1. Neutron Stars and the high density Equation of State T.Klähn (Main) Collaborators: D.Blaschke (Wrocław), H.Chen (Peking), C.D. Roberts (ANL), F.Sandin (Liege), S.Typel (GSI) High Density Constraints on the EoS Nuclear Matter Quark Matter Phase Transition 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. Danielewicz et al. (2002) Upper Bound: - sorts out stiffer EsoS - not very ( ) sensitive to T High Density Constraints → Symmetric Matter TK et al., PRC 74:035802 (2006)

5. 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. High Density Constraints → Symmetric Matter TK et al., PRC 74:035802 (2006)

6. 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) High Density Constraints → Symmetric Matter 2.1 1.26 TK et al., PRC 74:035802 (2006)

7. 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 High Density Constraints → Symmetric Matter TK et al., PRC 74:035802 (2006)

8. 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 High Density Constraints → Symmetric Matter TK et al., PRC 74:035802 (2006) Conclusion: Please, more flow calculations. Specific EoS. What exactly does finite T to UB?

9. High Density Constraints → Symmety Energy TK et al., PRC 74:035802 (2006) - 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 ( )

10. High Density Constraints → Symmety Energy TK et al., PRC 74:035802 (2006) - 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 ( )

11. High Density Constraints → Symmety Energy TK et al., PRC 74:035802 (2006) - 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

12. Quark Matter www.gsi.de Fundamental degrees of freedom: quarks, interacting via gluon exchange

13. 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 Dyson Schwinger Approach to in medium QCD

14. 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 Divide and Conquer! Dyson Schwinger Approach to in medium QCD

15. 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 Divide and Conquer! Dyson Schwinger Approach to in medium QCD 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...

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

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

18. 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! ) A ‚chemical‘ point of view on nucleons and quarks 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 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] 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! )

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!