Long-lived Habitable Zones around White Dwarfs undergoing Neon-22 Distillation

White dwarf stars have attracted considerable attention in the past 15 years as hosts for potentially habitable planets, but their low luminosity and continuous cooling are major challenges for habitability. Recently, astronomers have found that about 6% of massive white dwarfs seem to have "paused" their cooling for up to ~10 Gyr. The leading explanation for this cooling delay is the distillation of neutron-rich isotopes such as $^{22}$Ne in the white dwarf's interior, which releases a considerable amount of gravitational energy as the star's internal structure rearranges. Here, we consider the impact of $^{22}$Ne distillation on the evolution of white dwarf habitable zones. We find that $^{22}$Ne distillation in the white dwarf host dramatically increases the time that a planet can continuously reside within the habitable zone (giving more time for life to arise) and that long-lasting habitable zones are located farther from the star (decreasing the impact of tidal forces). These properties may make white dwarfs undergoing $^{22}$Ne distillation more promising locations for habitability than white dwarfs undergoing standard cooling.