Properties of Hypothetical Quark-Hadron Coulomb Lattices in the Cores of Neutron Stars

The tremendously high pressures in the cores of neutron
stars may break up neutrons, protons plus other baryonic particles
into their quark constituents. This could lead to an extended
quark-hadron mixed phase region in the cores of neutron stars that
would segregate phases by net charge to minimize the total energy of
the system, leading to the formation of a crystalline quark-hadron
Coulomb lattice. In this talk, we investigate the neutrino emissivity
due to the elastic scattering of electrons off the quark
Coulomb lattice sites, which are assumed to be made of ordinary (i.e.,
non-superconducting) as well as superconducting (CFL) quark structures.

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. The extent of the quark-hadron mixed phase
and its crystalline structure is determined using the Glendenning
construction, which allows for the formation of spherical blob, rod,
and slab rare phase geometries.

It is found that the contribution to the neutrino emissivity due to
the presence of a crystalline quark-hadron mixed phase is substantial
compared to other mechanisms only at fairly low temperatures and small
quark fractions.