Gravitational potential from small-scale clustering in action space: application to Gaia Data Release 2
Bibliographic record
Abstract
ABSTRACT Most measurements of mass in astronomy that use kinematics of stars or gas rely on assumptions of equilibrium that are often hard to verify. Instead, we develop a novel idea that uses the clustering in action space, as a probe of the underlying gravitational potential: the correct potential should maximize small-scale clustering in the action space. We provide a first-principle derivation of likelihood using the two-point correlation function in action space, and we test it against simulations of stellar streams. We then apply this method to the second data release of Gaia, and we use it to measure the radial force fraction fh and logarithmic slope α of the dark matter halo profile. We investigate stars within 9–11 kpc and 11.5–15 kpc from the Galactic Centre, and we find (fh, α) = (0.391 ± 0.009, 1.835 ± 0.092) and (0.351 ± 0.012, 1.687 ± 0.079), respectively. We also confirm that the set of parameters that maximize the likelihood function does correspond to the most clustering in the action space. The best-fitting circular velocity curve for the Milky Way potential is consistent with past measurements (although it is ∼5–10 per cent lower than previous methods that use masers or globular clusters). Our work provides a clear demonstration of the full statistical power that lies in the full phase space information, relieving the need for ad hoc assumptions such as virial equilibrium, circular motion or steam-finding algorithms.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| 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".