Neutron Star Matter with In-Medium Meson Mass C. H. Hyun, M. H Kim, - PowerPoint PPT Presentation

Neutron Star Matter with In-Medium Meson Mass C. H. Hyun, M. H Kim, S. W. Hong Sungkyunkwan University B. K. Jennings TRIUMF Origin of Matter and Evolution of the Galaxies, November 17 – 19, 2003, RIKEN, Wako, Japan

Outline 1. Introduction 2. Models 3. Results for neutron star matter 4. Summary

OMEG03 I 1 Introduction ⋆ Possible indication of hadron mass decrease in nuclear medium � Theory – Brown-Rho (BR) scaling (Brown and Rho, PRL66 (1991) 2720) ≈ m ∗ m ∗ ≈ m ∗ ≈ m ∗ ρ σ ω N . (1) m N m σ m ω m ρ – QCD-sum rule (Hatsuda and Lee, PRC46 (1992) R34) ≈ m ∗ m ∗ ρ ω ≃ 0 . 82 . (2) m ρ m ω – Quark-meson-coupling model (Saito, Tsushima and Thomas, PRC55 (1997) 4050) ≃ 0 . 79 , m ∗ m ∗ ≈ m ∗ ρ N ω ≃ 0 . 83 . (3) m N m ρ m ω

OMEG03 II � Experiment : Dilepton decay of ρ - and ω - mesons – KEK-PS E325 (Ozawa et al. , PRL86 (2001) 5019) – CERES/NA45 Collab. (Adamov´ a et al. , PRL 91 (2003) 042301) ⋆ Contraints of symmetric nuclear matter at saturation density � E B = 16MeV at ρ 0 = 0 . 17 fm − 3 � m ∗ N = (0 . 7 ∼ 0 . 8) m N � K = 200 ∼ 300MeV � a sym = 32 . 5MeV ⋆ Neutron star (NS) : Narrow mass zone (Thorsett and Chakrabarty, ApJ. 512 (1999) 288) M NS = (1 . 0 ∼ 1 . 6) M ⊙ (4) ⋆ Question : Can the properties of NS be affected by meson-mass changes in matter? Constant meson mass vs Density-dependent meson mass

OMEG03 III 2 Models ⋆ Models with constant meson mass (1) Walecka model (QHD) L MF QHD = L 0 + U (¯ σ ) , � � ω 0 − 1 ψ N − 1 σ 2 + 1 0 + 1 N − g ωN γ 0 ¯ 2 g ρN γ 0 ¯ L 0 = ¯ ρ ¯ iγ µ ∂ µ − m ∗ 2 m 2 2 m 2 ω 2 2 m 2 b 2 ψ N b 03 τ 3 σ ¯ ω ¯ 03 , m ∗ N = m N − g σN ¯ σ, σ ) = 1 σ ) 3 + 1 σ ) 4 . U (¯ 3 m N b ( g σN ¯ 4 c ( g σN ¯ ω 0 , ¯ – ¯ σ, ¯ b 03 : Mean field equation of motion – g σN , g ωN , b, c : From E B , ρ 0 , m ∗ N , K – g ρN : From a sym

OMEG03 IV (2) Modified Quark-meson coupling model (MQMC) (X. Jin and B. K. Jennings, PRC54 (1996) 1427) ω 0 − 1 ω γ 0 ¯ ρ γ 0 ¯ MQMC = ¯ ψ q [ iγ µ ∂ µ − ( m 0 q − g q σ ) − g q 2 g q L MF σ ¯ b 03 τ 3 − B ] × θ V ( R − r ) ψ q − 1 σ 2 + 1 0 + 1 ρ ¯ 2 m 2 2 m 2 ω 2 2 m 2 b 2 σ ¯ ω ¯ 03 , �� − 3 x 2 � 2 q m ∗ E N N = R 2 , bag bag = 3Ω q R − Z N R + 4 E N 3 πR 3 B, � q − g q ( m ∗ q = m 0 x 2 q + R 2 m ∗ 2 Ω q = q , σ ¯ σ ) , � δ � 4 σ ¯ 1 − g B B = B 0 σ δ m N – B 0 , Z N : From m N = 939 MeV at R = 0 . 6 fm – g q σ , g q ω , g B σ , δ : From E B , ρ 0 , m ∗ N , K – g q ρ : From a sym

OMEG03 V ⋆ Models with density-dependent meson mass (1) BR-scaled effective chiral Lagrangian (QHD-BR) (C. Song et al. , PRC56 (1997) 2244) L = L 0 ( m σ → m ∗ σ , m V → m ∗ V , g V N → g ∗ V N ) , ( V = ω, ρ ) m ∗ N = M ∗ N − g σN ¯ σ, � − 1 M ∗ = m ∗ = m ∗ � 1 + y ρ N σ V = , m N m σ m V ρ 0 � − 1 g ∗ � 1 + z ρ V N = g V N ρ 0 – g σN , g ωN , y, z : From E B , ρ 0 , m ∗ N , K (2) MQMC with scaled meson mass (SMQMC) L = L MF MQMC ( m σ → m ∗ σ , m V → m ∗ V ) – More parameters than the number of contraints : y fitted to BR-scaling law

OMEG03 VI (3) MQMC with meson bag (MQMC-MB) L = L MF MQMC ( m V → m ∗ V ) , �� − 2 x 2 � 2 q m ∗ E V V = R 2 , bag bag = 2Ω q R − Z V R + 4 3 π R 3 B E V – Z V : From m V (770 MeV for ρ -meson and 783 MeV for ω -meson) ⋆ Properties at the saturation Constant meson mass Density dependent meson mass QHD MQMC QHD-BR SMQMC MQMC-MB m ∗ N /m N 0.77 0.78 0.67 0.76 0.85 m ∗ V /m V 1.0 1.0 0.78 0.78 0.86 K (MeV) 311 286 265 592 324

OMEG03 VII 3 Results for neutron star matter ⋆ Equation of state (EoS) 700 700 600 QHD 600 MQMC QHD-BR SMQMC 500 500 P (MeV/fm 3 ) MQMC-MB 400 400 300 300 200 200 100 100 0 0 0 100 300 500 700 0 100 300 500 700 ε (MeV/fm 3 ) ε (MeV/fm 3 ) � Stiffer equation of state → Larger maximum mass of NS

OMEG03 VIII � Why is the EoS so stiff? P ≃ − P σ + P ω + P ρ + P N , P σ = 1 P ω = 1 P ρ = 1 ρ ¯ 2 m ∗ 2 σ 2 , 2 m ∗ 2 ω 2 2 m ∗ 2 b 2 σ ¯ ω ¯ 0 , 30 , � k N k 4 1 � P N = dk. k 2 + m ∗ 2 3 π 2 � 0 N N = n,p 250 250 P N P N QHD QHD-BR P σ P σ 200 200 P ω P ω P (MeV/fm 3 ) P ρ P ρ 150 150 100 100 50 50 0 0 0 1 2 3 4 0 1 2 3 4 ρ / ρ 0 ρ / ρ 0

OMEG03 IX ⋆ Particle fraction : ρ i /ρ ( i = n, p, e, µ ) 1 1 QHD QHD-BR Particle Fraction 0.1 0.1 n p n 0.01 e 0.01 p µ e µ 0.001 0 0.5 1 1.5 2 2.5 3 3.5 4 0.001 0 0.5 1 1.5 2 2.5 3 3.5 4 ρ / ρ 0 1 1 1 MQMC SMQMC MQMC-MB 0.1 0.1 0.1 n n n p p p 0.01 0.01 0.01 e e e µ µ µ 0.001 0.001 0.001 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4

OMEG03 X 4 Summary ⋆ The effect of density-dependent meson mass on the properties of NS matter was investigated. ⋆ EoS is sensitive to the behavior of meson mass. ⋆ Hyperon degrees of freedom need to be included. ⋆ Many possibilities are still wide open.