Neutron Stars and the high density Equation of State
description
Transcript of Neutron Stars and the high density Equation of State
![Page 1: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/1.jpg)
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
![Page 2: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/2.jpg)
High Density Constraints
TK et al., PRC 74:035802 (2006)
![Page 3: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/3.jpg)
High Density Constraints
TK et al., PRC 74:035802 (2006)
![Page 4: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/4.jpg)
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)
![Page 5: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/5.jpg)
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)
![Page 6: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/6.jpg)
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
![Page 7: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/7.jpg)
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
![Page 8: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/8.jpg)
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?
![Page 9: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/9.jpg)
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
![Page 10: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/10.jpg)
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
![Page 11: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/11.jpg)
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
![Page 12: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/12.jpg)
Quark Matter
www.gsi.de
Fundamental degrees of freedom: quarks, interacting via gluon exchange
![Page 13: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/13.jpg)
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
![Page 14: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/14.jpg)
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
![Page 15: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/15.jpg)
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 ...
![Page 16: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/16.jpg)
Divide and Conquer!Field theoretical approach to chiral Quark Matter - NJL
![Page 17: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/17.jpg)
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)
![Page 18: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/18.jpg)
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
![Page 19: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/19.jpg)
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
![Page 20: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/20.jpg)
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‘ ?
![Page 21: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/21.jpg)
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!
![Page 22: Neutron Stars and the high density Equation of State](https://reader036.fdocuments.in/reader036/viewer/2022062315/56815a9f550346895dc82728/html5/thumbnails/22.jpg)