Compact Stars within a SU(3) chiral Quark Meson Model Andreas Zacchi 1 Matthias Hanauske 1 , 3 Laura Tolos 2 urgen Schaffner-Bielich 1 J¨ 1 Institute for Theoretical Physics Goethe University Frankfurt 2 Institut de Ciencies de l Espai Bellaterra, Spain 3 FIAS Frankfurt Institute for Advanced Studies Astro coffee, January 17 2017
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Abstract Compact Objects and Ultradense Matter 1 Micro,- Macrophysics and constraints 2 The SU(3) Quark Meson Model 3 Compact Stars 4 Summary and Outlook 5 (2 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Supernova remnants: Compact stars Compact stars are either: Neutron stars (consisting mainly of neutrons) Hybrid stars (consisting of a hadronic shell and a quark-matter core) Quark stars (consisting of quark matter only) Size: R ≈ 10 − 15km Mass: M ≈ 1 . 5 M ⊙ Density: Credit: Chandra X-ray observatory (NASA) ρ 0 ≈ 2 . 5 · 10 14 g cm 3 ≈ 145 MeV fm 3 (3 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Different types of compact stars 2 Neutron Star Quark Star sequence sequence Characteristic mass radius M/M sun relations of 1 1 Neutron Stars ( M ∝ R − 3 ) 0 5 10 15 5 10 15 2 Quark Stars ( M ∝ R 3 ) 2 2 2 Hybrid Star Hybrid Star Hybrid Star Twin Star Twin Star 3 Hybrid Stars (Can sequences sequences sequences sequences sequences M/M sun M/M sun M/M sun masquerade as Neutron star) 1 1 1 4 Twin Stars (Two stable branches) 0 0 0 5 5 5 10 10 10 15 15 15 5 5 10 10 15 15 20 20 R[km] R[km] R[km] R[km] R[km] (4 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook The stars interior What do certain models predict for the star to consist of? 1 ...just neutrons? 2 ...hyperons? 3 ...kaon condensates? 4 ...quark matter (QM)? 5 ...color superconducting QM? → Equation of state (EoS) Credit: Fridolin Weber (5 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Constraints on different solutions Schwarzschild Radius → R > 2 GM / c 2 1 P < ∞ → R > 9 GM / 4 c 2 2 Causality → R > 2 . 9 GM / c 2 3 Star can not spin faster than 716Hz 4 � 1 / 2 � R nr � � 3 / 2 → 1 M ⊙ ν ≃ (0 . 96 ± 0 . 03) M nr 10 km Solutions need to fulfill the 2 M ⊙ 5 constraint → next slide Credit: Lattimer and Prakash (6 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook New pulsar mass measurements Recent measurements 1 Demorest et. al; 2010 PSR J1614-2230 with M = 1 . 97 ± 0 . 04 M ⊙ 2 Fonseca et. al; 2016 PSR J1614-2230 with M = 1 . 928 ± 0 . 017 M ⊙ 3 Antoniadis et. al; 2013 PSR J0348+0432 with M = 2 . 01 ± 0 . 04 M ⊙ ...also a constraint for quark Credit: Science Magazine matter based stars? (7 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Skalar and vector nonet Skalar and vector nonet as a base to constuct Lagrangian density σ n + a 0 a + K + 0 √ s 0 2 1 σ n − a 0 ϕ = √ a − K 0 0 √ 0 s 2 2 ¯ K − K 0 σ s s s ω µ n + ρ µ 0 ρ µ + K ∗ µ + √ 2 1 V µ = ω µ n − ρ µ 0 √ ρ µ − K ∗ µ 0 √ 2 2 ¯ K ∗ µ − K ∗ µ 0 φ µ (8 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook The SU(3) Quark Meson Model SU(3) Lagrangian L = L F n , s + L ϕ + L V ¯ ∂ − g ω γ 0 ω − g ρ � τγ 0 ρ − g φ γ 0 φ − g n , s σ n , s � � = Ψ n , s i ✓ Ψ n , s L F n , s tr ( ∂ µ ϕ ) † ( ∂ µ ϕ ) − λ 1 [ tr ( ϕ † ϕ )] 2 − λ 2 tr ( ϕ † ϕ ) 2 = L ϕ � � 0 tr ( ϕ † ϕ ) − tr [ ˆ m 2 H ( ϕ + ϕ † )] + c det( ϕ † ) + det( ϕ ) − tr ( ∂ µ V ) † ( ∂ µ V ) − m 2 v tr ( V † V ) = L V couples quarks to mesons via Yukawa type coupling effective quark masses generated by the σ n and σ s -fields ω , ρ and φ : vector mesons as repulsive mediators (9 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Symmetries of QCD realized in the SU(3) Quark Meson Model L = L F n , s + L ϕ + L V respects symmetries of QCD Apart from color- and flavour symmetry, L exhibits chiral symmetry spontaneously broken due to chiral condensate < ¯ Ψ n , s Ψ n , s > explicitly broken due to non vanishing quark masses m q � = 0 Restoration of chiral symmetry Chiral symmetry restored at high densities, i.e. chemical potential µ q Quarks (nearly) massless Right handed and left handed quarks are (nearly) indistinguishable (10 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook The EoS from the SU(3) Quark Meson model at T = 0 Once the pressure is known... s ) − m 2 s ) + σ 2 λ 1 s ) 2 − λ 2 n σ s 4 ( σ 2 n + σ 2 4 ( σ 4 n + σ 4 2 ( σ 2 0 n + σ 2 p = √ − c 2 2 + h n σ n + h s σ s − B + 1 ω ω 2 + m 2 ρ ρ 2 + m 2 m 2 φ φ 2 � � 2 � k f �� � − 3 F � k 2 + ˜ dk · k 2 m 2 f − ˜ µ f π 2 0 f = u , d , s ... the energy density follows from the Gibbs-Duhem relation, F ) 3 /π 2 is the density associated f µ f n f , where n f = ( k f Ω = ǫ + � to each quark flavour. (11 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Important Parameters of the model √ Repulsive vector meson coupling g ω = g ρ = 2 g φ Models the repulsive interaction (0 ≤ g ω ≤ 10) The Bag constant B 1 / 4 B 1 / 4 acts as an additive vacuum pressure (0 ≤ B 1 / 4 ≤ 150 MeV) (Depending on the used model) Sigma meson mass m σ experimentally not well determined Variation: 400 ≤ m σ ≤ 1000 MeV (12 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Hybrid stars: Maxwell construction SU(3)-EoS for the ultradense core and DD2-EoS for the stars outer layer 800 2.5 B=80MeV B=80MeV 700 B=100MeV B=100MeV B=120MeV 2 B=120MeV B=140MeV 2 600 B=140MeV B=160MeV 1 B=160MeV B=180MeV 0 B=180MeV 500 0 100 200 DD2 1.5 DD2 p [MeV] M/M sun 400 1 300 200 0.5 100 0 0 0 500 1000 1500 2000 0 5 10 15 20 25 ε [MeV] R(km) The other papameters: m q = 300 MeV, m σ = 600 MeV and g ω = 0 (13 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
Compact Objects and Ultradense Matter Micro,- Macrophysics and constraints The SU(3) Quark Meson Model Compact Stars Summary and Outlook Hybrid Stars → Twin Stars 800 1.8 Set A Set A unstable 700 Set B Set A stable 1.6 Set C Set B unstable DD2 600 Set B stable Set C unstable 500 1.4 Set C stable p [MeV/fm 3 ] M/M sun 400 1.2 300 200 1 100 0.8 0 0 500 1000 1500 2000 7 8 9 10 11 12 13 14 ε [MeV/fm 3 ] R(km) Parametrizied quark matter EoS yields Twin Stars with: ǫ ∗ := ǫ t + ∆ ǫ − 1 p ( ǫ ) = c 2 s ( ǫ − ǫ ∗ ) , p t , c 2 s Transition pressure p t and jump in energy density ∆ ǫ under direct influence ( c 2 s = 1 3 ) (14 / 25) Compact Stars within a SU(3) Quark Meson model Zacchi, Hanauske, Tolos, Schaffner-Bielich
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