The Intrinsic Scatter of Galaxy Scaling Relations
Bibliographic record
Abstract
Abstract We present a compendium of disk galaxy scaling relations and a detailed characterization of their intrinsic scatter. Observed scaling relations are typically characterized by their slope, intercept, and scatter; however, these parameters are a mixture of observational errors and astrophysical processes. We introduce a novel Bayesian framework for computing the intrinsic scatter of scaling relations that accounts for nonlinear error propagation and covariant uncertainties. Bayesian intrinsic scatters are ∼25% more accurate than those obtained with a first-order classical method, which systematically underestimates the true intrinsic scatter. Structural galaxy scaling relations based on velocity (V 23.5), size (R 23.5), luminosity (L 23.5), color (g − z), central stellar surface density (Σ1), stellar mass (M *), dynamical mass (M dyn), stellar angular momentum (j *), and dynamical angular momentum (j dyn) are examined to demonstrate the power and importance of the Bayesian formalism. Our analysis is based on a diverse selection of over 1000 late-type galaxies from the Photometry and Rotation Curve Observations from Extragalactic Surveys compilation with deep optical photometry and extended rotation curves. We determine the tightest relation for each parameter by intrinsic orthogonal scatter, finding M * − V 23.5, R 23.5 − j *, and L 23.5 − j dyn to be especially tight. The scatter of the R 23.5 − L 23.5, V 23.5 − (g − z), and R 23.5 − j dyn relations is mostly intrinsic, making them ideal for galaxy formation and evolutionary studies. Our code to compute the Bayesian intrinsic scatter of any scaling relation is also presented. We quantify the correlated nature of many uncertainties in galaxy scaling relations and scrutinize the uncertain nature of disk inclination corrections and their effect on scatter 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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".