The Dynamics of Tightly-packed Planetary Systems in the Presence of an Outer Planet: Case Studies Using Kepler-11 and Kepler-90
Bibliographic record
Abstract
Abstract We explore the effects of an undetected outer giant planet on the dynamics, observability, and stability of Systems with Tightly-packed Inner Planets (STIPs). We use direct numerical simulations along with secular theory and synthetic secular frequency spectra to analyze how analogues of Kepler-11 and Kepler-90 behave in the presence of a nearly co-planar, Jupiter-like outer perturber with semimajor axes between 1 and 5.2 au. Most locations of the outer perturber do not affect the evolution of the inner planetary systems, apart from altering precession frequencies. However, there are locations at which an outer planet causes system instability due to, in part, secular eccentricity resonances. In Kepler-90, there is a range of orbital distances for which the outer perturber drives planets b and c, through secular interactions, onto orbits with inclinations that are ∼16° away from the rest of the planets. Kepler-90 is stable in this configuration. Such secular resonances can thus affect the observed multiplicity of transiting systems. We also compare the synthetic apsidal and nodal precession frequencies with the secular theory and find some misalignment between principal frequencies, indicative of strong interactions between the planets (consistent with the system showing TTVs). First-order libration angles are calculated to identify MMRs in the systems, for which two near-MMRs are shown in Kepler-90, with a 5:4 between b and c, as well as a 3:2 between g and h.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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 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".