The MOG weak field approximation and observational test of galaxy rotation curves
Bibliographic record
Abstract
As an alternative to dark matter models, Modified Gravity (MOG) theory is a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each particle has a charge proportional to its inertial mass. The weak field approximation of MOG is derived by perturbing the metric and the fields around Minkowski space–time. We obtain an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, GN, has two additional constant parameters α and μ. We use The H i Nearby Galaxy Survey catalogue of galaxies and fix the two parameters α and μ of the theory to be α = 8.89 ± 0.34 and μ = 0.042 ± 0.004 kpc−1. We then apply the effective potential with the fixed universal parameters to the Ursa Major catalogue of galaxies and obtain good fits to galaxy rotation curve data with an average value of χ2 = 1.07. In the fitting process, only the stellar mass-to-light ratio (M/L) of the galaxies is a free parameter. As predictions of MOG, our derived M/L is shown to be correlated with the colour of galaxies. We also fit the Tully–Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".