The Neptunian Final Parsec Problem: How Inertial Waves Enable Neptunes and Gas Giants to Survive Tidal Migration

Observations indicate that some hot Neptunes and Jupiters underwent high eccentricity migration (HEM). A longstanding issue facing HEM theory remains, however: in order to shrink their orbits by about 1 - 2 orders of magnitude, planets must dissipate 10 times more orbital energy than is contained in their structural binding energy. Previous work suggests that excitation of planets' fundamental modes ('' f-modes'') at very high eccentricities, e about 0.99, can shrink semi-major axes by about an order of magnitude (about 5 to 0.5 au) while safely bleeding tidal energy to space. We examine how planets traverse the remaining order of magnitude in orbital shrinkage, a about 0.5 to 0.05 au, which still poses a danger for Neptunian planets due to their lower binding energies (their ''final parsec'' problem). To assess whether tidally-migrating Neptunes balance their energy budgets, we perform coupled orbit/structure calculations tracking their frequency-dependent tidal response under inertial waves (IWs). We show that tidal radius inflation at moderate eccentricities sweeps Neptunes' fundamental modes back into resonance with tidal forcing; only a small amount of tidal heat relative to a Neptune's binding energy is needed to drive this f-mode excitation. This excitation of Neptunes' f-modes may offer a route to safe circularization, provided the f-mode dissipates without harming the planet. In contrast, eccentric gas giants (e about 0.9) circularize without drama over about Gyr. Our theory predicts that warm Neptunes on a HEM track (a 0.1 au, e 0.8) should be rare, in opposition to warm gas giants and lower eccentricity Neptunes. Observational confirmation of our predictions would constrain the interior structures of Neptunian planets via tidal theory.