Phase transitions and crystalline structures in neutron star cores

The mixed phase of a fully equilibrated nuclear system that is asymmetric in isospin (i.e. in charge) will develop a geometrical structure of the rarer phase immersed in the dominant one. This happens because the isospin asymmetry energy will exploit the degree of freedom available to a system of more than one independent component (or conserved charge) by rearranging the proportion of charge to baryon number between the two equilibrium phases so as to lower the energy; that is, to effectively reduce the isospin asymmetry in the normal nuclear phase. Consequently, the two phases will have opposite charge; competition between Coulomb and surface energy will be resolved by formation of a Coulomb lattice of the rarer phase situated at sites in the dominant phase. The geometric form, size, and spacing of the phase occupying the lattice sites will depend on the pressure or density of matter. Thus, a neutron star containing a mixed phase region of whatever kind, will have a varying geometric structure of one phase embedded in the other. This is expected to effect transport properties of the star as well as to effect the glitch behavior of pulsars that contain a mixed phase region. We study in particular, the quark deconfinement and kaon condensation phase transitions as examples of this general phenomenon.