Knowing the unknowns: uncertainties in simple estimators of galactic dynamical masses
Bibliographic record
Abstract
The observed stellar kinematics of dispersion-supported galaxies are often used to measure dynamical masses. Recently, several analytical relationships between the stellar line-of-sight velocity dispersion, the projected (2D) or deprojected (3D) half-light radius and the total mass enclosed within the half-light radius, relying on the spherical Jeans equation, have been proposed. Here, we use the APOSTLE cosmological hydrodynamical simulations of the Local Group to test the validity and accuracy of such mass estimators for both dispersion and rotation-supported galaxies, for field and satellite galaxies, and for galaxies of varying masses, shapes and velocity dispersion anisotropies. We find that the mass estimators of Walker et al. and Wolf et al. are able to recover the masses of dispersion-dominated systems with little systematic bias, but with a 1σ scatter of 25 and 23 per cent, respectively. The error on the estimated mass is dominated by the impact of the 3D shape of the stellar mass distribution, which is difficult to constrain observationally. This intrinsic scatter becomes the dominant source of uncertainty in the masses estimated for galaxies like the dwarf spheroidal (dSph) satellites of the Milky Way, where the observational errors in their sizes and velocity dispersions are small. Such scatter may also affect the inner density slopes of dSphs derived from multiple stellar populations, relaxing the significance with which Navarro–Frenk–White profiles may be excluded, depending on the degree to which the relevant properties of the different stellar populations are correlated. Finally, we derive a new optimal mass estimator that removes the residual biases and achieves a statistically significant reduction in the scatter to 20 per cent overall for dispersion-dominated galaxies, allowing more precise and accurate mass estimates.
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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 | 0.013 | 0.097 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".