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Habitable Planets Around White and Brown Dwarfs: The Perils of a Cooling Primary

White and brown dwarfs are astrophysical objects that are bright enough to support an insolation habitable zone (IHZ). Unlike hydrogen-burning stars, they cool and become less luminous with time, and hence their IHZ moves in with time. The inner edge of the IHZ is defined as the orbital radius at which a planet may enter a moist or runaway greenhouse, phenomena that can remove a planet's surface water forever. Thus, as the IHZ moves in, planets that enter it may no longer have any water, and are still uninhabitable. Additionally, the close proximity of the IHZ to the primary leads to concern that tidal heating may also be strong enough to trigger a runaway greenhouse, even for orbital eccentricities as small as 10^-6. Water loss occurs due to photolyzation by UV photons in the planetary stratosphere, followed by hydrogen escape. Young white dwarfs emit a large amount of these photons as their surface temperatures are over 10^4 K. The situation is less clear for brown dwarfs, as observational data do not constrain their early activity and UV emission very well. Nonetheless, both types of planets are at risk of never achieving habitable conditions, but planets orbiting white dwarfs may be less likely to sustain life than those orbiting brown dwarfs. We consider the future habitability of the planet candidates KOI 55.01 and 55.02 in these terms and find they are unlikely to become habitable.