A Bayesian periodogram finds evidence for three planets in 47 Ursae Majoris
Bibliographic record
Abstract
A Bayesian analysis of 47 Ursae Majoris radial velocity data confirms and refines the properties of two previously reported planets with periods of 1079 and 2325 d. The analysis also provides orbital constraints on an additional long-period planet with a period of ∼10 000 d. The three-planet model is found to be 105 times more probable than the next most probable model which is a two-planet model. The non-linear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel tempering, simulated annealing and genetic crossover operations. Each of these features facilitate the detection of a global minimum in χ2. By combining all three, the HMCMC greatly increases the probability of realizing this goal. When applied to the Kepler problem, it acts as a powerful multiplanet Kepler periodogram. The measured periods are 1078 ± 2 d, 2391+100−87 d and 14002+4018−5095 d, and the corresponding eccentricities are 0.032 ± 0.014, 0.098+.047−.096 and 0.16+.09−.16. The results favour low-eccentricity orbits for all three. Assuming the three signals (each one consistent with a Keplerian orbit) are caused by planets, the corresponding limits on planetary mass (M sin i) and semimajor axis are (2.53+.07−.06MJ, 2.10 ± 0.02 au), (0.54 ± 0.07 MJ, 3.6 ± 0.1 au) and (1.6+0.3−0.5MJ, 11.6+2.1−2.9 au), respectively. Based on a three-planet model, the remaining unaccounted for noise (stellar jitter) is 5.7 m s−1. The velocities of model fit residuals were randomized in multiple trials and processed using a one-planet version of the HMCMC Kepler periodogram. In this situation, periodogram peaks are purely the result of the effective noise. The orbits corresponding to these noise-induced periodogram peaks exhibit a well-defined strong statistical bias towards high eccentricity. We have characterized this eccentricity bias and designed a correction filter that can be used as an alternate prior for eccentricity to enhance the detection of planetary orbits of low or moderate eccentricity.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".