Exomoonlight Sonata: On the Fate of Exomoons Around Migrating White Dwarf Planets

The survival of exomoons around close-in white dwarf planets offers a potential constraint on their migration histories and an alternative pathway to post-main-sequence habitability. We investigate whether moons can survive the tidal circularization of planets via high-eccentricity migration, and consider a hierarchical three-body system (white dwarf-planet-moon) after an initial eccentricity excitation of the planetary orbit. Using an analytic equilibrium tidal model, we compare the evolution of the planetary and satellite orbits and examine the conditions required for an evection resonance. We show that the moons of pseudosynchronously rotating planets always migrate inwards since the planetary corotation radius always exceeds the Hill radius, independent of mass and orbital eccentricities. Comparing the migration timescales for the moon and the planet shows that compact moons undergo rapid tidal decay relative to the outer orbit. However, the wider separations favored by slower migration timescales experience pericenter perturbations whose work constitutes a substantial fraction of the moon's orbital energy. Together, our results indicate that moons likely do not survive during a planet's high-eccentricity migration phase in a three-body configuration.