Rigid Crystalline Color Superconducting Quark Matter

Abstract

Cold three flavor quark matter at large (but not asymptotically large) densities may exist in a crystalline color superconducting phase. These phases are characterized by a gap parameter Δ that varies periodically in space, forming a crystal structure. A Ginzburg-Landau expansion in Δ shows that two crystal structures based on cubic symetry are particularly favorable, and may be the ground state of matter at densities present in neutron star cores. By deriving the effective action for the phonon fields that describe spaceand time-dependent fluctuations of the crystal structure formed by Δ, one can obtain its shear modulus. Within a Ginzburg-Landau approximation, we find shear moduli which are 20 to 1000 times larger than those of neutron star crusts. This phase of matter is thus more rigid than any known material in the universe, but at the same time the crystalline color superconducting phase is also superfluid. These properties raise the possibility that the presence of this phase within neutron stars may have distinct implications for their phenomenology. For example, (some) pulsar glitches may originate in crystalline superconducting neutron star cores.