The Neptunian Final Parsec Problem: How Inertial Waves Enable Neptunes and Gas Giants to Survive Tidal Migration
Abstract
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 ∼1−2 orders of magnitude, planets must dissipate ≳10× 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∼0.99, can shrink semi-major axes by ∼an order of magnitude (∼5→0.5 au) while safely bleeding tidal energy to space. We examine how planets traverse the remaining order of magnitude in orbital shrinkage, a∼0.5→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∼0.9) circularize without drama over ∼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.
Related
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BibTeX
@misc{hallatt2026neptunian,
title = {{The Neptunian Final Parsec Problem: How Inertial Waves Enable Neptunes and Gas Giants to Survive Tidal Migration}},
author = {Tim Hallatt and Adrian J. Barker and Sarah C. Millholland},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12968},
eprint = {2610.12968},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12968},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Neptunian Final Parsec Problem: How Inertial Waves Enable Neptunes and Gas Giants to Survive Tidal Migration
AU - Tim Hallatt
AU - Adrian J. Barker
AU - Sarah C. Millholland
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12968
UR - https://arxiv.org/abs/2610.12968
AB - 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 ∼1−2 orders of magnitude, planets must dissipate ≳10× 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∼0.99, can shrink semi-major axes by ∼an order of magnitude (∼5→0.5 au) while safely bleeding tidal energy to space. We examine how planets traverse the remaining order of magnitude in orbital shrinkage, a∼0.5→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∼0.9) circularize without drama over ∼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.
ER -