1. Phase transitions in neutron stars with BHF
Ang Li (李昂)
with
W. Zuo & G.-X. Peng, China
G.-F. Burgio & U. Lombardo & H.-J. Schulze, Catania
"Theory of Nuclear Interaction for Heavy-Ion Collisions and Astrophysics NNINT2015"
INFN LNS, Catania, Jun 18-20, 2015

2. Outline Introduction (Proto-)neutron star (NS) Summary
NS EoS models: kaons, hyperons, quarks in the core
Summary

3. Introduction 05: 3 months' scholarship in Asia-Europe Link program
Kaon condensation in neutron star matter
Deconfinement phase transistion and hybrid stars

4. Introduction
07: graduation.

5. Introduction: Strangeness in NSs’ inner cores
And other astrophysical implications for hot nuclear matter with BHF…
Free quarks*, strange mesons**, hyperons***
Many thanks to my two supervisors: Prof. Zuo and Prof. Lombardo!
* Peng, AL, Lombardo, PRC 2008
AL, Zuo, Peng, PRC 2015
**AL, Zhou, Burgio, Schulze, PRC 2010
AL, Burgio, Lombardo, Zuo, PRC 2006
Zuo, AL, Li, Lombardo, PRC 2004
***AL, Zuo, Mi, Burgio, CP 2007
Burgio, Schulze, AL, PRC 2011
AL, Hiyama, Zhou, Sagawa, PRC 2013
(on hypernuclei)
Hu, AL, Toki, Zuo, PRC 2014
Neutron star Interior Composition ExploreR (NICER)

6. Outline Introduction (Proto-)neutron star (NS) Summary and Outlook
NS EoS models: kaons, hyperons, quarks in the core
Summary and Outlook

7. Introduction: Strangeness in NSs’ inner cores
Heavy-ion flow investigations
2 precisely-measured heavy pulsars’ masses
Ab-initio lattice QCD simulations
Planned space missions LOFT and NICER
Demorest et. al, Nature 2010
Antoniadis et al., Science 2013
eg: It is a crossover (m =0, T~150MeV) Y. Aoki, et al, Nature 2006
(Large Observatory for X-ray Timing)
(Neutron star Interior Composition ExploreR)
Neutron star Interior Composition ExploreR (NICER) Large Observatory for X-ray Timing (LOFT) 

8. Introduction: Nuclear matter
An infinite uniform system of nucleons (baryons) interacting through the strong force
Infinite system
Uniform system
No electromagnetic force
(Also, no external magnetic field included for the study of NS)
Where is nuclear matter?
Heavy ion collision (HIC)
Core of NS
NOW,
Phase diagram at (T~0, m≠0) is not achievable from HIC (experiment),
LQCD (simulation) or pQCD (first-principle theory);
But it is important for NS (or pure quark star?).
No available one theory model for both hadron phase and quark phase;
Model calculations.

9. From schulze BOMBACI’s talk
M(R) relation is unique to the underlying EoS;
EoS must support massive NS observed recently.
BOMBACI’s talk

10. Introduction: Strangeness in NSs’ inner cores
Strangeness in NS core is usually unavoidable at such high densities;
Uncertainty of NS EoS comes from the controversial core part and model limitations;
Mass calculation is rather independent of the details of EoS, only the stiffness matters.
In the following
K- (us) condensation
Hyperons (L0, S0,±, X0,-);
Phase transition to deconfined quark matter (uds).

11. (Proto-)neutron star Composition: Kaons, hyperons, quarks in the core;
Mass-radius relation

12. Proto-NS
Beta equilibrium
Charge neutrality

13. Proto-NS Beta equilibrium Charge neutrality Finite temperature
Neutrino trapping
Conservation of lepton numbers;
From gravitational collapse calculations of the electrondegenerate core of massive stars:

14. Proto-NS Beta equilibrium Charge neutrality Finite temperature
Neutrino trapping
Lepton (proton) concentration becomes sizably higher.
AL, Burgio, Lombardo, Zuo, PRC 2006
untrapped
trapped
Zero temperature
AV18 + micro TBF

15. Kaon condensation
Temperature effects mainly in the low-density region;
Temperature plays a minor role in comparison with neutrino trapping;
AL, Zhou, Burgio, Schulze, PRC 2010
AV18 + micro TBF + KN

16. Kaon condensation KN interaction models
Standard chiral model for kaon-nucleon(KN) contribution:
Kaonic (charge) density
a3 is related to the strangeness content of the proton:
Tatsumi & Yasuhira, 1998,1999
KN interaction parameters

17. Kaon condensation mass-radius relation of stars
2-solar mass is possible.
However,…
AL, Zhou, Burgio, Schulze, PRC 2010
PSR J

18. Kaon condensation Kaons strongly disfavored, because…
a3ms > -143 MeV
Onset density strongly dependent on a3ms (y).
Fairly large onset densities~5r0.
H.Ohki et al, PRD 2008.
y= y= y= 0
AL, Zhou, Burgio, Schulze, PRC 2010
Kaons strongly disfavored, because…

19. Because the early presence of hyperons/quarks will hinder kaons
An estimate using two kinds of hyperon-hyperon interaction indicated by double-lambda hypernuclei (strong and weak):
Takahashi H, et al. PRL 2001
Relativistic mean
field model using
TM1parameter set.
AL, Zuo, Mi, Burgio, CP 2007
~2r0

20. Because the early presence of hyperons/quarks will hinder kaons
G. Q. Li, et al, PRL 1997
Weber, PPNP 2005
We take the antikaon dispersion relation constrained by the heavy-ion data, together with the present hadron/quark models to calculate the effective kaon mass in hybrid stars;
Hardly present unless rather large confinement parameter D.
Peng, AL, Lombardo, PRC 2008

21. Hot hyperon matter “Hyperon puzzle” Hyperons appear ~2r0; <1.4Mʘ!
Universal repulsive TBF?
The necessity of quark core?
“Hyperon puzzle”
AV18 + UIX + NSC89
Burgio, Schulze, AL, PRC 2011

22. Deconfinement phase transition to quark phase
Suppose it is 1st order phase transition;
BLASCHKE's talk
For a certain temperature T and total density rt ,
and Global neutrality
, Where quark fraction : (0 -1)
AL, Zuo, Peng, PRC 2015
Gibbs construction
Low density: Pure nuclear matter;
Middle: Hadron-quark mixed phase;
High density: Pure quark matter.

23. Deconfinement phase transition to quark phase
The variation of the quark mass with density mimics the strong interaction between quarks.
PENG’s talk
Quark
confinement
Asymptotic
freedom
D term: linear confinement;
Stability window for D1/2: ( )MeV
Lower limit from nuclear physics,
D’s Upper limit from vacuum quark condensation. LQCD favored area (D1/2: 161 MeV~195 MeV).
Aoki, et al. hep-lat/
(95±25MeV)
Peng, AL, Lombardo, PRC 2008

24. Deconfinement phase transition to quark phase
Previous results
Peng, AL, Lombardo, PRC 2008
Transition occurs (Too low); Pure quark occurs ;
Only low-mass hybrid stars obtained: The necessity of a repulsive interaction in quark matter?
D1/2 = 170MeV
Transition occurs
~ 0.15 fm-3
Pure quark occurs
~ 0.95 fm-3

25. Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
The variation of the quark mass with density mimics the strong interaction between quarks.
Extend the present model to include high-order term;
C. J. Xia, G. X. Peng, et al. PRC 2014
Extra chemical potential
D term: linear confinement;
C term: leading-order perturbative interactions
C term:
high density important.

26. EoS of quark matter Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
C = 0; 0.7
D1/2 = 170MeV; 190MeV
LQCD favored (161 MeV~195 MeV).
D term: linear confinement;
C term: leading-order perturbative interactions.
EoS of quark matter

27. EoS of quark matter Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
C = 0; 0.7
D1/2 = 170MeV; 190MeV
LQCD favored (161 MeV~195 MeV).
D term: linear confinement;
C term: leading-order perturbative interactions.
EoS of quark matter
C term stiffs EoS;
D term softens EoS.

28. Quark matter fraction Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
C = 0; 0.7
D1/2 = 170MeV; 190MeV
Quark matter fraction
D term: linear confinement;
C term: leading-order perturbative interactions.

29. Quark matter fraction Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
C = 0; 0.7
D1/2 = 170MeV; 190MeV
Quark matter fraction
D term: linear confinement;
C term: leading-order perturbative interactions.
(positive) C term push quark threshold,
0.16 to 0.57 fm-3 at D1/2=170MeV.

30. Hybrid star Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
C = 0; 0.7
D1/2 = 170MeV; 190MeV
D term: linear confinement;
C term: leading-order perturbative interactions.
Hybrid star
Increasing of C value makes high mass possible.

31. Hybrid star Deconfinement phase transition to quark phase
Present results
AL, Zuo, Peng, PRC 2015
C = 0; 0.7
D1/2 = 170MeV; 190MeV
D term: linear confinement;
C term: leading-order perturbative interactions.
Hybrid star
Increasing of C value makes high mass possible.
High-order quark interaction in CDDM will push the appearance of the quark phase, stiff EoS, and finally a high-mass hybrid star is possible with a mixed-phase core.

32. Summary NS
Hyperons appear for sure, but too soft EoS;
Need universal repulsive TBF, or stiff quark core;
Both hyperons and quarks hinder kaons, not relevant in NS core!
The competition of hyperons and quarks?
PNS
Neutrino trapping influence largely the composition and the EoS;
Temperature plays a minor role in comparison with neutrino trapping.
A universal theory for strongly interacting many-body system (for both hadron phase and quark phase) is very hard;
Observations may be a way out.

33. Thank you very much for your attention!