Fast Estimation of Orbital Parameters in Milky Way-like Potentials
Bibliographic record
Abstract
Orbital parameters, such as eccentricity and maximum vertical excursion, of stars in the Milky Way are an important tool for understanding its dynamics and evolution, but calculation of such parameters usually relies on computationally-expensive numerical orbit integration. We present and test a fast method for estimating these parameters using an application of the St\"ackel fudge, used previously for the estimation of action-angle variables. We show that the method is highly accurate, to a level of $<1\%$ in eccentricity, over a large range of relevant orbits and in different Milky Way-like potentials, and demonstrate its validity by estimating the eccentricity distribution of the RAVE-TGAS data set and comparing it to that from orbit integration. Using the method, the orbital characteristics of the $\sim 7$ million $\textit{Gaia}$ DR2 stars with radial velocity measurements are computed with Monte Carlo sampled errors in $\sim 116$ hours of parallelised cpu time, at a speed that we estimate to be $\sim 3$ to $4$ orders of magnitude faster than using numerical orbit integration. We demonstrate using this catalogue that $\textit{Gaia}$ DR2 samples a large range of orbits in the solar vicinity, down to those with $r_\mathrm{peri} \lesssim 2.5$ kpc, and out to $r_\mathrm{ap} \gtrsim 13$ kpc. We also show that many of the features present in orbital parameter space have a low mean $z_\mathrm{max}$, suggesting that they likely result from disk dynamical effects.
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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 | 0.000 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".