispersion relation (bd-gs) gapless phase

32 Another Interpolation 21/29 Phenomenological interpolation: "( ) " = " H f + " Q f + P = ) f ± = 1 ± tanh( ) 2 H-EOS: TNI2u, Q-EOS: NJL (, )=(3 0, 0 ) g v =0.5G s

33 Results (7): Effects of Method 22/29 M-R relation (, )=(3 0, 0 ) M/M M/M P ( ) "( ) The " -interpolation makes EOS stiff more drastically than the P-interpolation. Even for (g v, ) =(0, 3 0 ), the maximum mass can exceed 1.97M

34 Crossover vs. 1st order Transition 15/16 Pressure (P) ``H ``QM Crossover 1st order Transition Pressure (P) ``H ``QM Baryon chemical potential (µ) ``QM Baryon chemical potential (µ) Pressure (P) Pressure (P) ``H hadron crossover quark ``H ``QM Baryon density ( ) ``QM stiffens EOS ``QM softens EOS M>2M M<2M

35 Crossover vs. 1st order Transition (Example) In the case of g V =1.0, 1.5G S, H-EOS and Q-EOS do not cross at all densities

36 Neutron Star Observation Observables: binary period P b projection of the pulsar s semimajor axis on the line of sight eccentricity e time of periastron T 0 longitude of periastron! 0 x asini/c mass function f = (m 2sini) 3 M 2 + General relativity effects: Plane+of+the+sky the advance of periastron of the orbit Doppler + gravitational redshift the orbital decay P b range parameter shape parameter r s! centre+of+mass! 0 i ascending+node periastron Shapiro delay: =2rlog 1+ecos 1 ssin(! + ) Mass fraction f + 2 general relativity effects Mass estimation Observer

37 Universal 3-body force TNI model Urbana UIX model

38 H-EOS: Universal 3-body force 3-body force is needed for saturation property Akmal et al. (1998) From the point of view of NS observation, 3-body force is needed for the stiffness of EOS 3-body force between YN and YY can delay the appearance of the exotic components Universal 3-body force TNI3 TNI3u TNI model: G-matrix NN : Reid soft-core potential YN,YY: Nijmegen type-d hard-core potential TNI2(3): κ=250(300)mev Nishizaki et al. (2002)

39 Cooling Problem Rapid cooling is occurred by hyperons (Y-Durca) κ=280mev! p + l + l,p+ l! + l! + l + l, + l! + l Y-mixed Tsuruta et al. (2009)