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Register a new userNeutrino emissivity in the quark-hadron mixed phase of neutron stars
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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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In this work we investigate the effect a crystalline quark-hadron mixed phase can have on the neutrino emissivity from the cores of neutron stars. To this end we use relativistic mean-field equations of state 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. There are a number of open issues that need to be addressed in a future study on the neutrino emission rates caused by electron-quark blob bremsstrahlung. Chiefly among them are the role of collective oscillations of matter, electron band structures, and of gaps at the boundaries of the Brillouin zones on bremsstrahlung, as discussed in the summary section of this paper. We hope this paper will stimulate studies addressing these issues.
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.
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.
A recent solution of the hyperon puzzle by a first order phase transition to color superconducting quark matter is revisited in order to replace the Maxwell construction by an interpolation method which describes a mixed phase. To do this, we apply for the first time the finite-range polynomial interpolation method for constructing a transition between hadronic and quark matter phases to the situation that is characterized in the literature as the reconfinement problem. For the description of the hadronic phase the lowest order constrained variational method is used while for the quark phase the nonlocal Nambu-Jona-Lasinio model with constant (model nlNJLA) and with density-dependent (model nlNJLB) parameters is employed. Applying the replacement interpolation method to both quark matter models results in a hybrid equation of state that allows a coexistence of nuclear matter, hypernuclear matter and quark matter in a mixed phase between the pure hadronic and quark phases which can also be realized in the structure of the corresponding hybrid star sequences. The predicted hybrid stars fulfill the constraints on the mass-radius relation for neutron stars obtained from recent observations.
We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral invariant mass ($m_0 gtrsim 500$ MeV, which is favored by the neutron star observations) predicts the mild chiral restoration, and the significant chiral condensate remains to baryon density $n_B sim 2-3n_0$ ($n_0simeq 0.16,{rm fm}^{-3}$: nuclear saturation density), smoothly approaching the NJL predictions for the color-flavor-locked phase at $n_B gtrsim 5n_0$. The same method is applied to estimate diquark condensates, number densities of up-, down- and strange-quarks, and the lepton fraction. In our descriptions the chiral restoration in the interpolated domain proceeds with two conceptually distinct chiral restoration effects; the first is associated with the positive scalar density in a nucleon, relevant in dilute regime, and the other primarily arises from the modification of the quark Dirac sea, which is triggered by the growth of the quark Fermi sea. We discuss several qualitative conjectures to interpolate the microphysics in nuclear and quark matter.
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