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

This paper investigates whether moons can survive around giant planets migrating into close orbits around white dwarfs. Such moons could potentially occupy temperate environments as the white dwarfs cool, but they must first survive their host planets’ migration. The authors focus on high-eccentricity migration, in which a planet is driven onto a highly elongated orbit that subsequently circularizes through tidal dissipation. Specifically, they ask whether a moon that survives stellar evolution and the initial excitation of planetary eccentricity can also survive the subsequent migration phase. The study uses an analytic, orbit-averaged equilibrium-tide model of a hierarchical white dwarf–planet–moon system. It separately examines tidal orbital evolution, potential encounters with evection resonance, and gravitational perturbations during planetary pericenter passages. The reference system consists of a white dwarf with 0.5 solar masses, a planet with 10 Jupiter masses and 1.2 Jupiter radii, and a Ganymede-like moon with 0.025 Earth masses and 0.413 Earth radii. The planet initially has a semimajor axis of 4.5 astronomical units and an eccentricity of 0.995. If orbital angular momentum is approximately conserved, these parameters imply a final circular orbit near 0.045 astronomical units. Satellite separations are expressed as fractions of the planet’s Hill radius at pericenter. The reference tidal quality factors are one million for the planet and 100 for the moon. A central result concerns the direction of satellite migration. For a planet rotating pseudosynchronously with its stellar orbit, the corotation radius always lies outside the pericenter Hill radius. Under the assumed mass hierarchy, the ratio of these radii depends only on planetary eccentricity, decreasing from approximately 1.44 for a circular orbit to about 1.30 at extreme eccentricity. Consequently, circular prograde moons within the Hill sphere orbit faster than the planet rotates and migrate inward through tidal interactions. Retrograde moons also migrate inward. Moons on compact orbits generally spiral inward faster than their host planets migrate. In the initial configuration, a moon at half the pericenter Hill radius has a planet-to-moon migration-timescale ratio of approximately 150 for a one-Jupiter-mass planet and approximately three for the reference ten-Jupiter-mass planet. Ratios greater than one indicate faster fractional contraction of the satellite orbit. For the ten-Jupiter-mass planet, the migration timescales are equal near 0.59 Hill radii. Wider satellite orbits and more massive planetary companions therefore provide longer tidal lifetimes. Under the adopted prescription, the satellite migration timescale depends steeply on orbital separation, scaling approximately as separation to the power of 6.5. However, wider moons are more vulnerable to stellar perturbations. At separations of 0.8–0.9 Hill radii, the estimated work done by these perturbations during a single planetary pericenter passage reaches approximately 56–73 percent of the satellite’s binding energy. Such perturbations could lead to collisions or ejection. Evection resonance provides another potential loss mechanism. As planetary migration changes the relationship between the satellite’s apsidal precession rate and the planet’s orbital frequency, the resonance boundary can sweep through satellite orbits and potentially excite destructive eccentricities. The study identifies candidate resonance configurations but does not establish capture or disruption probabilities. The authors conclude that primordial moons are unlikely to survive high-eccentricity planetary migration under the adopted assumptions. Discovering a moon around a close-orbiting white dwarf planet could therefore constrain the planet’s migration history, although subsequent capture would complicate that interpretation. Key limitations include uncertain tidal dissipation, the assumption of sustained pseudosynchronous planetary rotation, and the separate rather than fully coupled treatment of the three loss mechanisms. Dynamical or chaotic tides could accelerate planetary migration, reducing the time available for satellite inspiral. Coupled, long-term three-body simulations are needed to determine whether any window for moon survival remains.

Can Moons Survive a Giant Planet’s Journey Toward a White Dwarf?

A moon orbiting a giant planet near a white dwarf offers an intriguing possibility: a world that could experience temperate conditions as the stellar remnant cools. But before considering whether such a moon might support habitable environments, astronomers must answer a more basic question. Could it survive the journey there?

A new theoretical study examines that problem for planets undergoing high-eccentricity migration. Its conclusion is cautionary: under the assumptions explored, primordial moons are unlikely to survive. The challenge is a balancing act. Moons close to their planets face rapid tidal inspiral, while more distant moons are exposed to stronger stellar disturbances.

A Dangerous Route to a Close Orbit

White dwarfs are the dense remnants left behind after stars like the Sun exhaust their fuel and shed their outer layers. A giant planet found close to one may have arrived after this dramatic stellar evolution, rather than remaining nearby throughout it.

One possible route is high-eccentricity migration. Gravitational interactions push a planet onto an extremely elongated orbit, bringing it close to the white dwarf at each pericenter passage. Tidal dissipation then removes orbital energy, gradually shrinking and circularizing the orbit.

The researchers focus on a specific stage of this history. They assume a moon has already survived both stellar evolution and the initial excitation of the planet’s eccentricity. They then ask whether it can survive the migration itself.

The Reference System

The study uses an analytic, orbit-averaged equilibrium-tide model of a white dwarf, giant planet, and moon. Its reference system includes:

• A white dwarf with half the Sun’s mass.
• A planet with 10 Jupiter masses and 1.2 Jupiter radii.
• A Ganymede-like moon with 0.025 Earth masses and 0.413 Earth radii.
• An initial planetary orbit with a semimajor axis of 4.5 astronomical units and an eccentricity of 0.995.

If orbital angular momentum remains approximately conserved, the planet would finish on a circular orbit near 0.045 astronomical units. The reference tidal quality factors are one million for the planet and 100 for the moon, parameters that describe the efficiency of tidal dissipation.

The Inner Threat: Moons Spiral Toward Their Planet

A central result concerns the direction of the moon’s tidal migration. This depends on the relationship between the planet’s rotation and the moon’s orbital motion.

The model assumes that the planet rotates pseudosynchronously: its spin follows a tidal equilibrium appropriate to its eccentric stellar orbit. Under this assumption, the corotation radius—where a moon’s orbital period would match the planet’s rotation period—always lies outside the planet’s Hill radius at pericenter. That Hill radius measures the approximate extent of the planet’s gravitational domain during its closest stellar approach.

The ratio of these two radii depends only on planetary eccentricity under the assumed mass hierarchy. It ranges from approximately 1.44 for a circular orbit to about 1.30 at extreme eccentricity. Consequently, circular prograde moons within this region orbit faster than the planet spins and migrate inward through tides. Retrograde moons also migrate inward.

For compact moons, this inward movement can outpace the planet’s own migration. Initially, a moon at half the pericenter Hill radius has a planet-to-moon migration-timescale ratio of about 150 around a one-Jupiter-mass planet, compared with about three around the reference ten-Jupiter-mass planet. Values above one mean the moon’s orbit contracts faster in fractional terms.

The Outer Threat: Stellar Disturbances

Moving a moon outward improves its tidal lifetime. Under the adopted prescription, the satellite migration timescale scales approximately with orbital separation to the power of 6.5. For the reference planet, the planetary and satellite migration timescales become equal near 0.59 pericenter Hill radii.

But wider orbits introduce another danger. During each close stellar passage, the white dwarf can strongly perturb the moon. At separations of 0.8–0.9 pericenter Hill radii, the estimated work done by these disturbances in a single passage reaches roughly 56–73 percent of the moon’s binding energy.

Those estimates do not establish a disruption probability, but they indicate that collisions or ejections could threaten moons far enough out to avoid rapid tidal inspiral.

A Resonance Could Add Another Hazard

The researchers also examine evection resonance, which can arise when the moon’s apsidal precession becomes commensurate with the planet’s orbital motion. As migration changes these frequencies, a resonance boundary may sweep across satellite orbits and potentially excite destructive eccentricities. The study identifies candidate configurations, but does not determine capture or disruption probabilities.

What a Surviving Moon Could Reveal

The findings suggest that primordial moons face substantial obstacles during high-eccentricity migration. Finding one around a close-orbiting white dwarf planet could therefore help constrain that planet’s history, although later capture would complicate the interpretation.

This is not a definitive exclusion. Tidal dissipation remains uncertain, sustained pseudosynchronous rotation is an assumption, and the three loss mechanisms were examined separately rather than in a fully coupled calculation. Dynamical or chaotic tides might also speed up planetary migration, leaving less time for moon inspiral. Long-term, coupled three-body simulations are needed to discover whether a narrow survival window remains.