Structure and cooling of (hybrid) neutron stars based on microscopic equations of state

Neutron stars (NSs) are the most compact objects in the Universe. The average mass of a NS is about 1.4 solar mass and its radius is about 10 km, hence the inner density can reach about 10 rho_0, being rho_0 the nuclear saturation density (rho_0 = 2.8 × 10^14 gcm−3). This makes a NS the natural‘laboratory’ for studying the four fundamental interactions, especially a unique environment for the study of the strongly interacting components at high densities. The equation of state (EOS) is a key ingredient in the NS study, however, it still suffers from the scarce knowledge of the strong interaction. This leads to the constructions of EOSs which are derived from different theoretical approaches, and being used to analyze many properties of NSs, e.g., the mass-radius relation, the moment of inertia and cooling properties in the evolutionary process. On the other hand, the observation of NSs allows us to constrain the EOS of the dense matter well beyond the densities available in earth laboratories. For example, observations of the NS mass, radius and the tidal deformability can be compared with the theoretical results, and from these the NS EOS can be inferred with some uncertainty. With this purpose, we employ the Brueckner-Hartree-Fock (BHF) theory for nuclear matter and two models (Field correlator and Dyson-Schwinger quark model) for quark matter, to study the properties of NSs, especially for the tidal deformability. Besides the astrophysical observations, heavy-ion collisions could also give rise to certain constraints on nuclear-matter properties, for instance, the binding energy per baryon at saturation, the symmetry energy and the incompressibility. One may think that there are correlations between constraints of nuclear matter properties and of a gravitational wave event. Based on this idea, we investigate properties of nuclear matter and examine possible correlations with NS observables for a set of microscopic nuclear EOSs derived within the BHF formalism employing compatible three-body forces. We find good candidates for a realistic nuclear EOS up to high density and confirm strong correlations between NS radius, tidal deformability, and the pressure of beta-stable matter. No correlations are found with the saturation properties of nuclear matter. Another possible way that could be used in the study of dense matter properties is NS cooling. A NS is born hot ( ∼ 10^11 K) in a supernova explosion. Afterwards, it cools through three stages, i.e., thermal relaxation, neutrino cooling stage and photon cooling stage. Most NSs are supposed to be in the neutrino cooling stage since this stage lasts ∼ 10^5 years. A simulation of NS cooling basically requires more quantities from the EOS, which we hope is able to reveal more facts about the dense matter. Therefore, we study the cooling of NSs and extend the work to the case of hybrid stars. We find that all BHF EOSs feature strong Direct Urca processes which lead to a too fast cooling. Accordingly, the pairing gaps, especially the proton 1S0 gap, are necessary and enough to describe well the current set of cooling data for isolated NSs. In all possible scenarios with and without quark matter, the possibility of a neutron 3P2 gap can be excluded.