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Neutron Stars and the high density Equation of State

Neutron Stars and the high density Equation of State. High Density Constraints on the EoS Nuclear Matter Quark Matter Phase Transition. T.Klähn (Main) Collaborators: D.Blaschke (Wrocław), H.Chen (Peking), C.D. Roberts (ANL), F.Sandin (Liege), S.Typel (GSI).

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Neutron Stars and the high density Equation of State

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  1. Neutron Stars and the high density Equation of State High Density Constraints on the EoS Nuclear Matter Quark Matter Phase Transition T.Klähn (Main) Collaborators: D.Blaschke (Wrocław), H.Chen (Peking), C.D. Roberts (ANL), F.Sandin (Liege), S.Typel (GSI) 5th ANL/MSU/JINA/INT FRIB Workshop on Bulk Nuclear Properties Michigan State University, November 21, 2008

  2. High Density Constraints TK et al., PRC 74:035802 (2006)

  3. High Density Constraints ? TK et al., PRC 74:035802 (2006)

  4. High Density Constraints → Symmetric Matter • Danielewicz et al. (2002) • Upper Bound: • - sorts out stiffer EsoS • not very ( ) sensitive to T ? TK et al., PRC 74:035802 (2006)

  5. High Density Constraints → Symmetric Matter • Danielewicz et al. (2002) • Upper Bound: • - sorts out stiffer EsoS • not very ( ) sensitive to T • UB EoS: • Evidence for high M • ... no, rather a limit ... • that amazingly well agrees with maximum estimates of • NS masses. ? ? TK et al., PRC 74:035802 (2006)

  6. High Density Constraints → Symmetric Matter • Danielewicz et al. (2002) • Upper Bound: • - sorts out stiffer EsoS • not very ( ) sensitive to T • UB EoS: • Evidence for high M • PSR B1516+02B (Freire 08) • EXO 0748-676 (Özel 07) • 4U 1636-536 (Barret 05) 2.1 ? 1.26 ? TK et al., PRC 74:035802 (2006)

  7. High Density Constraints → Symmetric Matter • Danielewicz et al. (2002) • Upper Bound: • - sorts out stiffer EsoS • not very ( ) sensitive to T • UB EoS: • Evidence for high M • maximum mass rather robust • with respect to different • Lower Bound: • certainly disagrees with • any NS max. mass limit ? ? TK et al., PRC 74:035802 (2006) TK et al., PRC 74:035802 (2006)

  8. High Density Constraints → Symmetric Matter • Danielewicz et al. (2002) • Upper Bound: • - sorts out stiffer EsoS • not very ( ) sensitive to T • UB EoS: • Evidence for high M • maximum mass rather robust • with respect to different • Observe that • certainly disagrees with • any NS max. mass limit ? ? Conclusion: Please, more flow calculations. Specific EoS. What exactly does finite T to UB? TK et al., PRC 74:035802 (2006) TK et al., PRC 74:035802 (2006)

  9. High Density Constraints → Symmety Energy - maximum mass (UB a la Flow) rather robust with respect to different DU cooles NSs very efficiently Threshold between (11-15)% proton fraction Statistical Argument: Thermal observable NSs have typical masses ( ) TK et al., PRC 74:035802 (2006) TK et al., PRC 74:035802 (2006)

  10. High Density Constraints → Symmety Energy - maximum mass (UB a la Flow) rather robust with respect to different DU cooles NSs very efficiently Threshold between (11-15)% proton fraction Statistical Argument: Thermal observable NSs have typical masses ( ) TK et al., PRC 74:035802 (2006) TK et al., PRC 74:035802 (2006)

  11. High Density Constraints → Symmety Energy - maximum mass (UB a la Flow) rather robust with respect to different DU cooles NSs very efficiently Threshold between (11-15)% proton fraction Statistical Argument: Thermal observable NSs have typical masses ( ) Conclusion: stiff symmetry energy disagrees with cooling phenomenology TK et al., PRC 74:035802 (2006) TK et al., PRC 74:035802 (2006)

  12. Quark Matter Fundamental degrees of freedom: quarks, interacting via gluon exchange • quarks are .... • confined/deconfined • chiral particles • There is no modell on • the market describing • nucleons in medium • in terms of QM DoF • in this sense. www.gsi.de

  13. Dyson Schwinger Approach to in medium QCD Problem is not unknown: Dyson Schwinger Approach Cloet, Roberts (ANL) Eichman, Alkofer (Graz) Faddeev Equations Baryons as composites of confined quarks and diquarks q-propagator, d-propagator, Bethe-Salpeter-Ampl., Fadeev Ampl. Bethe Salpeter Equations

  14. Dyson Schwinger Approach to in medium QCD Divide and Conquer! • Inverse Quark Propagator: • Renormalised Self Energy: • Loss of Poincaré covariance increases complexity of propagator... • General Solution: • Differences to zero density case • 1. One more Gap • 2. Gaps depend on energy, momentum and chemical potential revokes Poincaré covariance Louis XI the Prudent

  15. Dyson Schwinger Approach to in medium QCD Divide and Conquer! • Inverse Quark Propagator: • Renormalised Self Energy: • Loss of Poincaré covariance increases complexity of propagator... • General Solution: • Differences to zero density case • 1. One more Gap • 2. Gaps depend on energy, momentum and chemical potential • On this level: • 1st order chiral phase transition • accompanied by deconfinement • H. Chen, W. Yuan, L. Chang, Y.-X. Liu, • T.K., C.D. Roberts arXiv:0807.2755 • PRC (accepted) • Work in progress ... revokes Poincaré covariance Louis XI the Prudent

  16. Field theoretical approach to chiral Quark Matter - NJL Divide and Conquer!

  17. 09/25/2008 Field theoretical approach to chiral Quark Matter - NJL Maxwell phase transition EXO constraint rules out soft EoS F.Özel Nature 441, 2006 few % change in η Danielewicz et al. (2002) Alford et al., Nature 445:E7-E8,2007 T.K. et al., Phys.Lett.B654:170-176,2007 Conclusion: stiff QM EoS possible → almost direct crossover from NM to QM? (masquerade)

  18. A ‚chemical‘ point of view on nucleons and quarks • Nuclear matter ... n,p,e • n, p as QM-boundstates → mixed phase? • conditions for equilibrium: • global charge neutrality • in particular: protons (+1) ↔ d-quarks (-1/3) • Sequential ‚deconfinement‘: • analogous to dissociation • of nuclear clusters • d-quark drip line? • mixture of nucleons and 1f d-quark-matter • Pre-condition: • (asymmetry driven effect! ) D. Blaschke et al. J. Phys. G: Nucl. Part. Phys. In press (2008) [arXiv:0807.0414]

  19. A ‚chemical‘ point of view on nucleons and quarks • Nuclear matter ... n,p,e • n, p as QM-boundstates → mixed phase? • conditions for equilibrium: • global charge neutrality • in particular: protons (+1) ↔ d-quarks (-1/3) • Sequential ‚deconfinement‘: • analogous to dissociation • of nuclear clusters • d-quark drip line? • mixture of nucleons and 1f d-quark-matter • Pre-condition: • (asymmetry driven effect! ) 1f phase spread over the whole star. -> No onion structure. Caveats: No surface or Coulomb effects here. Mixture of quarks and nucleons? NJL is chiral model. Confinement? D. Blaschke et al. J. Phys. G: Nucl. Part. Phys. In press (2008) [arXiv:0807.0414]

  20. Summary • Combination of NS-constraints and flow as a valuable tool to explore the high density behaviour of the EoS. Waiting curiously for what comes next... • Applying different constraints provides a way to • - investigate several aspects of EoS ‚simultaneously‘ • - stimulate understanding/improvement of constraints themself • Example: Flow constrains ‚maximum‘ stiffnes • NS (minimum) max. masses constrain ‚minimum‘ stiffness (LB) • If interested: TK et al PRC74(2006), Lattimer/Prakash Phys.Rept.442(2007) • Quark Matter ... • Microscopic Approach: Schwinger-Dyson • Phenomenological: ‚Walecka-like‘ fieldtheoretical description. • flow-constraint as a tool to adjust model parameters • stiff QM-EoS (high massive hybrid stars) are not problematic at all (masquerade) • - d-Dripline - sequential ‚deconfining‘ ?

  21. Summary • Combination of NS-constraints and flow as a valuable tool to explore the high density behaviour of the EoS. Waiting curiously for what comes next... • Applying different constraints provides a way to • - investigate several aspects of EoS ‚simultaneously‘ • - stimulate understanding/improvement of constraints themself • Example: Flow constrains ‚maximum‘ stiffnes • NS (minimum) max. masses constrain ‚minimum‘ stiffness (LB) • If interested: TK et al PRC74(2006), Lattimer/Prakash Phys.Rept.442(2007) • Quark Matter ... • Microscopic Approach: Schwinger-Dyson • Phenomenological: ‚Walecka-like‘ fieldtheoretical description. • flow-constraint as a tool to adjust model parameters • stiff QM-EoS (high massive hybrid stars) are not problematic at all (masquerade) • d-Dripline - sequential ‚deconfining‘ ? • Thank you!

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