M 10M. Masses 2.0M. Radii 15km. T<10 6 K < KeV (T 0 30MeV) n 15ρ 0 (ρ 0 =0.16fm 3 )

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2 M 10M Masses 2.0M Radii 15km T<10 6 K < KeV (T 0 30MeV) n 15ρ 0 (ρ 0 =0.16fm 3 )

3 Outline: P (µ B,B, Λ,m s ) Phadronic(µpt) = Pquark(µpt)

4 Introduction: T 0µ<T p(t, µ) µ > T Nc T = 0

5 Introduction: T 0µ<T p(t, µ) µ > T Nc T = 0

6 Introduction: T 0µ<T p(t, µ) µ > T Nc T = 0 α s (µ) 1/ log(µ 2 )

7 T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD 1 Hot Quark Matter ( p SB /T LQCD P(T,)/P (0) (T) hadron resonance gas pqcd, T pqcd, T pqcd, T T [GeV] (α s 5/2) p/t 4 p4 asqtad T [MeV] Bazavov et al

8 T 0.2 GeV Quark-Gluon Gas Hadron gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD nucleons nucleons+kaon cond. nucleons+hyperons nucl-th/ v18 P/P (0) c s >1 1 2 B [GeV]

9 Physical EoS at high density: p(µ u (µ),µ d (µ),µ s (µ)) = p(µ) p(µ) =p(µ, Λ) p(µ) =p (pert) (µ, Λ) B p(µ = 0) = 0,

10 T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD flavor 3 flavor 2+1 flavor n()/n (0) ( N f =2, [GeV] µq n(µ B, Λ) = µb p(µ B, Λ)

11 Pairing instability: < 100MeV p p kf µ kf p(µ) =p (pert) B +# 2 µ 2 B 3π 2

12 Maxwell construction: µpt T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD B(µpt), Λ Cold Quark Matter (T=0) npt > 0.16/fm 3 P/P (0) nucleons, c s <1 nucleons+kaon cond. nucleons+hyperons pqcd, B=0, 3 B pqcd, B=0, 3 B pqcd, B=0, 3 B 0.2 c s > B [GeV]

13 Maxwell construction: µpt T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD

14 Maxwell construction: µpt T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD Matching possible in two disjoint regions: 1 Case I ( low ) Matching 1 Case II ( high ) Matching P/P (0) nucleons nucleons+kaon cond. nucleons+hyperons matched, matched, GeV P/P (0) nucleons matched, matched, GeV B [GeV] 0.16fm 3 < ρ c B 0.32fm B [GeV] ρ c B > 0.64fm 3 Represents the best educated guess available for the true EoS on full µ-range µ

15 Glendenning construction: p A p * p B Q e hadron + Q e qm =0 0.3 e Q hadron =0 Q e = µe p µ e p A p * p B µ B [GeV] e Q qm =0

16 Glendenning construction:

17 Outline: P (µ B,B, Λ,m s ) Phadronic(µpt) = Pquark(µpt)

18 T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD E/A =3µ c =0.93GeV 56 Fe teq~1/λqcd teq~10 60 years for A > 6

19 T 0.2 GeV Hadron gas Quark-Gluon Gas Color Nuclear Superconductor Vacuum matter µ B GeV ? GeV µb ΛQCD B, ns > 0, quark mass essential! E/A < 0.93 GeV Normal Quark matter, MS =0.378GeV CSC, MeV, MS =0.378GeV Λ m(2gev) E/A>0.93GeV (unstable) E/A<0.93 GeV (stable) E/A=0.93 GeV u d s ) m(2gev) E/A>0.93GeV (unstable) E/A<0.93 GeV (stable) E/A=0.93 GeV u d s )

20 Outline: P (µ B,B, Λ,m s ) Phadronic(µpt) = Pquark(µpt)

21 Compact stars: dm(r) = 4πr 2 ε(r)dr, dp (r) = G (P (r)+ε(r)) M(r)+4πr 3 P (r) ε(p) r (r 2GM(r)) dr, Let s consider compact stars made of: Pure Nuclear matter Pure Strange Quark matter Hybrid stars with large quark core with thin nucleonic crust (case I) small quark core with thick nucleonic crust (case II) 2-phase admixture of quarks and hadrons

22 Compact stars: dm(r) = 4πr 2 ε(r)dr, dp (r) = G (P (r)+ε(r)) M(r)+4πr 3 P (r) dr, r (r 2GM(r)) 1 Pressure [GeV/fm 3 ] Hybrid EoS Nucleon EoS Kaon EoS Hyperon EoS Strange quark matter Energy density [GeV/fm 3 ]

23 M/M solar EXO SAX J pure phases mixed phases Min-χ 2 observations Case II 4U U RXJ Case I 4U R [km]

24 Profile of a star with mixed phases µ pt =1.43GeV 1.2 Surface of the star Energy density [GeV/fm 3 ] Ratio of quark matter Radius [km]

25 Conclusions: ms α s 2 µb µb M > 2Msolar

26 Outlook: αs 2 log(αs): αs 3:

27 Outlook: αs 2 log(αs): αs 3: