Equation of state for hybrid stars with strangeness

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1 Equation of state for hybrid stars with strangeness Tsuyoshi Miyatsu, Takahide Kambe, and Koichi Saito Department of Physics, Faculty of Science and Technology, Tokyo University of Science The 26th International Nuclear Physics Conference Adelaide, Australia September 12, 2016 T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 1/11

2 Table of contents 1 Introduction 2 Hadronic EoS for neutron stars 3 Hadron-quark phase transition in a neutron star 4 Summary T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 2/11

3 Introduction The equations of state (EoSs) for neutron stars should be satisfied with the nuclear properties and the astrophysical constrains. Since the discovery of massive neutron stars, the discrepancy between the observations and theories becomes a big problem (2M problem). PSR J with 1.97 ± 0.04M : P. B. Demorest et al., Nature 467 (2010) and PSR J with 2.01 ± 0.04M : J. Antoniadis et al., Science 340 (2013) Other exotic degrees of freedom are expected in the core of a neutron star: hyperons, quark matter, some unusual condensations of boson-like matter, dark matter etc. The EoS for neutron stars with hyperons and quark matter T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 3/11

Hadronic EoS for neutron stars 1 The variation in internal (quark) structure of baryons in matter using the chiral quark-meson coupling (C) model [ g σb (σ) = g σb b B 1 a ] [ ] B 2 (g σnσ), g σ B(σ

4 Hadronic EoS for neutron stars 1 The variation in internal (quark) structure of baryons in matter using the chiral quark-meson coupling (C) model [ g σb (σ) = g σb b B 1 a ] [ ] B 2 (g σnσ), g σ B(σ ) = g σ Bb B 1 a B 2 (g σ Λσ ). T. M., M. K. Cheoun, and K. Saito, Phys. Rev. C 88 (2013) Hidden strange (σ and ϕ) mesons in SU(3) flavor symmetry SU(6) symmetry based on quark model: θ v = and z = 1/ 6 SU(3) flavor symmetry: θ v = and z = T. A. Rijken, M. M. Nagels, and Y. Yamamoto, Prog. Theor. Phys. Suppl. 185 (2010) Relativistic many-body calculation: Hartree approximation: Hartree-Fock approximation: Σ Baryon self-energy tadpole exchange T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 4/11

5 Lagrangian density Lagrangian density for uniform hadronic matter: L H = L B + L M + L int. We consider the octet baryons (B): proton (p), neutron (n), Λ, Σ +0, and Ξ 0. In addition, not only the mesons which is composed of light quarks (σ, ω, π, and ρ) but also the strange quarks (σ and ϕ) are taken into account. L int = [ field-dependent C.C. using the C model ψ B g σb (σ) σ + g σ B (σ ) σ g ωb γ µ ω µ + f ωb 2M σ µν ν ω µ B g ϕb γ µ ϕ µ + f ϕb 2M σ µν ν ϕ µ g ρb γ µ ρ µ I B + f ρb 2M σ µν ν ρ µ I B f ] πb m γ 5γ µ µ Hartree-Fock approximation π I B ψ B, (tensor couplings) pion contribution (pseudovector) with M being the scale mass (= M p ). T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 5/11

6 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O C (RHF) C (RH-SU3) C (RH) Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

7 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O C (RHF) C (RH-SU3) C (RH) Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

8 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O C (RHF) C (RH-SU3) C (RH) +OGE+OPE Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

9 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O C (RHF) C (RH-SU3) C (RH) +OGE+OPE Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

10 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O C (RHF) C (RH-SU3) C (RH) SU(3) +OGE+OPE Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

11 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O C (RHF) C (RH-SU3) C (RH) Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

12 EoS for neutron stars 1 Baryon-structure variation in matter using the C model 2 SU(3) flavor symmetry 3 Relativistic many-body calculation Hartree approximation Hartree-Fock approximation These effects make the EoS stiff and the maximum mass can reach the 2M constraint. P (MeV/fm 3 ) P = ε C (RHF) C (RH-SU3) C (RH) ε (MeV/fm 3 ) K 0 (MeV) 269 M / M O RHF RH C (RHF) C (RH-SU3) C (RH) Radius (km) Hyperons are taken into account. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 6/11

13 Quark matter description EoS for quark matter MIT bag model with the density-dependent bag constant Nambu Jona-Lasinio (NJL) model: HK-type parameter set L = q ( iγ µ µ m ) q G S [( qλ a q) 2 + ( qiγ 5 λ a q) 2] a=0 [ G D detf ( q(1 + γ 5 )q) + det f ( q(1 γ 5 )q) ] 1 2 g V ( qγ µ q) 2, with a universal repulsion among different flavors, 0 g V 1.5G S. K. Masuda, T. Hatsuda, and T. Takatsuka, PTEP 2013 (2013) no.7, 073D01. Hadron-quark phase transition First-order phase transition under Gibbs criterion Hadron-quark crossover T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 7/11

14 First-order phase transition (Gibbs) Particle Fraction Y i p e µ n P HP (µ n, µ e) = P QP (µ n, µ e) = P MP (µ n, µ e) Λ Ξ u ρ (fm -3 ) d s M max = 1.98M µ c = 1334 MeV T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 8/11

Hadron-quark crossover Energy density - baryon density interpolation Pressure - baryon density interpolation Pressure - energy density interpolation P-ρ interpolation e.g. P(ϵ) = P HP (ϵ)f (ϵ) + P QP (ϵ)f + (ϵ), dρ ρ = dϵ P(ϵ)+ϵ.

15 Hadron-quark crossover Energy density - baryon density interpolation Pressure - baryon density interpolation Pressure - energy density interpolation P-ρ interpolation e.g. P(ϵ) = P HP (ϵ)f (ϵ) + P QP (ϵ)f + (ϵ), dρ ρ = dϵ P(ϵ)+ϵ. Particle Fraction Y i T. Hell and W. Weise, Phys. Rev. C 90 (2014) µ n e Λ p Ξ d u ρ (fm -3 ) Nuclear physics Crossover region moves to higher densities. Astrophysics The 2M constant s T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 9/11

16 Pressure-energy density interpolation Particle Fraction Y i d n p e µ Λ Ξ u s Ξ (g V = 1.5G S ) ρ (fm -3 ) T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 10/11

17 Particle Fraction Y i Outline Introduction Hadronic EoS Hadron-quark phase transition Summary 1.0 Pressure-energy density interpolation 0.8 d n p e µ Λ Ξ u s Ξ (g V = 1.5G S ) ρ (fm -3 ) T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 10/11 dp / d ε ε - = 1100 (MeV fm -3 ), Γ = 110 (MeV fm -3 ) ε - = 1430 (MeV fm -3 ), Γ = 190 (MeV fm -3 ) ε - = 1790 (MeV fm -3 ), Γ = 270 (MeV fm -3 ) ρ (fm -3 )

18 Particle Fraction Y i Outline Introduction Hadronic EoS Hadron-quark phase transition Summary 1.0 Pressure-energy density interpolation 0.8 n p e µ Λ Ξ u s d Ξ 0 dp / d ε ε - = 1100 (MeV fm -3 ), Γ = 110 (MeV fm -3 ) ε - = 1430 (MeV fm -3 ), Γ = 190 (MeV fm -3 ) ε - = 1790 (MeV fm -3 ), Γ = 270 (MeV fm -3 ) ρ (fm -3 ) (g ρ (fm -3 V = 1.5G S ) ) Radius (km) M / M O only hadron core 1st order phase transition (β = 0.025) ε - = 1100 (MeV fm -3 ), Γ = 110 (MeV fm -3 ) ε - = 1430 (MeV fm -3 ), Γ = 190 (MeV fm -3 ) ε - = 1790 (MeV fm -3 ), Γ = 270 (MeV fm -3 ) T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 10/11

19 Summary Hadronic EoS: 1 The variation in internal (quark) structure of baryons in matter using the chiral quark-meson coupling (C) model 2 Hidden strange (σ and ϕ) mesons in SU(3) flavor symmetry 3 Relativistic Hartree-Fock approximation The EoS with hyperons can support 2M neutron stars. Hybrid stars: Hadron-quark phase transition: first-order phase transition under Gibbs criterion and hadron-quark crossover In order to suppress the amount of quarks at low densities, the center of crossover moves to higher densities. If the stiff Hadronic and quark EoSs are taken into account, the pressure-energy density interpolation can satisfy the constrains from nuclear physics and astrophysics. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 11/11

20 Thank You for Your Attention. T. Miyatsu et.al. Equation of state for hybrid stars with strangeness 11/11

Possibility of hadron-quark coexistence in massive neutron stars

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