[PPT] - Hadron-quark phase transition in hybrid stars Introduction Hybrid PowerPoint Presentation

SLIDE 1

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Hadron-quark phase transition in hybrid stars and first insights for generating a new supernova EOS

Oliver Heinimann F.-K. Thielemann, Matthias Hempel

University of Basel Department of Physics

17.08.2015

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SLIDE 2

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Overview

1 Introduction 2 Hybrid Star Modeling

Model

3 Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

4 Quark Models

Interacting Results Where to search

5 Summary

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SLIDE 3

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Quark matter in SN and NS

Figure : Type IIb Supernova SN 1993J

Source: http://imgsrc.hubblesite.org/hu/db/images/ hs-2004-29-b-full_jpg.jpg

Figure : Cross-section NS

Source: Dany Page, http://inspirehep.net/record/1266411/plots

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SLIDE 4

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Hadron-Quark Phase Transition in NS

Figure : Cross-section NS

Source: Dany Page, http://inspirehep.net/record/1266411/plots

Observations 2 precise measurements of 2 M⊙ neutron stars. Demorest pulsar: PSR J1614-2230, (1.97 ± 0.04) M⊙. Antoniadis pulsar: PSR J0348+0432, (2.01±0.04) M⊙. Quark matter (QM) plausible due to high densities in the core of NS. Pure quark stars possible (Witten 1984), as well as hybrid stars. Inset of QM leads to softening of EOS → lowering of maximum mass. 2 M⊙ NS are possible (Benic 2014, Weissenborn 2011, Alford 2005, 2013, Blaschke 2015)

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SLIDE 5

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Hadron-Quark Phase Transition in SN

Figure : Type IIb Supernova SN 1993J

Source: http://imgsrc.hubblesite.org/hu/ db/images/hs-2004-29-b-full_jpg.jpg

Working mechanism shown by Sagert et al. (2009) Second collapse → second shockwave → triggers delayed SN explosion 2nd shockwave visible in ν signal Works in 1D Promising due to high explosion energies and self-consistent mechanism. Problem Until now, only shown with EOS that do not support 2 M⊙ NS.

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SLIDE 6

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

SN to NS

Figure : SN and NS

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SLIDE 7

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Key Questions

Which kind of hybrid stars are still possible? → Classification Which quark models are compatible? Which parameter configuration might be promising for a new SN EOS?

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SLIDE 8

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Hybrid Star Model

Definition Hybrid stars are neutron stars that consist of both, hadronic and quark matter. Overview of the model used: Scenario introduced by Alford et al. (2013) Hadronic phase: HS(DD2) (new) Quark phase: Constant Speed of Sound approach (CSS) with density independent speed of sound (Alford 2013) Phase transition: Maxwell construction (Alford 2013)

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SLIDE 9

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Hadronic EOS: HS(DD2)

Supernova EOS table at finite temperature and variable proton fraction available (Hempel & Schaffner-Bielich 2010, Fischer et al. 2014). Density-dependent relativistic mean field theory (DD2, Typel et al. 2010) Matter consists of n, p, e, A Nuclear matter properties are in good agreement with many different nuclear experiments. Maximum mass: 2.42 M⊙ 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.

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SLIDE 10

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Quark EOS

In this work: Generic quark EOS proposed by Alford et al. Constant Speed of Sound EOS ǫQM(p) = c−2

QM(p − ptrans)

Properties: density-independent speed of sound cQM c2

QM = 1/3 corresponds to weakly interacting massless quarks.

c2

QM = 1 corresponds to strongly interacting quarks. Maximal

value to be still consistent with SRT. Isn’t it too simple? CSS shows good agreement for case c2

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).

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Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

The Hybrid EOS

Figure : Schematic representation of the hybrid star EOS used Source:

Alford, 2013

ǫ(p) =

ǫHS(DD2)(p)

p < ptrans ǫHS(DD2)(ptrans) + ∆ǫ + c−2

QM(p − ptrans)

p > ptrans Maxwell Construction 1st order phase transition with a density jump at constant pressure from hadron to quark matter, based on local charge neutrality.

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SLIDE 12

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Sequence of Calculations

Determination of M-R relation by solving TOV equations. Variation of input parameters ptrans, ∆ǫ. 60 x 60 parameter combinations ptrans min = 1 · 10−4 MeV/fm3 (nB ∼ 0.10 fm−3) ptrans max ≈ 700 MeV/fm3 (nB ∼ 0.96 fm−3) c2

QM 0 = 1/3

∆ǫ/ǫ = [0, 1.2]

0.2 0.4 0.6 0.8 1 1.2 0.1 0.2 0.3 0.4 0.5 0.6 ∆ε/ε ptrans/εtrans ptrans/εtrans vs. ∆ε/ε Parameter Combinations

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SLIDE 13

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Results: Mass-Distribution

M vs. ptrans/εtrans and ∆ε/ε M [M⊙] 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 0.1 0.2 0.3 0.4 0.5 0.6 ptrans/εtrans 0.2 0.4 0.6 0.8 1 1.2 ∆ε/ε 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 M [M⊙] 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 13 / 22

SLIDE 14

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Mass-Distribution: Contour Lines

Masses over maximum mass of HS(DD2) (Mmax = 2.42 M⊙) Stars with high maximum masses are almost pure quark stars.

0.1 0.2 0.3 0.4 0.5 0.6 0.2 0.4 0.6 0.8 1 1.2 M vs. ptrans/εtrans and ∆ε/ε M [M⊙] 3 2.5 2 1.5 ptrans/εtrans ∆ε/ε 14 / 22

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Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Alford’s Classification of Hybrid Stars

Figure : Four different possible M-R relation curves Source: Alford, 2013

Two criteria for distinction: 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

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SLIDE 16

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Results: Alfords Cases and Mass Contour Lines

0.2 0.4 0.6 0.8 1 1.2 0.1 0.2 0.3 0.4 0.5 0.6 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line Contour Lines Maximum Mass 1.5 2 2.5

d b a c

Stable Hybrid Star Line Analytic criterion derived by Seidov 1971 ∆ǫcrit ǫtrans = 1 2 + 3 2 ptrans ǫtrans

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SLIDE 17

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Comparison of Quark Models

CSS is not a common parameterization for quark models! Often bag model is used. Question: How do these models compare to the CSS model used before?

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SLIDE 18

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Interacting model of Alford respectively Weissenborn 2005

Idea: Introduce phenomenological interaction term a4 (and possibly a2). Alford (Weissenborn) model ΩQM =

i=u,d,s,e

Ωi − 3µ4 4π2 (1 − a4) + Beff

Weissenborn et al. (2011)

+ 3µ2 4π2 a2

Alford et al. (2005)

a4 term accounts for strong interaction QCD corrections a2 can be interpreted as a term to take color superconductivity into

account. In this case: a2 = m2

s − 4∆2 (∆ pairing gap).

Here: Parameters are treated as generic interaction terms, which are freely varied without respect to their physical meaning. Direct identification of Weissenborn’s BAG model with CSS EOS Assumptions: ms = 0 and c2

s = 1/3, a2 = 0, non-vanishing a4 term.

a4 = 2 − π2 3 ǫ0 + P0 µ4 Beff = 1 4ǫ0 − 3 4P0

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SLIDE 19

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Interacting model with fixed a4-term, ms = 0, c2

s = 1/3 and varying B1/4

0.2 0.4 0.6 0.8 1 1.2 0.01 0.1 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε

Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line Maximum Mass CL a4 = 1 a4 = 1.1 a4 = 1.2 a4 = 1.3 a4 = 1.4 a4 = 1.5 a4 = 1.6

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SLIDE 20

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Existing hadron-quark SN EOS

B1/4 = 162 MeV Sagert et al. 2009 1.56 M⊙ explosion B1/4 = 165 MeV Sagert et al. 2009 1.50 M⊙ explosion B1/4 = 155 MeV, as = 0.3 Sagert et al. 2011 1.67 M⊙ explosion B1/4 = 139 MeV, as = 0.7 Sagert et al. 2011 2.04 M⊙ B1/4 = 145 MeV, as = 0.7 Sagert et al. 2011 1.97 M⊙

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SLIDE 21

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Restricting the parameter space

1 2 3 4 5 6 7 0.01 0.1 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε

Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line

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SLIDE 22

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Restricting the parameter space

1 2 3 4 5 6 7 0.01 0.1 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε

Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line Contour Lines Maximum Mass

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SLIDE 23

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Restricting the parameter space

1 2 3 4 5 6 7 0.01 0.1 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε

Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line Contour Lines Maximum Mass B1/4 = 139 MeV, ac = 0.7 B1/4 = 145 MeV, ac = 0.7 B1/4 = 155 MeV, ac = 0.3 B1/4 = 162 MeV, ac = 0 B1/4 = 165 MeV, ac = 0

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SLIDE 24

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Restricting the parameter space

1 2 3 4 5 6 7 0.01 0.1 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε

Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line Contour Lines Maximum Mass B1/4 = 139 MeV, ac = 0.7 B1/4 = 145 MeV, ac = 0.7 B1/4 = 155 MeV, ac = 0.3 B1/4 = 162 MeV, ac = 0 B1/4 = 165 MeV, ac = 0 ms = 100 MeV, a4 = 1.4 ms = 100 MeV, a4 = 1.48

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SLIDE 25

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Restricting the parameter space

1 2 3 4 5 6 7 0.01 0.1 ∆ε/ε ptrans/εtrans All Four Alfordcases: ptrans/εtrans vs. ∆ε/ε

Alford case b Alford case d Alford case a Alford case c Stable Hybrid Star Line Contour Lines Maximum Mass B1/4 = 139 MeV, ac = 0.7 B1/4 = 145 MeV, ac = 0.7 B1/4 = 155 MeV, ac = 0.3 B1/4 = 162 MeV, ac = 0 B1/4 = 165 MeV, ac = 0 ms = 100 MeV, a4 = 1.4 ms = 100 MeV, a4 = 1.48 Example Case

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Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

Example

0.5 1 1.5 2 2.5 3 5 10 15 20 25 M [M⊙] R [km] Case: ms = 100 MeV, a4 = 1.48, B1/4 = 135.8 MeV

2 M⊙ line Maximum Mass HS(DD2) HS(DD2) EOS B1/4 = 135.55 MeV, a4 = 1.48 21 / 22

SLIDE 27

Introduction Hybrid Star Modeling

Model

Parameterscan

Setup Results Alford’s Classification of Hybrid Stars

Quark Models

Interacting Results Where to search

Summary

What have we (hopefully) learned today? Hybrid stars with third family branches and masses over 2 M⊙ are found. Very high mass stars are almost pure quark stars. 1:1 correspondence between Constant Speed of Sound model and bag model exists. Parameter space for hybrid SN EOS candidates is very restricted. A promising candidate with ms = 100 MeV, a4 = 1.48 and B1/4 = 135.8 MeV is presented. Thank you for your attention

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