Thomas Klähn

Modern compact star observations and the quark matter equation of state

Abstract 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 ⊙ ) 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 ∼ 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 are consistent with modern CS observations. Hybrid star configurations with a CFL quark core are unstable within the present model.

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.

Symmetry Energy of Dilute Warm Nuclear Matter

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

Implications of the measurement of pulsars with two solar masses for quark matter in compact stars and heavy-ion collisions: A Nambu-Jona-Lasinio model case study

The precise measurement of the high masses of the pulsars PSR J1614-2230 (M1614 = 1.97 ± 0.04 M⊙) and PSR J0348-0432 (M0348 = 2.01 ± 0.04 M⊙) provides an important constraint for the equation of state of cold, dense matter and is suited to give interesting insights regarding the nature and existence of the possible phase transition to deconfined quark matter in the cores of neutron stars. We analyze the stability and composition of compact star sequences for a class of hybrid nuclear – quark-matter equations of state. The quark matter phase is described in the framework of a standard color superconducting 3-flavor Nambu–Jona-Lasinio model and the hadronic phase is given by the Dirac-BruecknerHartree-Fock equation of state for the Bonn-A potential. The phase transition is obtained by a Maxwell construction. Within this model setup we aim to constrain otherwise not strictly fixed parameters of the NJL model, namely the coupling strengths in the vector meson and diquark interaction channels. We perform this investigation for two different parameterizations characterized by a different scalar coupling constant. The analysis of flow data obtained in heavy-ion collisions resulted in a further constraint which we account for in our discussion. Massive hybrid stars with extended quark matter cores can be obtained in accordance with all of the considered constraints.

Survey of Nucleon Electromagnetic Form Factors

A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincaré covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; namely, a diquark charge radius. It is argued to be commensurate with the pion’s charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are:

Exploring the light-quark interaction

{r_1^{n,u} > r_1^{n,d}}

Chemical potential and the gap equation

, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.

Cold quarks in medium: an equation of state

For quark matter studies in astrophysics the thermodynamic bag model (tdBAG) has been widely used. Despite its success it fails to account for various phenomena expected from Quantum-ChromoDynamics (QCD). We suggest a straightforward extension of tdBAG in order to take the dynamical breaking of chiral symmetry and the influence of vector interactions explicitly into account. As for tdBAG the model mimics confinement in a phenomenological approach. It is based on an analysis of the Nambu–Jona-Lasinio (NJL) model at finite density. Furthermore, we demonstrate how NJL and bag models in this regime follow from the more general and QCD based framework of DysonSchwinger (DS) equations in medium by assuming a simple gluon contact interaction. Based on our simple and novel model, we construct quark hadron hybrid equations of state (EoS) and study systematically chiral and deconfinement phase transitions, the appearance of s-quarks and the role of vector interaction. We further study these aspects for matter in β-equilibrium at zero temperature, with particular focus on the current ∼ 2 M⊙ maximum mass constraint for neutron stars. Our approach indicates that the currently only theoretical evidence for the hypothesis of stable strange matter is an artifact of tdBAG and results from neglecting the dynamical breaking of chiral symmetry. Subject headings: dense matter — equation of state — elementary particles: quarks — stars: neutron