Resonance Overlap is Responsible for Ejecting Planets in Binary Systems
Bibliographic record
Abstract
A planet orbiting around a star in a binary system can be ejected if it lies too far from its host star. We find that instability boundaries first obtained in numerical studies can be explained by overlap between sub-resonances within mean-motion resonances (mostly of the j:1 type). Strong secular forcing from the companion displaces the centroids of different sub-resonances, 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. Our analytical calculations reproduce the instability boundaries observed in numerical studies and yield the following two additional results. Firstly, the instability boundary as a function of eccentricity is jagged; thus, the widest stable orbit could be reduced from previously quoted values by as much as 20%. Secondly, very high order resonances (e.g., 50:3) do not significantly modify the instability boundary despite the fact that these weak resonances can produce slow chaotic diffusion which may be missed by finite-duration numerical integrations. 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 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".