Empirical Stability Criteria for 3D Hierarchical Triple Systems. I. Circumbinary Planets
Bibliographic record
Abstract
Abstract In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We derive critical semimajor axes based on simulating and analyzing the dynamical behavior of 3 × 10 8 binary star–planet configurations. For the first time, three-dimensional and eccentric planetary orbits are considered. We explore systems with a variety of binary and planetary mass ratios, binary and planetary eccentricities from 0 to 0.9, and orbital mutual inclinations ranging from 0° to 180°. Planetary masses range between the size of Mercury and the lower fusion boundary (approximately 13 Jupiter masses). The stability of each system is monitored over 10 6 planetary orbital periods. We provide empirical expressions in the form of multidimensional, parameterized fits for two borders that separate dynamically stable, unstable, and mixed zones. In addition, we offer a machine learning model trained on our data set as an alternative tool for predicting the stability of circumbinary planets. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary systems with very good results. The empirical formulae are also applied to the Kepler and TESS circumbinary systems, confirming that many planets orbit their host stars close to the stability limit of those systems. Finally, we present a REST application programming interface with a web-based application for convenient access to our simulation data set.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 teacher head, 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".