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We compare two classes of hybrid equations of state with a hadron-to-quark matter phase transition in their application to core collapse supernova simulations. The first one uses the quark bag model and describes the transition to three-flavor quark matter at low critical densities. The second one employs a Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with parameters describing a phase transition to two-flavor quark matter at higher critical densities. These models possess a distinctly different temperature dependence of their transition densities which turns out to be crucial for the possible appearance of quark matter in supernova cores. During the early post bounce accretion phase quark matter is found only if the phase transition takes place at sufficiently low densities as in the study based on the bag model. The increase critical density with increasing temperature, as obtained for our PNJL parametrization, prevents the formation of quark matter. The further evolution of the core collapse supernova as obtained applying the quark bag model leads to a structural reconfiguration of the central proto-neutron star where, in addition to a massive pure quark matter core, a strong hydrodynamic shock wave forms and a second neutrino burst is released during the shock propagation across the neutrinospheres. We discuss the severe constraints in the freedom of choice of quark matter models and their parametrization due to the recently observed 2 solar mass pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram., Comment: 19 pages, 4 figures, CPOD2010 conference proceeding

We discuss a hybrid equation of state (EoS) that fulfills constraints for mass-radius relationships and cooling of compact stars. The quark matter EoS is obtained from a Polyakov-loop Nambu--Jona-Lasinio (PNJL) model with color superconductivity, and the hadronic one from a relativistic mean-field (RMF) model with density-dependent couplings (DD-RMF). For the construction of the phase transition regions we employ here for simplicity a Maxwell construction. We present the phase diagram for symmetric matter which exhibits two remarkable features: (1) a "nose"-like structure of the hadronic-to-quark matter phase border with an increase of the critical density at temperatures below T ~ 150 MeV and (2) a high critical temperature for the border of the two-flavor color superconducting (2SC) phase, T_c > 160 MeV. We show the trajectories of heavy-ion collisions in the plane of excitation energy vs. baryon density calculated using the UrQMD code and conjecture that for incident energies of 4 ... 8 A GeV as provided, e.g., by the Nuclotron-M at JINR Dubna or by lowest energies at the future heavy-ion collision experiments CBM@FAIR and NICA@JINR, the color superconducting quark matter phase becomes accessible., Comment: 5 pages, 1 figure, Poster presented at the XXVI. Max Born Symposium "Three Days of Strong Interactions", Wroclaw (Poland), July 9-11, 2009

We discuss a Nambu--Jona-Lasinio (NJL) type quantum field theoretical approach to the quark matter equation of state with color superconductivity and construct hybrid star models on this basis. It has recently been demonstrated that with increasing baryon density, the different quark flavors may occur sequentially, starting with down-quarks only, before the second light quark flavor and at highest densities also the strange quark flavor appears. We find that color superconducting phases are favorable over non-superconducting ones which entails consequences for thermodynamic and transport properties of hybrid star matter. In particular, for NJL-type models no strange quark matter phases can occur in compact star interiors due to mechanical instability against gravitational collapse, unless a sufficiently strong flavor mixing as provided by the Kobayashi-Maskawa-'t Hooft determinant interaction is present in the model. We discuss observational data on mass-radius relationships of compact stars which can put constraints on the properties of dense matter equation of state., Comment: 7 pages, 2 figures, to appear in the Proceedings of the International Conference SQM2009, Buzios, Rio de Janeiro, Brazil, Sep.27-Oct.2, 2009

One of the key ingredients to understand the properties of neutrons stars is the equation of state at finite densities far beyond nuclear saturation. Investigating the phase structure of quark matter that might be realized in the core of NS inspires theory and observation. We discuss recent results of our work to point out our view on challenges and possibilities in this evolving field by means of a few examples., Comment: 10 pages, 6 figures, Proc. 5th ANL/MSU/JINA/INT FRIB Workshop on Bulk Nuclear Properties, E. Lansing, Nov. 19-22, 2008

We suggest a scenario where the three light quark flavors are sequentially deconfined under increasing pressure in cold asymmetric nuclear matter as found, e.g., in neutron stars. The basis for our analysis is a chiral quark matter model of Nambu--Jona-Lasinio (NJL) type with diquark pairing in the spin-1 single flavor (CSL), spin-0 two flavor (2SC) and three flavor (CFL) channels. We find that nucleon dissociation sets in at about the saturation density, n_0, when the down-quark Fermi sea is populated (d-quark dripline) due to the flavor asymmetry induced by beta-equilibrium and charge neutrality. At about 3n_0 u-quarks appear and a two-flavor color superconducting (2SC) phase is formed. The s-quark Fermi sea is populated only at still higher baryon density, when the quark chemical potential is of the order of the dynamically generated strange quark mass. We construct two different hybrid equations of state (EoS) using the Dirac-Brueckner Hartree-Fock (DBHF) approach and the EoS by Shen et al. in the nuclear matter sector. The corresponding hybrid star sequences have maximum masses of, respectively, 2.1 and 2.0 M_sun. Two- and three-flavor quark-matter phases exist only in gravitationally unstable hybrid star solutions in the DBHF case, while the Shen-based EoS produce stable configurations with a 2SC phase-component in the core of massive stars. Nucleon dissociation via d-quark drip could act as a deep crustal heating process, which apparently is required to explain superbusts and cooling of X-ray transients., Comment: 9 pages, 7 figures, 1 figure removed, section IV revised, references added

Recent indications for high neutron star masses (M \sim 2 M_sun) and large radii (R > 12 km) could rule out soft equations of state and have provoked a debate whether the occurence of quark matter in compact stars can be excluded as well. We show that modern quantum field theoretical approaches to quark matter including color superconductivity and a vector meanfield allow a microscopic description of hybrid stars which fulfill the new, strong constraints. For these objects color superconductivity turns out to be an essential ingredient for a successful description of the cooling phenomenology in accordance with recently developed tests. We discuss the energy release in the neutrino untrapping transition as a new aspect of the problem that hybrid stars masquerade themselves as neutron stars. Quark matter searches in future generations of low-temperature/high-density nucleus-nucleus collision experiments such as low-energy RHIC and CBM @ FAIR might face the same problem of an almost crossover behavior of the deconfinement transition. Therefore, diagnostic tools shall be derived from effects of color superconductivity., Comment: 8 pages, 3 figures, To appear in the proceedings of EXOCT 2007: International Symposium on Exotic States of Nuclear Matter, Catania, Italy, 11-15 Jun 2007

Recently, observations of compact stars have provided new data of high accuracy which put strong constraints on the high-density behaviour of the equation of state of strongly interacting matter otherwise not accessible in terrestrial laboratories. The evidence for neutron stars with high mass (M =2.1 +/- 0.2 M_sun for PSR J0751+1807) and large radii (R > 12 km for RX J1856-3754) rules out soft equations of state and has provoked a debate whether the occurence of quark matter in compact stars can be excluded as well. In this contribution it is shown that modern quantum field theoretical approaches to quark matter including color superconductivity and a vector meanfield allow a microscopic description of hybrid stars which fulfill the new, strong constraints. The deconfinement transition in the resulting stiff hybrid equation of state is weakly first order so that signals of it have to be expected due to specific changes in transport properties governing the rotational and cooling evolution caused by the color superconductivity of quark matter. A similar conclusion holds for the investigation of quark deconfinement in future generations of nucleus-nucleus collision experiments at low temperatures and high baryon densities such as CBM @ FAIR., Comment: 6 pages, 2 figures, accepted for publication in J. Phys. G. (Special Issue)

We discuss possible ways to observationally detect the superdense cosmic objects composed of hypothetical sub-constituent fermions beneath the quark/lepton level, recently proposed by us. The characteristic mass and size of such objects depend on the compositeness scale, and their huge density cannot arise within a context of quarks and leptons alone. Their eventual observation would therefore be a direct vindication of physics beyond the standard model of particle physics, possibly far beyond the reach of the Large Hadron Collider (LHC), in a relatively simple and inexpensive manner. If relic objects of this type exist, they can possibly be detected by present and future x-ray observatories, high-frequency gravitational wave detectors, and seismological detectors. To have a realistic detection rate, i.e., to be observable, they must necessarily constitute a significant fraction of cold dark matter., Comment: 8 pages, 4 figures. Added one reference [24]. Reformulated the discussion at the end of Section II. Accepted for publication in Phys. Rev. D

We study the effect of neutrino trapping in new-born quark stars within a three-flavor Nambu - Jona-Lasinio (NJL) model with self-consistently calculated quark masses. The phase diagrams and equations of state for charge neutral quark matter in beta-equilibrium are presented, with and without trapped neutrinos. The compact star sequences for different neutrino untrapping scenarios are investigated and the energy release due to neutrino untrapping is found to be of the order of 10^53 erg. We find that hot quark stars characterized, e.g., by an entropy per baryon of 1-2 and a lepton fraction of 0.4, as models for the cores of newborn protoneutron stars, are in the two-flavor color superconducting (2SC) state. High temperatures and/or neutrino chemical potentials disfavor configurations with a color-flavor-locked (CFL) phase. Stable quark star solutions with CFL cores exist only at low temperatures and neutrino chemical potentials., Comment: 18 pages, 25 figures, accepted for publication in Phys. Rev. D. Updated references and acknowledgements

We present a hybrid equation of state (EoS) for dense matter that satisfies phenomenological constraints from modern compact star (CS) observations which indicate high maximum masses (M = 2 M_sun) and large radii (R> 12 km). The corresponding isospin symmetric EoS is consistent with flow data analyses of heavy-ion collisions and a deconfinement transition at approx. 0.55 fm^{-3}. The quark matter phase is described by a 3-flavor Nambu--Jona-Lasinio model that accounts for scalar diquark condensation and vector meson interactions while the nuclear matter phase is obtained within the Dirac-Brueckner-Hartree-Fock (DBHF) approach using the Bonn-A potential. We demonstrate that both pure neutron stars and neutron stars with quark matter cores (QCSs) are consistent with modern CS observations. Hybrid star configurations with a CFL quark core are unstable., Comment: 16 pages, 4 figures; published version, important note added in proof

We present an exact condition for the existence of gapless quasiparticle excitations in NJL models of color superconducting quark matter with a quark-quark interaction in the scalar color-antitriplet channel. The condition can be represented by a rotated ellipse in the plane of mass and chemical potential differences for the paired quark fields., Comment: Accepted for publication in PRC. 5 pages, 4 figures; Corrected typos and added one more term to the series expansion in (19)

The phase diagram of three-flavor quark matter under compact star constraints is investigated within a Nambu--Jona-Lasinio model. Local color and electric charge neutrality is imposed for beta-equilibrated superconducting quark matter. The constituent quark masses and the diquark condensates are determined selfconsistently in the plane of temperature and quark chemical potential. Both strong and intermediate diquark coupling strengths are considered. We show that in both cases, gapless superconducting phases do not occur at temperatures relevant for compact star evolution, i.e., below T ~ 50 MeV. The stability and stucture of isothermal quark star configurations are evaluated. For intermediate coupling, quark stars are composed of a mixed phase of normal (NQ) and two-flavor superconducting (2SC) quark matter up to a maximum mass of 1.21 M_sun. At higher central densities, a phase transition to the three-flavor color flavor locked (CFL) phase occurs and the configurations become unstable. For the strong diquark coupling we find stable stars in the 2SC phase, with masses up to 1.326 M_sun. A second family of more compact configurations (twins) with a CFL quark matter core and a 2SC shell is also found to be stable. The twins have masses in the range 1.301 ... 1.326 M_sun. We consider also hot isothermal configurations at temperature T=40 MeV. When the hot maximum mass configuration cools down, due to emission of photons and neutrinos, a mass defect of 0.1 M_sun occurs and two final state configurations are possible., Comment: 12 pages, 11 figures

In the context of the standard model of particle physics, there is a definite upper limit to the density of stable compact stars. However, if a more fundamental level of elementary particles exists, in the form of preons, stability may be re-established beyond this limiting density. We show that a degenerate gas of interacting fermionic preons does allow for stable compact stars, with densities far beyond that in neutron stars and quark stars. In keeping with tradition, we call these objects "preon stars", even though they are small and light compared to white dwarfs and neutron stars. We briefly note the potential importance of preon stars in astrophysics, e.g., as a candidate for cold dark matter and sources of ultra-high energy cosmic rays, and a means for observing them., Comment: 10 pages, 3 figures

In the context of the standard model of particle physics, there is a definite upper limit to the density of stable compact stars. However, if there is a deeper layer of constituents, below that of quarks and leptons, stability may be re-established far beyond this limiting density and a new class of compact stars could exist. These objects would cause gravitational lensing of white dwarfs and gamma-ray bursts, which might be observable as a diffraction pattern in the spectrum. Such observations could provide means for obtaining new clues about the fundamental particles and the origin of cold dark matter., Comment: 16 pages, 6 figures, contribution to the 42nd course of the international school of subnuclear physics, 'How and where to go beyond the standard model', Erice, Aug. 29 - Sep. 7, 2004