The Fraction of Distilled White Dwarfs with Long-Lived Habitable Zones

After carbon and oxygen, ${}^{22}$Ne is the most abundant element in white dwarf interiors. As C/O white dwarfs (WDs) crystallize, they are predicted to go through a distillation process in the central layers if they have a sufficiently high ${}^{22}$Ne mass fraction of $\gtrsim 2.5$%. Observational evidence for distillation comes from an over-density of WDs on the Q-branch in Gaia color-magnitude diagrams, which indicates that $\sim 6$% of massive WDs are delayed in their cooling by as much as $\sim 10$ Gyr. However, it is unclear how these stars end up with such a high concentration of ${}^{22}$Ne and if a significant fraction of the more common average-mass WDs go through distillation. We argue that a significant metal-rich stellar population in the solar neighborhood should lead to distilled WDs, without requiring a binary merger. We use MESA along with the CNO abundances derived from high-resolution spectroscopy of stars included in the Hypatia catalog to predict the ${}^{22}$Ne mass fraction in their descendant WDs. We find that 0.6-2.5% of the WDs in the solar neighborhood have sufficient ${}^{22}$Ne in their interiors to go through multi-Gyr cooling delays, which could significantly inflate their numbers in the observed samples. Hence, ${}^{22}$Ne distillation and long-lived habitable zones around WDs should be relatively common in the solar neighborhood. We also use a Galactic model to predict the fraction of WDs that go through distillation as a function of Galactocentric distance. The fraction of distilled WDs is $\sim 2$-8% near the Galactic center, and declines steadily toward the outer disk.