SPACING OF<i>KEPLER</i>PLANETS: SCULPTING BY DYNAMICAL INSTABILITY
Bibliographic record
Abstract
We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N -body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find that the observed spacings are tightly clustered around 12 mutual Hill radii, when transit geometry and sensitivity limits are accounted for. In comparison, dynamical integrations reveal that the minimum spacing required for systems of similar masses to survive dynamical instability for as long as 1 billion yr is ∼10 if all orbits are circular and coplanar and ∼12 if planetary orbits have eccentricities of ∼0.02 (a value suggested by studies of planet transit-time variations). This apparent coincidence, between the observed spacing and the theoretical stability threshold, leads us to propose that typical planetary systems were formed with even tighter spacing, but most, except for the widest ones, have undergone dynamical instability, and are pared down to a more anemic version of their former selves, with fewer planets and larger spacings. So while the high-multiple systems (five or more transiting planets) are primordial systems that remain stable, the single or double planetary systems, abundantly discovered by the Kepler mission, may be the descendants of more closely packed high-multiple systems. If this hypothesis is correct, we infer that the formation environment of Kepler systems should be more dissipative than that of the terrestrial planets.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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".