Resonance Overlap Is Responsible for Ejecting Planets in Binary Systems
Bibliographic record
Abstract
A planet orbiting around a star in a binary system experiences both secular and resonant perturbations from the companion star. It may be dislodged from its host star if it is simultaneously affected by two or more resonances. We find that overlap between subresonances lying within mean-motion resonances (mostly of the j : 1 type) can account for the boundary of orbital stability within binary systems first observed in numerical studies (e.g., Holman & Wiegert). Strong secular forcing from the companion displaces the centroids of different subresonances, producing large regions of resonance overlap. Planets lying within these overlapping regions experience chaotic diffusion, which in most cases leads to their eventual ejection. The overlap region extends to shorter period orbits as either the companion's mass or its eccentricity increase, with boundaries largely agreeing with those obtained by Holman & Wiegert. Furthermore, we find the following two results: First, at a given binary mass ratio, the instability boundary as a function of eccentricity appears jagged, with jutting peninsulas and deep inlets corresponding to islands of instability and stability, respectively; as a result, the largest stable orbit could be reduced from the Holman & Wiegert values by as much as 20%. Second, very high-order resonances (e.g., 50 : 3) do not significantly modify the instability boundary; these weak resonances, while producing slow chaotic diffusion that may be missed by finite-duration numerical integrations, do not contribute markedly to planet instability. We present some numerical evidence for the first result. More extensive experiments are called for to confirm these conclusions. For the special case of circular binaries, we are intrigued to find that the Hill criterion (based on the critical Jacobi integral) yields an instability boundary that is very similar to that obtained by resonance overlap arguments, making the former both a necessary and a sufficient condition for planet instability.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".