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Register a new userModelling Hybrid Stars in Quark-Hadron Approaches
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The density in the core of neutron stars can reach values of about 5 to 10 times nuclear matter saturation density. It is, therefore, a natural assumption that hadrons may have dissolved into quarks under such conditions, forming a hybrid star. This star will have an outer region of hadronic matter and a core of quark matter or even a mixed state of hadrons and quarks. In order to investigate such phases, we discuss different model approaches that can be used in the study of compact stars as well as being applicable to a wider range of temperatures and densities. One major model ingredient, the role of quark interactions in the stability of massive hybrid stars is discussed. In this context, possible conflicts with lattice QCD simulations are investigated.
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The study of neutron stars, or more general compact stars, is a topic of central interest in nuclear astrophysics. Furthermore, neutron stars serve as the only physical systems whose properties can be used to infer information on cold and dense matter at several times nuclear saturation density. Therefore, neutron star physics is ideally suited to complement the studies of ultra-relativistic heavy-ion collisions that sample strongly interacting matter at high temperature and relatively small net baryon density. In general, in order to pin down or at least constrain the properties of dense matter, accurate measurements of neutron star properties like masses, radii, rotational frequency, and cooling behavior are needed. Here, in relatively recent times the reliable mass determination of the pulsar PSR J1614-2230 of $M = 1.97 pm 0.04 M_odot$ has introduced an important benchmark for modeling stars and strongly interacting matter. It puts constraints on the structure of compact stars and possible exotic phases in the core of the stars as will be discussed in this article. In order to investigate this point we will consider a model for star matter that includes hyperonic and quark degrees of freedom, and present results for compact star properties in the following.
In the first part of this paper, we investigate the possible existence of a structured hadron-quark mixed phase in the cores of neutron stars. This phase, referred to as the hadron-quark pasta phase, consists of spherical blob, rod, and slab rare phase geometries. Particular emphasis is given to modeling the size othis phase in rotating neutron stars. We use the relativistic mean-field theory to model hadronic matter and the non-local three-flavor Nambu-Jona-Lasinio model to describe quark matter. Based on these models, the hadron-quark pasta phase exists only in very massive neutron stars, whose rotational frequencies are less than around 300 Hz. All other stars are not dense enough to trigger quark deconfinement in their cores. Part two of the paper deals with the quark-hadron composition of hot (proto) neutron star matter. To this end we use a local three-flavor Polyakov-Nambu-Jona-Lasinio model which includes the t Hooft (quark flavor mixing) term. It is found that this term leads to non-negligible changes in the particle composition of (proto) neutron stars made of hadron-quark matter.
We investigate the surface tension $sigma$ and the curvature energy $gamma$ of quark matter drops in the MIT bag model with vector interactions. Finite size corrections to the density of states are implemented by using the multiple reflection expansion (MRE) formalism. We find that $sigma$ and $gamma$ are strongly enhanced by new terms arising from vector interactions. With respect to the noninteracting case they are increased by a large factor, which can be as high as $sim 10$ when the vector coupling constant $g$ varies within the range used in the literature. This behavior may have major consequences for the hadron-quark mixed phase speculated to exist at neutron star (NS) interiors, which may be totally suppressed or have its extension substantially reduced.
The mixed phase of quarks and hadrons which might exist in the dense matter encountered in the varying conditions of temperature and trapped neutrino fraction in proto-neutron stars is studied. The extent that the mixed phase depends upon the thermodynamical parameters as well as on the stiffness of matter in the hadronic and quark phases is discussed. We show that hadronic equations of state that maximize the quark content of matter at a given {it density} generally minimize the extent of the mixed phase region in a neutron star of a given mass, and that only in extreme cases could a pure quark star result. For both the Nambu Jona-Lasinio and MIT bag quark models, neutrino trapping inhibits the appearance of a mixed phase which leads to possible proto-neutron star metastability. The main difference between the two quark models is the small abundance of strange quarks in the former. We also demonstrate that $partial T/partial n<0$ along adiabats in the quark-hadron mixed phase, opposite to what is found for the kaon condensates-hadron mixed phase. This could lead to core temperatures which are significantly lower in stars containing quarks than in those not containing quarks.
Numerous theoretical studies using various equation of state models have shown that quark matter may exist at the extreme densities in the cores of high-mass neutron stars. It has also been shown that a phase transition from hadronic matter to quark matter would result in an extended mixed phase region that would segregate phases by net charge to minimize the total energy of the phase, leading to the formation of a crystalline lattice. The existence of quark matter in the core of a neutron star may have significant consequences for its thermal evolution, which for thousands of years is facilitated primarily by neutrino emission. In this work we investigate the effect a crystalline quark-hadron mixed phase can have on the neutrino emissivity from the core. To this end we calculate the equation of state using the relativistic mean-field approximation to model hadronic matter and a nonlocal extension of the three-flavor Nambu-Jona-Lasinio model for quark matter. Next we determine the extent of the quark-hadron mixed phase and its crystalline structure using the Glendenning construction, allowing for the formation of spherical blob, rod, and slab rare phase geometries. Finally we calculate the neutrino emissivity due to electron-lattice interactions utilizing the formalism developed for the analogous process in neutron star crusts. We find that the contribution to the neutrino emissivity due to the presence of a crystalline quark-hadron mixed phase is substantial compared to other mechanisms at fairly low temperatures ($lesssim 10^9$ K) and quark fractions ($lesssim 30%$), and that contributions due to lattice vibrations are insignificant compared to static-lattice contributions.
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