Neutrino Emissivity in the Quark-Hadron Mixed Phase

Abstract

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.

Phases of Hadron-Quark Matter in (Proto) Neutron Stars

“…For matter described by global electric charge neutrality, this is the same as minimizing the contributions to the total energy due to phase segregation, which includes the surface and Coulomb energy contributions. Mathematically, the relations for the Coulomb ( C ) and the surface ( S ) energy densities are given by [1,2,32]…”

“…The spherical blobs populate sites in a three dimensional (D = 3) body centered cubic (BCC) lattice, the rods in a two dimensional (D = 2) triangular lattice, and the slabs in a simple one dimensional (D = 1) lattice. At a volume ratio of χ = 0.5 both hadronic and quark matter exist as slabs in the same proportion, and at χ > 0.5 the hadronic phase becomes the rare phase with its geometry evolving in reverse order (from slabs to rods to blobs) with increasing density [1,2,32]. The determination of the surface tension, α, of the quark-hadro interface is hampered by the fact that a single theory that can accurately describe both hadronic matter and quark matter does not exist.…”

“…lattice in the core of a neutron star and the neutrino emissivity in this phase have been investigated in Refs. [32,[34][35][36]].…”

Phase transitions in neutron stars and their links to gravitational waves

“…The effect of a crystalline quark-hadron mixed phase on the neutrino emissivity from the cores of NSs has been recently studied in Refs. [136,137].…”

Effects of Hadron-Quark Phase Transitions in Hybrid Stars within the NJL Model

“…Table 1. Properties of nuclear matter at saturation density for the hadronic GM1(L) parametrization [29,54].…”