Galaxy Rotation Curves
14,760 GalaxiesGalaxy rotation curves are the most important empirical test for any theory of gravity at galactic scales. Stars and gas in the outer regions of disk galaxies orbit faster than Newtonian gravity predicts from visible mass alone. The Radial Acceleration Relation (RAR) captures this: observed acceleration correlates tightly with the acceleration predicted from baryonic mass, but systematically exceeds it below a critical scale.
Synchronism's coherence function predicts how and where rotation curves should flatten. We tested this against two major datasets.
Dataset Results
SPARC Dataset
175 galaxies with high-quality photometry and resolved rotation curves (Lelli, McGaugh & Schombert 2016). The gold standard for RAR studies. [Public data]
- Tight RAR confirmed (σint ≈ 0.057 dex)
- Coherence function fits within observational scatter
- Environment-dependent effects visible but sample too small for strong statistics
ALFALFA-SDSS Dataset
14,585 galaxies from the ALFALFA HI survey cross-matched with SDSS photometry. Unresolved rotation curves but massive statistical power. [ALFALFA data] [SDSS DR17]
- Environment-dependent RAR scatter detected at p = 5 × 10−6
- σint = 0.086 ± 0.003 dex (below CDM prediction)
- Cluster vs. field galaxies show different scatter — as predicted
The Coherence Prediction
This is the standard RAR interpolation function (McGaugh et al. 2016). In Synchronism, the acceleration scale a₀ is not a free parameter — it emerges from cosmology as cH₀/(2π). The coherence function provides the physical mechanism: at accelerations below a₀, the system crosses a coherence threshold and gravitational dynamics change.
Key Results Summary
Honest Caveat
The environment-dependent scatter is real and statistically significant, but it explains only 14% of the total RAR scatter (R² = 0.14). The remaining 86% is unexplained by the coherence model. Furthermore, standard MOND plus mass-to-light ratio corrections already explains essentially all of the RAR variance. Synchronism adds a small, detectable effect on top of what MOND already provides — it does not replace MOND's success.