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Forging neon-distilling white dwarfs in the stellar engulfments of helium white dwarfs

Once carbon--oxygen white dwarfs cool sufficiently, they crystallize from the inside out. If the white dwarf is rich enough in ${}^{22}\mathrm{Ne}$, these crystallized solids are buoyant and rapidly rise, efficiently liberating potential energy which may halt the cooling of the white dwarf or power magnetic phenomena. Although this ${}^{22}\mathrm{Ne}$ distillation process may explain the cooling anomaly in Q-branch white dwarfs and anomalous emission lines in DAHe white dwarfs, its operation demands unusually high ${}^{22}\mathrm{Ne}$ abundances not generically predicted by isolated stellar evolution. We show that the engulfments of helium white dwarfs by both main-sequence and red giant stars can result in carbon--oxygen white dwarfs with ${}^{22}\mathrm{Ne}$ abundances high enough to distill ${}^{22}\mathrm{Ne}$. This enhancement occurs because carbon dredged up following an especially energetic and off-center helium flash can be processed into ${}^{22}\mathrm{Ne}$ by subsequent hydrogen shell burning and helium shell burning. ${}^{22}\mathrm{Ne}$-distilling white dwarfs from these merger channels are predicted to be somewhat more massive than typical white dwarfs (up to $\simeq0.7M_\odot$) and may have anomalous rotation rates, consistent with DAHe white dwarfs. These binary formation channels for ${}^{22}\mathrm{Ne}$-rich white dwarfs reveal new connections between binary interactions and white dwarf cooling phenomena.