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In this work we study compact stars, i.e. neutron stars, as cosmic laboratories for the nuclear matter. With a mass of around 1 - 3 solar masses and a radius of around 10km, compact stars are very dense and, besides nucleons, can contain exotic matter such as hyperons or quark matter. The KaoS collaboration studied nuclear matter for densities up to 2-3 times saturation density by analysing kaon multiplicities from Au+Au and C+C collisions. The results show that nuclear matter in the corresponding density region is very compressible, with a compressibility of <200MeV. For such soft nuclear equations of state the maximum masses of neutron stars are ca. 1.8 - 1.9 solar masses, whereas the central densities are higher than 5 times nuclear saturation density and therefore point towards a possible phase transition to quark matter. If quark matter would be present in the interior of neutron stars, so-called hybrid stars, it could be produced already during their birth in supernova explosions. To study this we implement a quark matter phase transition in a hadronic equation of state which is used in supernova simulations. Supernova simulations of low and intermediate mass progenitors and two different bag constants show a collapse of the proto neutron star due to the softening of the equations of state in the quark-hadron mixed phase. The stiffening of the equation of state for pure quark matter halts the collapse and leads to the production of a second shock wave. The second shock wave is energetic enough to lead to an explosion of the star and produces a neutrino burst when passing the neutrinospheres. Furthermore, first studies of the longtime cooling of hybrid stars show, that colour superconductivity can significantly influence the cooling behaviour of hybrid stars, if all quarks form Cooper Pairs. For the so-called CSL phase (colour-spin locking) with pairing energies of several MeV, the cooling of the quark phase is suppressed and the hybrid star appears as a pure hadronic star.
High-energy astrophysics plays an increasingly important role in the understanding of our universe. On one hand, this is due to ground-breaking observations, like the gravitational-wave detections of the LIGO and Virgo network or the black-hole shadow observations of the EHT collaboration. On the other hand, the field of numerical relativity has reached a level of sophistication that allows for realistic simulations that include all four fundamental forces of nature. A prime example of how observations and theory complement each other can be seen in the studies following GW170817, the first detection of gravitational waves from a binary neutron-star merger. The same detection is also the chronological starting point of this Thesis. The plethora of information and constraints on nuclear physics derived from GW170817 in conjunction with theoretical computations will be presented in the first part of this Thesis. The second part goes beyond this detection and prepares for future observations when also the high-frequency postmerger signal will become detectable. Specifically, signatures of a quark-hadron phase transition are discussed and the specific case of a delayed phase transition is analyzed in detail. Finally, the third part of this Thesis focuses on the inclusion of radiative transport in numerical astrophysics. In the context of binary neutron-star mergers, radiation in the form of neutrinos is crucial for realistic long-term simulations. Two methods are introduced for treating radiation: the approximate state-of-the-art two-moment method (M1) and the recently developed radiative Lattice-Boltzmann method. The latter promises
to be more accurate than M1 at a comparable computational cost. Given that most methods for radiative transport or either inaccurate or unfeasible, the derivation of this new method represents a novel and possibly paradigm-changing contribution to an accurate inclusion of radiation in numerical astrophysics.
In dieser Arbeit wurden thermodynamische Eigenschaften eines chiralen Quark Meson Modelles untersucht. Das chirale Quark Meson Model beschreibt die starke Wechselwirkung über den Austausch von Mesonen und zudem die thermische und dichteabhängige Entwicklung der Quarkmassen im Medium über die chirale Symmetrie.Im SU(2) Model wurde zunächst in mean field approximation gearbeitet, um im Anschluss den divergenten Vakuumterm mit einzubeziehen. Nach eingehender Untersuchung der Ergebnisse, wurden dann die thermischen Mesonenfluktuationen studiert. In beiden Ansätzen verschiebt die Nullpunktsenergie den chiralen Phasenübergang zu höheren Temperaturen, wodurch die Massen bei höheren Temperaturen entarten. Beide Ansätze wurden dann zu einem gemeinsamen Modell kombiniert, um den Einfluss der Mesonenfluktuationen auf Ordnungsparameter, Massen und thermodynamische Grössen zu untersuchen. Als Fazit der Studie kann behauptet werden, dass sich der Einfluss der Mesonenfluktuationen in grösserem Maÿ auf die Thermodynamik, als auf den Ordnungsparameter und die Massen auswirkt. Im SU(3) Modell wurden ebenfalls regularisiert und zudem Vektormesonen mitberücksichtigt, welche die Repulsion zwischen den einzelnen Freiheitsgraden modelliert. Die Zustandsgleichung wird durch den Vakuum Term etwas softer und zeigt ein ähnliches Verhalten im niederen Energiebereich. Untersucht wurde neben der Temperatur T, die Elektron Baryon Rate Ye, die Sigma Meson Masse noch der Einfluss der Vektorkopplung. Aus der Zustandsgleichung konntendann Isentropen im T-mu Phasendiagramm errechnet werden, welche in naher Zukunft Aufschluss über eine dritte Familie von kompakten Sternen in Zusammenhang mit der entsprechenden Supernova Explosion geben könnte. Um die Existenz von kompakten Sternen genauer zu analysieren, wurde das chiraleSU(3) Quark Meson Modell bei T = 0 benutzt, um über die aus dem Formalismusgewonnenen Grössen Druck und Energiedichte die Tolmann-Oppenheimer-Volkoff zu lösen. Diese stellen die Masse-Radius Beziehungen kompakter Objekte dar. Auf der Suche nach Twin Stern Lösungen aus dem chiralen SU(3) Quark Meson Model wurde zunächst ein Modell für Hybridsterne entwickelt. Im untersuchten Parameterbereich fanden wir Hybrid Stern Lösungen, bei welchen der Einfluss der Quarkmaterie auf die Stabilität des Sternes untersucht wurde, denn das Einsetzen des Phasenüberganges übt einen zusätzlichen gravitativen Zug auf die hadronische Kruste aus. Der Stern ist stabil, wenn der Druck der Quarkmaterie diesem zusätzlichen Zug standzuhalten vermag. Für einen zu grossen Sprung in der Energiedichte werden die Lösungen jedoch instabil. Zwillingssterne waren nicht unter den Lösungen, da der Übergangsdruck relativklein sein muss, während der Energiedichtesprung eher gross sein sollte. Das Auftreten zweier stabiler Äste in der Masse Radius Relation kann allerdingsmit dem SU(3) Modell und entsprechendem chiralen Phasenübergang modelliert werden. Für einen gewissen Parameterbereich einhergehend mit kleinem Wert des Vakuum Druckes B konnten Nicht-Linearitäten in der Zustangsgleichungzur Lösung der TOV Gleichung beitragen. Im Weitern ist das Zusammenspiel der Vektorkopplung und der Sigma Mesonen Masse einflussreich auf die Lösungen, welche auf Kausalität, Stabilität und neben der 2 Sonnenmassen Bedingung noch auf Restriktionen vom millisecond pulsar PSR J1748-2446ad untersucht wurden.Mit Weltraummissionen wie etwa NICER (Neutron star Interior CompositionExploreR) sollte die Radiusbestimmung kompakter Objekte in Zukunft bis auf einen Kilometer genau bestimmt werden können. Die Entdeckung von zweiSternen mit der gleichen Masse und unterschiedlichen Radien wäre in der Tat ein Beweis für die Existenz von Zwillingssternen, welche dann die Theorie des Phasenüberganges in dichter Materie untermauern würde. Das Kollaps-Szenario eines Zwillingssternes würde weiteren Aufschluss über Neutrino-Emmissivität, Gamma-ray burster und Gravitationswellen Signale geben können. Dynamische Simulationen in allgemein relativistischem Kontext für compact star merger mit den hier diskutierten Zustandsgleichungen sind bereits in Planung, um Eigenschaftenwie beispielsweise das Temperatur- und Dichteprofil solcher Objekte genauer zu analysieren.
The chiral phase transition of Quantum Chromo Dynamics (QCD) is investigated with the help of the linear-sigma model and a numerical transport simulation. The scope are non-equilibrium and critical effects of the different type of orders of the transition. Additionally, a mathematical and numerical method is developed which allows to simulate a particle-wave duality and non-continuous interactions, even for classical systems.
This thesis has light mesons and their vacuum interactions as its topic. In particular, the work examines the question where the scalar antiquark-quark states are found in the physical spectrum -- in the energy region below or above 1 GeV. Contrary to the naive expectation, the mentioned states are found in the region above 1 GeV. This has consequences for the building of order parameters for the chiral symmetry breaking of Quantum Chromodynamics (QCD).
In this thesis, I study the phase diagram of dense, locally neutral three-flavor quark matter as a function of the strange quark mass, the quark chemical potential, and the temperature, employing a general nine-parameter ansatz for the gap matrix. At zero temperature and small values of the strange quark mass, the ground state of quark matter corresponds to the color–flavor-locked (CFL) phase. At some critical value of the strange quark mass, this is replaced by the recently proposed gapless CFL (gCFL) phase. I also find several other phases, for instance, a metallic CFL (mCFL) phase, a so-called uSC phase where all colors of up quarks are paired, as well as the standard two-flavor color-superconducting (2SC) phase and the gapless 2SC (g2SC) phase. I also study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of a Nambu–Jona-Lasinio (NJL) model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength. In addition, I study the effect of neutrino trapping on the phase diagram of dense, locally neutral three-flavor quark matter within the same NJL model. The phase diagrams in the plane of temperature and quark chemical potential, as well as in the plane of temperature and leptonnumber chemical potential are presented. I show that neutrino trapping favors two-flavor color superconductivity and disfavors the color–flavor-locked phase at intermediate densities of matter. At the same time, the location of the critical line separating the two-flavor color-superconducting phase and the normal phase of quark matter is little affected by the presence of neutrinos. The implications of these results for the evolution of protoneutron stars are briefly discussed.
In this thesis we investigate the role played by gauge fields in providing new observable signatures that can attest to the presence of color superconductivity in neutron stars. We show that thermal gluon fluctuations in color-flavor locked superconductors can substantially increase their critical temperature and also change the order of the transition, which becomes a strong first-order phase transition. Moreover, we explore the effects of strong magnetic fields on the properties of color-flavor locked superconducting matter. We find that both the energy gaps as well as the magnetization are oscillating functions of the magnetic field. Also, it is shown that the magnetization can be so strong that homogeneous quark matter becomes metastable for a range of parameters. This points towards the existence of magnetic domains or other types of magnetic inhomogeneities in the hypothesized quark cores of magnetars. Obviously, our results only apply if the strong magnetic fields observed on the surface of magnetars can be transmitted to their inner core. This can occur if the superconducting protons expected to exist in the outer core form a type-I I superconductor. However, it has been argued that the observed long periodic oscillations in isolated pulsars can only be explained if the outer core is a type-I superconductor rather than type-I I. We show that this is not the only solution for the precession puzzle by demonstrating that the long-term variation in the spin of PSR 1828-11 can be explained in terms of Tkachenko oscillations within superfluid shells.
Neutron stars are unique laboratories for the investigation of the high density properties of bulk matter. In this work, the astrophysical constraints for a phase transition from hadronic matter to deconfined quark matter are examined thoroughly. A scheme for relating known astrophysical observables such as mass, radius and tidal deformability to the parameter space of such a transition is devised and applied to the set of data currently available.
In order to span a wide parameter space, a highly parameterizable relativistic mean field equation in compliance with chiral effective field theory results is used, where the stiffness of the equation of state can be varied via the effective mass at saturation density. The phase transitions are modelled using a Maxwell construction and assumed to be of first order, with a constant speed of sound quark matter model. The resulting equations of state are analyzed and divided into four categories, which can be used to constrain the parameter space that allows phase transition. It is highlighted, that a subset of this parameter space would even be detectable without the need of higher precision measurements. A phase transition at high densities is shown to be particularly promising in this regard. Finally, the groundwork is laid to apply the equation of state used in this work for supernova or merger simulations, by extending it to non-zero temperatures.
I derive a general effective theory for hot and/or dense quark matter. After introducing general projection operators for hard and soft quark and gluon degrees of freedom, I explicitly compute the functional integral for the hard quark and gluon modes in the QCD partition function. Upon appropriate choices for the projection operators one recovers various well-known effective theories such as the Hard Thermal Loop/ Hard Dense Loop Effective Theories as well as the High Density Effective Theory by Hong and Schaefer. I then apply the effective theory to cold and dense quark matter and show how it can be utilized to simplify the weak-coupling solution of the color-superconducting gap equation. In general, one considers as relevant quark degrees of freedom those within a thin layer of width 2 Lambda_q around the Fermi surface and as relevant gluon degrees of freedom those with 3-momenta less than Lambda_gl. It turns out that it is necessary to choose Lambda_q << Lambda_gl, i.e., scattering of quarks along the Fermi surface is the dominant process. Moreover, this special choice of the two cutoff parameters Lambda_q and Lambda_gl facilitates the power-counting of the numerous contributions in the gap-equation. In addition, it is demonstrated that both the energy and the momentum dependence of the gap function has to be treated self-consistently in order to determine the imaginary part of the gap function. For quarks close to the Fermi surface the imaginary part is calculated explicitly and shown to be of sub-subleading order in the gap equation.