Hadron-quark phase transition in hybrid stars Introduction Hybrid Star and first insights for generating a new Modeling Model supernova EOS Parameterscan Setup Results Alford’s Classification of Hybrid Stars Oliver Heinimann Quark Models F.-K. Thielemann, Matthias Hempel Interacting Results Where to search University of Basel Summary Department of Physics 17.08.2015 1 / 22
Overview 1 Introduction 2 Hybrid Star Modeling Introduction Model Hybrid Star Modeling Model 3 Parameterscan Parameterscan Setup Setup Results Results Alford’s Classification of Hybrid Stars Alford’s Classification of Hybrid Stars Quark Models Interacting 4 Quark Models Results Where to search Interacting Summary Results Where to search 5 Summary 2 / 22
Quark matter in SN and NS Introduction Hybrid Star Modeling Model Parameterscan Setup Results Alford’s Classification of Hybrid Stars Quark Models Interacting Results Where to search Figure : Type IIb Supernova SN 1993J Summary Source: http://imgsrc.hubblesite.org/hu/db/images/ Figure : Cross-section NS hs-2004-29-b-full_jpg.jpg Source: Dany Page, http://inspirehep.net/record/1266411/plots 3 / 22
Hadron-Quark Phase Transition in NS Observations 2 precise measurements of 2 M ⊙ neutron stars. Introduction Demorest pulsar: PSR J1614-2230, Hybrid Star (1.97 ± 0.04) M ⊙ . Modeling Antoniadis pulsar: PSR J0348+0432, Model (2.01 ± 0.04) M ⊙ . Parameterscan Setup Results Quark matter (QM) plausible due to high Alford’s densities in the core of NS. Classification of Hybrid Stars Pure quark stars possible (Witten 1984), as well Quark Models as hybrid stars. Interacting Inset of QM leads to softening of EOS → Results Where to search lowering of maximum mass. 2 M ⊙ NS are possible (Benic 2014, Weissenborn Summary Figure : Cross-section NS 2011, Alford 2005, 2013, Blaschke 2015) Source: Dany Page, http://inspirehep.net/record/1266411/plots 4 / 22
Hadron-Quark Phase Transition in SN Working mechanism shown by Sagert et al. (2009) Introduction Second collapse → second shockwave Hybrid Star → triggers delayed SN explosion Modeling 2nd shockwave visible in ν signal Model Parameterscan Works in 1D Setup Promising due to high explosion Results Alford’s energies and self-consistent Classification of Hybrid Stars mechanism. Quark Models Interacting Results Problem Where to search Figure : Type IIb Supernova Until now, only shown with EOS that do Summary SN 1993J not support 2 M ⊙ NS. Source: http://imgsrc.hubblesite.org/hu/ db/images/hs-2004-29-b-full_jpg.jpg 5 / 22
SN to NS Introduction Hybrid Star Modeling Model Parameterscan Setup Results Alford’s Classification of Hybrid Stars Quark Models Interacting Results Where to search Summary Figure : SN and NS 6 / 22
Key Questions Introduction Hybrid Star Modeling Which kind of hybrid stars are still possible? → Model Parameterscan Classification Setup Results Which quark models are compatible? Alford’s Classification of Hybrid Stars Which parameter configuration might be promising for a Quark Models new SN EOS? Interacting Results Where to search Summary 7 / 22
Hybrid Star Model Definition Hybrid stars are neutron stars that consist of both, hadronic and quark Introduction matter. Hybrid Star Modeling Overview of the model used: Model Scenario introduced by Alford et al. (2013) Parameterscan Setup Hadronic phase: HS(DD2) (new) Results Quark phase: Constant Speed of Sound approach (CSS) with Alford’s Classification of Hybrid Stars density independent speed of sound (Alford 2013) Quark Models Phase transition: Maxwell construction (Alford 2013) Interacting Results Where to search Summary 8 / 22
Hadronic EOS: HS(DD2) Supernova EOS table at finite temperature and variable proton fraction available Introduction (Hempel & Schaffner-Bielich 2010, Fischer et al. 2014). Hybrid Star Density-dependent relativistic mean field theory Modeling Model (DD2, Typel et al. 2010) Parameterscan Matter consists of n, p, e, A Setup Results Alford’s Nuclear matter properties are in good agreement with Classification of Hybrid Stars many different nuclear experiments. Quark Models Interacting Maximum mass: 2.42 M ⊙ Results Where to search Summary Important HS(DD2) EOS describes neutron star from crust to the outer core self-consistently. In this work: HS(DD2) at T = 0.1 MeV and β -equilibrium. 9 / 22
Quark EOS In this work: Generic quark EOS proposed by Alford et al. Constant Speed of Sound EOS Introduction Hybrid Star ǫ QM ( p ) = c − 2 QM ( p − p trans ) Modeling Model Parameterscan Properties: Setup Results density-independent speed of sound c QM Alford’s Classification of c 2 QM = 1 / 3 corresponds to weakly interacting massless quarks. Hybrid Stars c 2 Quark Models QM = 1 corresponds to strongly interacting quarks. Maximal Interacting value to be still consistent with SRT. Results Where to search Isn’t it too simple? Summary CSS shows good agreement for case c 2 QM = 1 / 3 to more sophisticated models, as e.g. Nambu-Jona-Lasinio (NJL) (e.g. Beni´ c 2014), Field-Correlator-Method (FCM) (Zappala 2014), pertubative quark matter EOS (pQCD) (Kurkela et al. 2010). 10 / 22
The Hybrid EOS Maxwell Construction 1st order phase transition Introduction with a density jump at Hybrid Star constant pressure from Modeling hadron to quark matter, Model based on local charge Parameterscan neutrality. Setup Results Alford’s Classification of Hybrid Stars Quark Models Interacting Results Where to search Figure : Schematic representation of the hybrid star EOS used Source: Summary Alford, 2013 � ǫ HS ( DD 2) ( p ) p < p trans ǫ ( p ) = ǫ HS ( DD 2) ( p trans ) + ∆ ǫ + c − 2 QM ( p − p trans ) p > p trans 11 / 22
Sequence of Calculations Introduction Hybrid Star Modeling Model Parameterscan Setup Results Alford’s Classification of Determination of M-R relation by p trans / ε trans vs. ∆ε / ε Hybrid Stars solving TOV equations. Parameter Combinations Quark Models 1.2 Variation of input parameters p trans , ∆ ǫ . Interacting 1 60 x 60 parameter combinations Results Where to search p trans min = 1 · 10 − 4 MeV/fm 3 0.8 ∆ε / ε Summary ( n B ∼ 0 . 10 fm − 3 ) 0.6 p trans max ≈ 700 MeV/fm 3 0.4 ( n B ∼ 0 . 96 fm − 3 ) 0.2 c 2 QM 0 = 1 / 3 0 0 0.1 0.2 0.3 0.4 0.5 0.6 ∆ ǫ/ǫ = [0 , 1 . 2] p trans / ε trans 12 / 22
Results: Mass-Distribution M vs. p trans / ε trans and ∆ε / ε Introduction Hybrid Star Modeling 3.2 M [M ⊙ ] 3.2 3 Model 3 3 2.8 2.8 2.8 Parameterscan 2.6 2.6 2.6 Setup 2.4 2.4 2.4 M [M ⊙ ] Results 2.2 2.2 2.2 2 2 Alford’s 2 Classification of 1.8 1.8 Hybrid Stars 1.8 1.6 1.6 1.6 1.4 1.4 Quark Models 1.2 1.4 1.2 Interacting 1.2 Results 1 Where to search 0.8 Summary 0.6 ∆ε / ε 0.4 0 0.1 0.2 0.2 0.3 0.4 0 0.5 0.6 p trans / ε trans 13 / 22
Mass-Distribution: Contour Lines M vs. p trans / ε trans and ∆ε / ε Introduction 1.2 Hybrid Star Masses over maximum Modeling 1 mass of HS(DD2) Model 0.8 (M max = 2.42 M ⊙ ) M [M ⊙ ] Parameterscan 3 Stars with high 0.6 ∆ε / ε Setup 2.5 maximum masses are Results 2 0.4 1.5 Alford’s almost pure quark Classification of Hybrid Stars stars. 0.2 Quark Models 0 Interacting 0 0.1 0.2 0.3 0.4 0.5 0.6 Results Where to search p trans / ε trans Summary 14 / 22
Alford’s Classification of Hybrid Stars Introduction Hybrid Star Modeling Model Parameterscan Setup Results Alford’s Classification of Hybrid Stars Figure : Four different possible M-R relation curves Source: Alford, 2013 Quark Models Interacting Results Where to search Two criteria for distinction: Summary Third family and continuous hybrid branch Third family: Hadronic phase building up → set in phase transition → phase of instability → new stable branch Case b) and d): 2 staged collapse → interesting for SN 15 / 22
Results: Alfords Cases and Mass Contour Lines All Four Alfordcases: p trans / ε trans vs. ∆ε / ε 1.2 Introduction d a 1 Hybrid Star 0.8 1.5 Modeling ∆ε / ε b Model 0.6 Parameterscan c 0.4 Setup Results Stable Hybrid Star Line 0.2 Alford’s 2.5 2 Analytic criterion derived Classification of 0 by Seidov 1971 Hybrid Stars 0.1 0.2 0.3 0.4 0.5 0.6 Quark Models ∆ ǫ crit = 1 2 + 3 p trans / ε trans p trans ǫ trans 2 ǫ trans Interacting Results Alford case b Alford case c Where to search Alford case d Stable Hybrid Star Line Alford case a Contour Lines Maximum Mass Summary 16 / 22
Comparison of Quark Models Introduction Hybrid Star Modeling Model CSS is not a common parameterization for quark models! Parameterscan Setup Often bag model is used. Results Alford’s Classification of Question: How do these models compare to the CSS Hybrid Stars model used before? Quark Models Interacting Results Where to search Summary 17 / 22
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