<p> Astrophysical environments probe matter in ways impossible on Earth. In particular, matter in compact objects are extraordinarily dense. In this thesis we discuss two phenomena that may occur at high density. </p><p> First, we study toroidal topological solitons called vortons, which can occur in the kaon-condensed color-flavor-locked phase of high-density quark matter, a candidate phase for the core of some neutron stars. We show that vortons have a large radius compared to their thickness if their electrical charge is on the order of 10⁴ times the fundamental charge. We show that shielding of electric fields by electrons dramatically reduces the size of a vorton. </p><p> Second, we study an unusual phase of degenerate electrons and nonrelativistic Bose-condensed helium nuclei that may exist in helium white dwarfs. We show that this phase supports a previously-unknown gapless mode, known as the half-sound, that radically alters the material's specific heat, and can annihilate into neutrinos. We provide evidence that this neutrino radiation is negligible compared to the star's surface photoemission.</p>