Neutron Stars and the high density Equation of State

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 onBulk Nuclear PropertiesMichigan State University, November 21, 2008

High Density Constraints

TK et al., PRC 74:035802 (2006)

High Density Constraints

TK et al., PRC 74:035802 (2006)

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)

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

sunmax M2M

TK et al., PRC 74:035802 (2006)

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

1.26sunmax M2M

TK et al., PRC 74:035802 (2006)

sunmax M19.008.2M

sunmax M28.010.2M

sunmax M1.00.2M

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

sunmax M2M

TK et al., PRC 74:035802 (2006)TK et al., PRC 74:035802 (2006)

(n)ES

sunLB 1MM

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

sunmax M2M

TK et al., PRC 74:035802 (2006)TK et al., PRC 74:035802 (2006)

(n)ES

sunLB 1MM

Conclusion: Please, more flow calculations. Specific EoS. What exactly does finite T to UB?

High Density Constraints → Symmety Energy

TK et al., PRC 74:035802 (2006)TK et al., PRC 74:035802 (2006)

(n)ES- 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 havetypical masses ( )sun1.4M

High Density Constraints → Symmety Energy

TK et al., PRC 74:035802 (2006)TK et al., PRC 74:035802 (2006)

(n)ES- 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 havetypical masses ( )sun1.4M

High Density Constraints → Symmety Energy

TK et al., PRC 74:035802 (2006)TK et al., PRC 74:035802 (2006)

(n)ES- 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 havetypical masses ( )sun1.4M

Conclusion: stiff symmetry energy disagrees with cooling phenomenology

Quark Matter

www.gsi.de

Fundamental degrees of freedom: quarks, interacting via gluon exchange

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.

Γ Ψ

Bethe Salpeter Equations

Dyson Schwinger Approach to in medium QCD

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

);())(();(bm442

1 pmipipiZpS

pi

q

aa

pqqSqpDgZp );,();(2

);()();( 21

revokes Poincaré covariance

0 )()()( 2212 pBpApipS

0 ),,(),,()(),,();,(4

24

2444

214

2 ppBppCipippApippS

Louis XI the Prudent

Divide and Conquer!

)()()( 222 pppipSBA

...);,(4

2 ppS

Dyson Schwinger Approach to in medium QCD

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

);())(();(bm442

1 pmipipiZpS

pi

q

aa

pqqSqpDgZp );,();(2

);()();( 21

revokes Poincaré covariance

0 )()()( 2212 pBpApipS

0 ),,(),,()(),,();,(4

24

2444

214

2 ppBppCipippApippS

Louis XI the Prudent

Divide and Conquer!

)()()( 222 pppipSBA

...);,(4

2 ppS

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:0807.2755PRC (accepted)

Work in progress ...

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

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)

eμ

pμ

nμ

eμ

uμ

dμ

uμ

dμ2

nμ

Nuclear matter ... n,p,en, 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-matterPre-condition: (asymmetry driven effect! )

uμ

dμ2

nμ

0du,e,p,iiniQ

0e

μ 0.2crit

px

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]

dμ

uμ2

pμ

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,en, 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-matterPre-condition: (asymmetry driven effect! )

uμ

dμ2

nμ

0du,e,p,iiniQ

0e

μ 0.2crit

px

dμ

uμ2

pμ

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‘ ?

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-DysonPhenomenological: ‚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!