Orbital Torus Imaging: Acceleration, Density, and Dark Matter in the Galactic Disk Measured with Element Abundance Gradients
Bibliographic record
Abstract
Abstract Under the assumption of a simple and time-invariant gravitational potential, many Galactic dynamics techniques infer the milky Way’s mass and dark matter distributions from stellar kinematic observations. These methods typically rely on parameterized potential models of the Galaxy and must take into account nontrivial survey selection effects, because they make use of the density of stars in phase space. Large-scale spectroscopic surveys now supply information beyond kinematics in the form of precise stellar label measurements (especially element abundances). These element abundances are known to correlate with orbital actions or other dynamical invariants. Here, we use the Orbital Torus Imaging framework that uses abundance gradients in phase space to map orbits. In many cases these gradients can be measured without detailed knowledge of the selection function. We use stellar surface abundances from the Apache Point Observatory Galactic Evolution Experiment survey combined with kinematic data from the Gaia mission. Our method reveals the vertical ( z -direction) orbital structure in the Galaxy and enables empirical measurements of the vertical acceleration field and orbital frequencies in the disk. From these measurements, we infer the total surface mass density, Σ, and midplane volume density, ρ 0 , as a function of Galactocentric radius and height. Around the Sun, we find Σ ⊙ ( z = 1.1 kpc ) = 72 − 9 + 6 M ⊙ pc − 2 and ρ ⊙ ( z = 0 ) = 0.081 − 0.009 + 0.015 M ⊙ pc − 3 using the most constraining abundance ratio, [Mg/Fe]. This corresponds to a dark matter contribution in surface density of Σ ⊙,DM ( z = 1.1 kpc) = 24 ± 4 M ⊙ pc −2 , and in total volume mass density of ρ ⊙,DM ( z = 0) = 0.011 ± 0.002 M ⊙ pc −3 . Moreover, using these mass density values we estimate the scale length of the low- α disk to be h R = 2.24 ± 0.06 kpc.
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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 | 0.000 | 0.001 |
| 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 | 0.000 | 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".