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

Motivation: the QCD phase diagram Lattice QCD low coupling low coupling μ ~ 1.5 GeV n B ~ 200 n 0 too large for neutron stars ! neutron star densities (core): to 10n 0 (2x10 15 gr/cm 3 ), 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. Quarkyonic

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

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

Neutron stars mergers  t ~ few 10 6 years later Bauswein et al Signals: 1)neutrinos 2)Short GRB 3)Gravitational Waves 4)Cosmic rays: strangelts

Supernova Explosion Begins with gravitational collapse of massive stars (M>8 M sun )Begins with gravitational collapse of massive stars (M>8 M sun ) Standard core collapse scenario: 1)the core collapses to nuclear density till repulsion due to nuclear force halts the collapse 2)Bounce of the inner core and formation of a shock wave 3)“Old model”: the shock reverses the infall and ejects the stellar envelope leaving behind a protoneutron star... 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 from T.Janka, Nature Phys. 2005

Janka (2008)

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

Nuclear matter EoS three different approaches: 1)relativistic mean field model (Walecka type models see Müller Serot 1996) 2)many body - microscopic nucleon-nucleon interactions (with also three body forces, see van Dalen-Fuchs-Faessler 2004) 3)chiral models (see Papazoglou et al 1999) RMF 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 Nuclear interaction realized by the exchange of mesons , ,  (also Hyperons can be included). Mean field approximation: the meson fields are assumed to be uniform.

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

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

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

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 μ d = μ s, high T and low proton fraction Y p favor Quark matter early onset of phase transition in Supernovae !

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

The shock wave formation see also Gentile et al. 1993

The neutrino signal the shock propagates into deleptonized hadronic matter, Y e =0.1, the matter is shock- heated and the electron degeneracy is lifted, weak equilibrium restored at Y e > 0.2the shock propagates into deleptonized hadronic matter, Y e =0.1, the matter is shock- heated and the electron degeneracy is lifted, weak equilibrium restored at Y e > 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 Y eWhen 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 Y e

Explosion energy, masses of PNS and Bag constant dependence two models with B 1/4 =162 and 165 MeV, two progenitor masses 10 and 15 M suntwo models with B 1/4 =162 and 165 MeV, two progenitor masses 10 and 15 M sun 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 More massive progenitor: earlier onset of phase transition and more massive proto neutron star Properties of second shock (onset and strength) and second neutrino burst (time delay and luminosity) related to the critical density (Bag).

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

Conclusions & outlook Better idea to model the phase transition? one Lagrangian with quark degrees of freedomBetter 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...) (NJL-like, nucleon as quark-diquark system, Bentz-Thomas (2001), Rezaeian- Pirner (2006), now also with color superconductivity..., Dyson-Schwinger...) 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 !!!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! Assumptions: first order phase transition at low density for SN matter! Problem1 “experimental test” : low event rate (2-3 supernovae per galaxy per century!!).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 ?Problem2 “theoretical test”: how long will LQCD need to study SN matter ? In the meantime : In the meantime :

Appendix

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