Systemic Deviations From The Radial Acceleration Relation?

There is weak evidence that the radial acceleration relation, which is implied by Milgrom's toy-model MOND theory of weak field gravity, requires a single parameter correction is correlated with the compactness of the galaxies measured, primarily in dwarf galaxies.

Query if this could be due to the external field effect or due to gravitationally bound systems that are not in equilibrium? It could also be due to underestimated systemic error in estimating gas fractions, which is much harder to determine that stellar mass.

We ask whether any one-parameter structural correction to the radial acceleration relation (RAR) can be uniquely recovered from SPARC rotation curves, and answer with an identifiability audit: each candidate is benchmarked against per-galaxy nuisance freedom, with predictive scoring against mass-only and data-quality baselines. 

In the full sample (N = 126) the answer is no: a hybrid compactness term improves the fit, but zero-point freedom absorbs the gain, and in cross-validation the model fails to out-predict a mass-only baseline and loses to a quality-flag baseline. 

One regime retains structural information: in gas-dominated, low-acceleration disks -- where MOND's strict locality and ΛCDM feedback models diverge most sharply -- the RAR residual correlates with compactness (r = 0.46, p = 1.3×10^−4), remains significant under hierarchical partial pooling (β = 0.23, p = 1.7×10^−5; N = 63), and survives canonical joint control for quality, sampling, mass, inclination error, and first-order pressure support (r = 0.30, p = 0.02). All significant results pass a Benjamini-Hochberg correction over the declared 27-test family. 

Three limits temper that survival: it is not significant under rank-based control over the widest proxy set; it resides in faint dwarfs independent surveys do not reach; and after mass control it is shared across the mass-size manifold. Pressure support brackets the interpretation -- isotropic drift correction absorbs a quarter of the amplitude, while a Jeans treatment overcorrects resolved cases -- leaving the physical origin undetermined. The audit's product is the extraction limit: claimed corrections must clear the 0.106 dex per-galaxy nuisance floor, a mass-only baseline, and data-quality stratification.

Lukas A. Sosna, "An Identifiability Audit of One-Parameter Structural Corrections to the Radial Acceleration Relation in SPARC" arXiv:2608.08945 (August 9, 2026).