Eur. Phys. J. A (2016) 52: 61
https://doi.org/10.1140/epja/i2016-16061-x

Regular Article - Theoretical Physics

Neutrino emissivity in the quark-hadron mixed phase of neutron stars

¹ Computational Science Research Center San Diego State University, 5500 Campanile Drive, 92182, San Diego, CA, USA
² Department of Physics, San Diego State University, 5500 Campanile Drive, 92182, San Diego, CA, USA
³ Center for Astrophysics and Space Sciences, University of California San Diego, 9500 Gilman Drive, 92093, La Jolla, CA, USA
⁴ CONICET, Rivadavia 1917, 1033, Buenos Aires, Argentina
⁵ IFLP, CONICET - Dpto. de Fısica, UNLP, La Plata, Argentina
⁶ Grupo de Gravitación, Astrofısica y Cosmologıa, Facultad de Ciencias Astronómicas y Geofısicas, Universidad Nacional de La Plata, Paseo del Bosque S/N (1900), La Plata, Argentina

^* e-mail: fweber@mail.sdsu.edu

Received: 24 June 2015
Revised: 12 January 2016
Accepted: 17 January 2016
Published online: 22 March 2016

Abstract

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 ( K) and quark fractions ( , and that contributions due to lattice vibrations are insignificant compared to static-lattice contributions.