Neutrino Emissivity in the Quark-Hadron Mixed Phase

TL;DR

This paper investigates how a crystalline quark-hadron mixed phase in neutron star cores affects neutrino emission, finding significant contributions at low temperatures and quark fractions, with implications for neutron star cooling models.

Contribution

It models the crystalline structure of the quark-hadron mixed phase and calculates its impact on neutrino emissivity, highlighting the importance of static lattice effects over vibrations.

Findings

Crystalline quark-hadron phase significantly enhances neutrino emissivity at low temperatures.

Static lattice contributions dominate over lattice vibrations in neutrino emission.

The study identifies key open issues for future research on neutrino bremsstrahlung processes.

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 ($\lesssim 10^9$ 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.