Abstract
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 (≲10 9 K) and quark fractions (≲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.
Highlights
It was shown by Glendenning [1,2] that if electric charge neutrality in a neutron star [3,4,5] is treated globally rather than locally, the possible first order phase transition from hadronic matter to quark matter in the neutron star core will result in a mixed phase in which both phases of matter coexist
Including the vector interaction (GV = 0.05 GS ) results in a slight increase in the mixed phase Bremsstrahlung (MPB) emissivity. Both additional baryonic degrees of freedom and inclusion of the vector interaction delay the onset of the quark–hadron phase transition, and it may be concluded that the greater the density in the mixed phase, the greater the contribution to the emissivity from MPB
In this work we determined that quark blob, rod, and slab structures may exist in a crystalline quark–hadron mixed phase
Summary
It was shown by Glendenning [1,2] that if electric charge neutrality in a neutron star [3,4,5] is treated globally rather than locally, the possible first order phase transition from hadronic matter to quark matter in the neutron star core will result in a mixed phase in which both phases of matter coexist. The presence of the Coulomb lattice and the nature of the geometric configurations of matter in the quark–hadron mixed phase may have a significant effect on the neutrino emissivity from the core. We consider three geometries for the range of possible structures in the mixed phase including spherical blobs, rods, and slabs, and calculate the associated static lattice contributions to the neutrino emissivity. The extent of the conversion to quark matter in the core was determined in [7], and this allows for a comparison between emissivity contributions from standard and enhanced neutrino emission mechanisms including the direct Urca (DU), modified. The results of the other parametrizations can be found in [7]
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