Three-body crystallization diagrams and the cooling of white dwarfs

The 3-body crystallization diagrams of C/O/Ne ionic mixtures characteristic of white dwarf interiors are examined within the framework of the density-functional theory of freezing. The crystallization process is described more accurately than in former calculations where the three-component system was treated as an effective two-component mixture (Segretain et al. 1994). The distillation process due to neon-crystallization is found to occur only for the late stages of crystallization. At the beginning, the presence of neon plays only a minor role and the phase diagram resembles a pure carbon-oxygen diagram. The final phase diagram is found to exhibit an azeotropic point with a neon concentration $x_{Ne}=0.22$, a carbon concentration $x_{C}=0.78$ and an oxygen concentration $x_O=0$, so that during the distillation process, the fluid crystallizes into a pure neon-carbon solid. The critical temperature is $T_A=0.85\,T_C$, where $T_C$ is the pure carbon crystallization temperature. We use this accurate phase diagram to calculate the total gravitational energy released during white dwarf crystallization and the related time delay. The final result yields $\Delta \tau \approx 2.6$ Gyr, among which about 20\% are due to the neon-distillation process.