White dwarfs as quantum crystals

Abstract

WHITE dwarfs are the most common endpoint of stellar evolution. Thermonuclear reactions have ceased, and the star settles into a compact object governed by relativistic, almost degenerate electrons. Bare nuclei of carbon and other heavier elements, normally considered as classical particles moving in the degenerate electron sea, are forced into a crystal lattice in the interior¹ as the star cools, and a freezing front moves outward. Numerical simulations of the freezing of classical point charges in a uniform neutralizing background have been used to model the crystallization of white dwarfs^2–4, but we show here that the classical approximation is not a good one: the energy per particle is significantly modified by quantum effects. The freezing process is then a transformation of a quantum liquid to a quantum solid, and the temperature of freezing may be reduced from the classical value. For lower mass stars particularly, the quantum corrections in liquid and solid seem to be comparable, and the physical conditions at freezing, classically typified by the ratio of the root-mean-square atomic displacement to the nearest-neighbour distance, are not greatly changed. Nevertheless, these new considerations may have an important effect on the cooling rate of white dwarfs, and thereby on their inferred evolution and ages.