The high density QCD phase transition in compact stars

1. The high density QCD phase transition in compact stars Giuseppe Pagliara Institut für Theoretische Physik Heidelberg, Germany Excited QCD 2010, Tatra National Park, Slovakia

2. Motivation: the QCD phase diagram low coupling Quarkyonic Lattice QCD neutron star densities (core): 10-1 to 10n0 (2x1015gr/cm3), excellent tools to test properties of matter at extreme conditions two phenomenological models: low density/temperature hadronic model and high density/temperature quark model (MIT bag, NJL, CDM...). Fixing the parameters in one point of the T-n plane. low coupling μ ~ 1.5 GeV nB ~ 200 n0 too large for neutron stars !

3. Search of Quark matter in violent phenomena of the Universe: Supernovae and GRBs Explosion of massive stars M > 8 Msun, Last close explosion SN1987 (50 kpc), E = 1053 ergs, optical signal + Some SN (Collapsar) responsible for the emission of Gamma-Ray-Bursts

4. t ~ few seconds later Protoneutron stars deleptonization path is the phase diagram ? from A. Steiner PhD-thesis Ruster et al hep-ph/0509073

5. t ~ few 106 years later Neutron stars mergers • Signals: • neutrinos • Short GRB • Gravitational Waves • Cosmic rays: strangelts Bauswein et al. 0910.5169

6. Begins with gravitational collapse of massive stars (M>8 Msun) Standard core collapse scenario: the core collapses to nuclear density till repulsion due to nuclear force halts the collapse Bounce of the inner core and formation of a shock wave “Old model”: the shock reverses the infall and ejects the stellar envelope leaving behind a protoneutron star Supernova Explosion from T.Janka, Nature Phys. 2005 ... but: in all simulations, due to the dissociation of heavy nuclei the shock looses energy and develops into a standing accretion shock, the “prompt mechanism ” does not work

7. Janka (2008)

8. Quark matter in compact stars • QCD phase diagram: first order phase transition at high density • Mass ~ 1.4 solar masses and Radius ~ 10 km • The central density in a compact star can reach values up to ten times the nuclear matter saturation density from F. Weber

9. three different approaches: • relativistic mean field model (Walecka type models see Müller Serot 1996) • many body - microscopic nucleon-nucleon interactions (with also three body forces, see van Dalen-Fuchs-Faessler 2004) • chiral models (see Papazoglou et al 1999) Nuclear matter EoS RMF Nuclear interaction realized by the exchange of mesons ,, (also Hyperons can be included). Mean field approximation: the meson fields are assumed to be uniform. 5 parameters: 3 mesons/nucleons couplings + 2 for the potential of the  fixed by 5 known properties of nuclear matter: saturation density, binding energy, incompressibility, effective mass of nucleon and symmetry energy at saturation

10. two conserved charges Nuclear matter in compact stars only one independent chemical potential! beta stability charge neutrality Thermodynamic potential Dispersion relations Glendenning, Compact stars,1997 particle fractions Pressure vs baryon density

11. modelling of confinement: 1) free or weekly interacting quarks in a finite volume, the Bag 2) confinement is provided by the vacuum pressure B Quark matter EoS: MIT bag model beta stability charge neutrality parameters: current quark masses mu and md few MeV and ms~ 100 MeV and B^1/4 145-200 MeV (+ s corrections)

12. Gibbs construction: two components system (baryon and electric charge), global charge neutrality Matching the EoSs: Gibbs construction (Schertler et al. 1998) - quark volumue fraction, two critical chemical potentials =0,1 - the pressure changes in the mixed phase, possible existence of mixed phase in compact stars !!

13. Quark matter during the early post bounce phase(Sagert, Fischer, Hempel, Pagliara, Schaffner-Bielich, Tielemann, Mezzacappa & Liebendörfer Phys.Rev.Lett. 2009) Small value of the Bag, beta equilibrium μd = μs, high T and low proton fraction Yp favor Quark matter early onset of phase transition in Supernovae !

14. “Hybrid”equation of state for HIC matter • production of Quark matter at low T and high density unfavored in HIC: 1) no net strangeness production 2) isospin symmetric nuclear matter is soft

15. The shock wave formation see also Gentile et al. 1993

16. The neutrino signal • the shock propagates into deleptonized hadronic matter, Ye=0.1, the matter is shock- heated and the electron degeneracy is lifted, weak equilibrium restored at Ye > 0.2 • When the shock reaches the neutrino sphere a second burst (the first being the neutronization burst during bounce ) of all neutrinos is released dominated by e-antineutrinos stemming from the positron capture that established the increase in Ye

17. Explosion energy, masses of PNS and Bag constant dependence Larger Bag: -)Longer proto neutron star accretion time due to higher critical density -)More massive proto neutron star with deeper gravitational potential -)Stronger second shock and larger explosion energies -)Second neutrino burst 100 ms later with larger peak luminosities • two models with B1/4 =162 and 165 MeV, two progenitor masses 10 and 15 Msun Properties of second shock (onset and strength) and second neutrino burst (time delay and luminosity) related to the critical density (Bag). More massive progenitor: earlier onset of phase transition and more massive proto neutron star

18. Detectability IceCube, SN events within 50 kpc SuperK, SN events within 20 kpc Dasgupta et al. 0912.2568

19. The dynamics of the formation of quark matter in compact stars might provide clear signatures in the neutrino signal (measurable in SuperK & IceCube). Possible mechanism for supernova explosions !!! • Assumptions: first order phase transition at low density for SN matter! • Problem1 “experimental test” : low event rate (2-3 supernovae per galaxy per century!!). • Problem2 “theoretical test”: how long will LQCD need to study SN matter ? • In the meantime: Conclusions & outlook • Better idea to model the phase transition? one Lagrangian with quark degrees of freedom (NJL-like, nucleon as quark-diquark system, Bentz-Thomas (2001), Rezaeian-Pirner (2006), now also with color superconductivity ..., Dyson-Schwinger...)

20. Appendix

21. When Quark matter is eventually formed? Pons et al. PRL 2001