Stability of CFL phase in hybrid stars

1. Stability of CFL phase in hybrid stars Giuseppe Pagliara in collaboration with Jürgen Schaffner-Bielich Institut für Theoretische Physik Frankfurt am Main Germany

2. Punchline • Within the NJL model of quark matter hybrid stars with CFL cores could be stable • Possible configurations with two phase transitions: NM - 2SC - CFL

3. QCD phase diagram in NJL Frankfurt-Darmstadt EoS Blaschke et al Phys.Rev.D 2005 Rüster et al Phys.Rev.D 2005 Two first order phase transitions: Hadronic matter 2SC CFL

4. CS in cold compact stars (NJL model) Klähn et al Phys.Lett.B 2007 M. Buballa Phys. Rep. 2005 CFL cores are unstable !! No CS in Compact stars or (small) 2SC cores in some cases

5. ...on the other hand: CFL in MIT bag model For small value of ms it is still convenient to have equal Fermi momenta for all quarks (Rajagopal Wilczek PRL 2001) Binding energy density of quarks near Fermi surface VN 2 2 Stable CFL hybrid stars Alford, Reddy Phys.Rev.D 2003 No 2SC in compact stars Alford, Rajagopal JHEP 2002

6. A toy model for the HM-QM transition Hadronic EOS: relativistic mean field model Quark EoS: p =a e free parameters: p0, e, a The pressure onset of phase transition is the most important parameter for the stability of a new phase

7. p() = -()+const. the const. is fixed by requiring p(0)=0 (Asakawa-Yazaki Nucl. Phs.A504 668) i.e. it is fixed in a regime where NJL EoS can not be applied due to its lack of confinement. It turns out that bag  (200 MeV)4, larger than the MIT bag. Pressure onset  200 MeV/fm3 the chemical potential of the phase transition is  1400 Mev by far larger than the chiral symmetry restoration chemical potential which is  1100 MeV Bag pressure in the NJL model Quarks in stars are present only in the mixed phase ! Schertler et al Phys.Rev.C 99

8. “Deconfinement” and chiral symmetry restoration The NJL model at finite density can be applied starting from the chiral symmetry restoration (before the density is vanishing!!) The bag can be fixed by requiring that the pressures of QM and NM are the same at the chiral phase transition : assumption that “deconfinement” and chiral symmetry restoration coincide (see also Bender et al. Phys.Lett.B 1998) Is the diquark condensate a good order parameter for deconfinement at finite density ?? (see also Bentz et al Nucl.Phys.A 2002) two phase transitions: chiral and superconducting

9. Mass-Radius for NJL without CS B*/B0 few %

10. Phase transition to CS

11. for smaller values of the bag p0 decreases Mass-radius relations for larger values of the gap ( 150 MeV as in Klähn et al Phys.Lett.B 2007) p0 decreases but e increases (even softer EoS!!) the effect of p0 dominates and the stars are stable Vector interactions: larger maximum of the mass (see Klähn et al Phys.Lett.B 2007) Hybrid stars with a crust of nucleonic matter a layer of 2SC and a core of CFL phase are stable ( if the bag is small and the gap  150 MeV ) G.P. and J. Schaffner-Bielich 2007

12. The mass of the strange quark Within the NJL model ms=550 MeV at =300 MeV Within the Schwinger-Dyson approach a smaller dynamical quark mass is obtained, CFL favored also at low density Nickel, Alkofer & Wambach, Phys.Rev.D 2006 Favors the stability of CFL phase in compact stars

13. Astrophysical implications • Double emission episodes in GRB • Quark formation during core collapse SN

14. The Quark-Deconfinement Nova model

15. Two families of CSs Conversion from HS to HyS (QS) with the same MB

16. How to generate GRBs The energy released is carried out by neutrinos and antineutrinos. The reaction that generates gamma-ray is: The efficency of this reaction in a strong gravitational field is: [J. D. Salmonson and J. R. Wilson, ApJ 545 (1999) 859]

17. Temporal structure of GRBs ANALYSIS of the distribution of peaks intervals “… the quiescent times are made by A different mechanism then the rest of the intervals” Nakar and Piran 2002 Lognormal distribution Dormant inner engine during QTs

18. Double GRBs generated by double phase transitions Drago, Pagliara ApJ 2007 • Two steps (same barionic mass): • transition from hadronic matter to unpaired or 2SC quark matter. “Mass filtering” • 2) the second phase transition triggered by cooling and deleptonization (see Sandin talk!! Sandin-Blaschke Phys.Rev.D2007) Burning of Hadronic stars into quark or hybrid stars Drago, Lavagno, Parenti ApJ 2007 Always a deflagration with an unstable front. Hydrodynamical instabilities can increase the velocity by up to 2 orders of magnitude, but in general do not transform the deflagration into a detonation Nucleation time of CFL phase

19. 2SC formation during SN ? Critical densities from NM to 2SC matter (NM within the Shen EoS) 2SC pairing is favored for symmetric matter MIT bag results Densities reachable during the collapse of a SN ?? Could the new energy released help SN to explode ?? Pagliara, Sagert, Schaffner-Bielich work in progress Di Toro et al. Nucl.Phys.A 2006

20. Conclusions Rich structure of the QCD phase diagram: chiral broken phase, 2SC, CFL... Two possible phase transitions in stable hybrid stars Possible signature: double emission in GRBs could be a signal of the two phase transitions as the central density of the star increases and the temperature decreases

21. Appendix

22. Mean field approach The vacuum in the NJL model Bogoliubov-Valatin variational approach two flavor NJL-like Hamiltonian Buballa, Phys.Rep. 2005 the pressure of the vacuum phase is positive (metastable phase which converts into a stable phase at a density of 0.3 fm-3) Alford, Rajagopal and Wilczek, Phys.Lett.B 1998

23. General features of GRBs • Duration 0.01-1000s • ~ 1 burst per day (BATSE) • Isotropic distribution - rate of ~2 Gpc-3 yr-1 • ~100keV photons • Cosmological Origin • The brightness of a GRB, E~1051ergs (beaming effect), is comparable to the brightness of the rest of the Universe combined. Very complex time-structure of prompt emission, Quiescent times

24. SN-GRB connection Time delays from second to years

25. Rotating massive stars, whose central region collapses to a black hole surrounded by an accretion disk. Outflows are collimated by passing through the stellar mantle. Detailed numerical analysis of jet formation. Fits naturally in a general scheme describing collapse of massive stars. - Large angular momentum needed, difficult to achieve. SN – GRB time delay: less then 100 s. Can it explain long time delay precursors ? The Collapsar model

26. Delayed formation of quark matter in Compact Stars Droplet potential energy: Quark matter cannot appear before the PNS has deleptonized (Pons et al 2001) Quantum nucleation theory nQ* baryonic number density in the Q*-phase at a fixed pressure P. μQ*,μHchemical potentials at a fixed pressure P. σ surface tension (=10,30 MeV/fm2) I.M. Lifshitz and Y. Kagan, Sov. Phys. JETP 35 (1972) 206 K. Iida and K. Sato, Phys. Rev. C58 (1998) 2538

27. Quark droplet nucleation time“mass filtering” Critical mass for s= 0 B1/4 = 170 MeV Critical mass for s = 30 MeV/fm2 B1/4 = 170 MeV Age of the Universe! Mass accretion triggers the transition, possible long SN-GRB time delay

28. Excluding QTs Deviation from lognorm & power law tail (slope = -1.2) Probability to find more than 2 QT in the same burst Drago & Pagliara 2005 Analysis on 36 bursts having long QT (red dots): the subsample is not anomalous

29. Analysis of PreQE and PostQE Same “variability”: the same emission mechanism, internal shocks

30. Same dispersions but different average duration PreQE: 20s PostQE:~40s QTs:~ 80s Three characterisitc time scales No evidence of a continuous time dilation

31. Huge energy requirements No explanation for the different time scales It is likely for short QT Interpretation: 1)Wind modulation model: during QTs no collisions between the emitted shells 2) Dormant inner engine during the long QTs Reduced energy emission Possible explanation of the different time scales in the Quark deconfinement model It is likely for long QT

32. Blaschke et al. Phys.Rev.D 2005