RAR Scatter
p = 5×10⁻⁶New Prediction #2 (NP2): The scatter in the Radial Acceleration Relation depends on environment. This is a prediction that standard models do not make — and it was confirmed with strong statistical significance.
What Is RAR Scatter?
The Radial Acceleration Relation plots observed gravitational acceleration (gobs) against the acceleration predicted from baryonic mass alone (gbar). Across thousands of galaxies, this relation is remarkably tight — but not perfectly tight. The scatter around the mean relation is measured as σint (intrinsic scatter in dex).
Standard models — both CDM and basic MOND — predict that this scatter should be constant regardless of a galaxy's environment. A galaxy in a dense cluster should scatter the same amount as an isolated field galaxy.
Synchronism's Prediction
The coherence function depends on local density. Galaxies in dense environments (clusters, groups) experience a different coherence gradient than isolated galaxies. This means the RAR scatter should vary with local density. Specifically:
Cluster Galaxies
Higher ambient density → steeper coherence gradient → tighter RAR (less scatter). The external density field “stiffens” the coherence profile.
Field Galaxies
Lower ambient density → shallower coherence gradient → more scatter. Isolated galaxies have more freedom in how their coherence profiles develop.
The Test
Using the ALFALFA-SDSS cross-matched sample (14,585 galaxies), we divided galaxies by local density proxy (Nth-nearest-neighbor density estimator) and measured σintin each bin. The result:
What This Means
The environment effect is real. It is statistically significant at better than 4.5σ. Standard MOND does not predict it. CDM simulations with baryonic feedback can potentially produce environment-dependent scatter, but the specific pattern (monotonic decrease with increasing density) matches the coherence prediction.
Honest Caveat
Even with the environment effect, 86% of the RAR scatter remains unexplained by Synchronism's coherence model (R² = 0.14). The effect is detectable but small. Most of the scatter likely comes from observational systematics (distance errors, inclination corrections, mass-to-light ratio assumptions) rather than any physical model. MOND plus standard M/L corrections already accounts for essentially all of the variance. The environment signal is a small, real perturbation on top of a well-understood baseline.