Lepton-Rich Cold Quark Matter

Transcription

1 Lepton-Rich Cold Quark Matter José C. Jiménez Eduardo S. Fraga Instituto de Física Universidade Federal do Rio de Janeiro 56th International School of Subnuclear Physics, Erice 2018 José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 1 / 17

2 Content Introduction 1 Introduction José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 2 / 17

3 Introduction Figure : QCD phase diagram for strong interactions [NICA]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 3 / 17

4 Introduction Figure : Possible neutron star interior [Weber, 1999]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 4 / 17

5 : Cold NSs [Kurkela et al., 2010] Under the constraints of local charge neutrality and β-equilibrium 2 3 n u 1 3 n d 1 3 n s n e = 0 µ s = µ d µ, µ u = µ µ e, one can write the total pressure as µ ( P(µ, X ) = d µ [n u 1 dµ ) e dµ s µ 0 (X ) where X = 3 Λ/µ B. ] dµ e + n d + n s + n e. dµ s José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 5 / 17

6 : Kurkela-Romatschke-Vuorinen KRV(X=4) P/PSB KRV(X=1) KRV(X=2) μ B [GeV] Figure : Total pressure of quarks and electrons normalized by the Stefan-Bolztmann free gas [Kurkela et al., 2010]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 6 / 17

7 : Pocket formula One can write the total cold pressure as ( ) a(x ) P QCD (µ B, X ) = P SB (µ B ) c 1 (µ B /GeV ) b(x ) Figure : Normalized pressure of quarks and electrons [Fraga et al., 2014]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 7 / 17

8 Figure : Core-collapse supernovae explosion [Pons et al., 2001]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 8 / 17

9 Lepton-rich pqcd EoS: Input Local Charge Neutrality: 2 3 n u 1 3 n d 1 3 n s = n Q e. Weak equilibrium : µ d + µ Q ν = µ u + µ Q e, µ d = µ s. Local Lepton fraction conservation of Y L = 0.4. Then the total pressure of quarks and leptons is µ ( P(µ, X ) = d µ [n u 1 + dµ ν dµ ) e µ 0 (X ) dµ s dµ s ] dµ e dµ ν + n d + n s + n e + n ν. dµ s dµ s José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 9 / 17

10 Lepton-rich pqcd EoS: Output KRV(X=4) Y L (X=4) P/PSB KRV(X=1) Y L (X=1) μ B [GeV] Figure : Normalized total pressure of quark and leptons, parametrized only by X [Jiménez and Fraga, 2018]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 10 / 17

11 One can find stable configurations of stable strange quark matter if, at P = 0, one has E/A 0.93GeV. P/PSB Y L (X=4) KRV(X=4)SQM Y L (X=3.75) Y L (X=3.5) Y L (X=3.45) 0.2 KRV(X=2.95)SQM μ B [GeV] Figure : Reduced SQM configurations [Jiménez and Fraga, 2018] José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 11 / 17

12 Thermal nucleation In the thin-wall approximation, the rate of nucleation of critical bubbles, per unit volume, per unit time is: Γ = T 4 exp [ 16π 3 σ 3 ] ( P) 2 T [Mintz et al, 2010]. Nucleation time The time it takes for the nucleation of one single critical bubble inside a volume of 1km 3 inside the core of the protoneutron star: ( ) 1 1 τ 1km 3 Γ. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 12 / 17

13 Lepton-poor astrophysical constraint Figure : Mass-Radius relations for recent measurements of neutron stars in binary systems [Demorest, 2010]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 13 / 17

14 Lepton-rich constrained band EoS 0.8 P/PSB TM1-PNS Y L (X=2.73) Y L (X=2.25) Y L (X=2) μ B [GeV] Figure : Allowed values of X to nucleate unpaired quark matter satisfying astrophysical constraints [Jiménez and Fraga, 2018]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 14 / 17

15 Lepton-rich exploration of parameter space σ[mev/fm 2 ] Y L (X=2.73) Y L (X=2.25) Y L (X=2) n B [n 0 ] Figure : Contour lines for the surface tension varying X for a nucleation time of τ = 100ms [Jiménez and Fraga, 2018]. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 15 / 17

16 Introduction We have explored protoneutron star matter in the framework of perturbative QCD. Stable strange quark matter have a more restricted parameter space due to presence of trapped neutrinos in the system. Need of nonperturbative techniques for QCD at finite density and astrophysical observables like, e.g., gravitational waves. José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 16 / 17

17 Thanks! José C. Jiménez, Eduardo S. Fraga Lepton-Rich Cold Quark Matter 17 / 17