Consequences of simultaneous chiral symmetry breaking and deconfinement for the isospin symmetric phase diagram

The thermodynamic bag model (tdBag) has been applied widely to model quark matter properties in both heavy-ion and astrophysics communities. Several fundamental physics aspects are missing in tdBag, e.g., dynamical chiral symmetry breaking (D$\chi$SB) and repulsions due to the vector interaction are both included explicitly in the novel vBag quark matter model of Kl\"ahn and Fischer (2015) (Astrophys. J. 810, 134 (2015)). An important feature of vBag is the simultaneous D$\chi$SB and deconfinement, where the latter links vBag to a given hadronic model for the construction of the phase transition. In this article we discuss the extension to finite temperatures and the resulting phase diagram for the isospin symmetric medium.Comment: 6 pages, 2 figures, Contribution to the Topical Issue Exploring strongly interacting matter at high densities - NICA White Paper edited by David Blaschke et a

Equations of state for supernovae and compact stars

A review is given of various theoretical approaches for the equation of state (EoS) of dense matter, relevant for the description of core-collapse supernovae, compact stars, and compact star mergers. The emphasis is put on models that are applicable to all of these scenarios. Such EoS models have to cover large ranges in baryon number density, temperature, and isospin asymmetry. The characteristics of matter change dramatically within these ranges, from a mixture of nucleons, nuclei, and electrons to uniform, strongly interacting matter containing nucleons, and possibly other particles such as hyperons or quarks. As the development of an EoS requires joint efforts from many directions, different theoretical approaches are considered and relevant experimental and observational constraints which provide insights for future research are discussed. Finally, results from applications of the discussed EoS models are summarized

How Well Do We Know The Supernova Equation of State?

We give an overview about equations of state (EOS) which are currently available for simulations of core-collapse supernovae and neutron star mergers. A few selected important aspects of the EOS, such as the symmetry energy, the maximum mass of neutron stars, and cluster formation, are confronted with constraints from experiments and astrophysical observations. There are just very few models which are compatible even with this very restricted set of constraints. These remaining models illustrate the uncertainty of the uniform nuclear matter EOS at high densities. In addition, at finite temperatures the medium modifications of nuclear clusters represent a conceptual challenge. In conclusion, there has been significant development in the recent years, but there is still need for further improved general purpose EOS tables

Equation of state at high densities and modern compact star observations

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

1-2-3-flavor color superconductivity in compact stars

We suggest a scenario where the three light quark flavors are sequentially deconfined under increasing pressure in cold asymmetric nuclear matter, e.g., as 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) and spin-0 two/three flavor (2SC/CFL) channels, and a Dirac-Brueckner Hartree-Fock (DBHF) approach in the nuclear matter sector. 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 imposed by beta-equilibrium and charge neutrality. At about 3n_0 u-quarks appear forming a two-flavor color superconducting (2SC) phase, while the s-quark Fermi sea is populated only at still higher baryon density. The hybrid star sequence has a maximum mass of 2.1 M_sun. Two- and three-flavor quark matter phases are found only in gravitationally unstable hybrid star solutions.Comment: 4 pages, 2 figures, to appear in the proceedings of Quark Matter 2008: 20th International Conference on Ultra-Relativistic Nucleus Nucleus Collisions (QM 2008), Jaipur, India, 4-10 Feb 200

Vector-Interaction-Enhanced Bag Model

A commonly applied quark matter model in astrophysics is the thermodynamic bag model (tdBAG). The original MIT bag model approximates the effect of quark confinement, but does not explicitly account for the breaking of chiral symmetry, an important property of Quantum Chromodynamics (QCD). It further ignores vector repulsion. The vector-interaction-enhanced bag model (vBag) improves the tdBAG approach by accounting for both dynamical chiral symmetry breaking and repulsive vector interactions. The latter is of particular importance to studies of dense matter in beta-equilibriumto explain the two solar mass maximum mass constraint for neutron stars. The model is motivated by analyses of QCD based Dyson-Schwinger equations (DSE), assuming a simple quark-quark contact interaction. Here, we focus on the study of hybrid neutron star properties resulting from the application of vBag and will discuss possible extensions.Comment: 9 pages, 4 figures, conference proceedings of CSQCD

Chaos in QCD? Gap Equations and Their Fractal Properties

In this study, we discuss how iterative solutions of QCD-inspired gap-equations at the finite chemical potential demonstrate domains of chaotic behavior as well as non-chaotic domains, which represent one or the other of the only two—usually distinct—positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach, gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cut-off. The transition domain between these two energy-separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, and determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition