On the Evidence for Violation of the Equivalence Principle in Disk Galaxies

TL;DR

The paper investigates whether external-field effects claimed in disk galaxies signal a violation of the equivalence principle. It introduces a General Relativity self-interaction (GR-SI) framework in which $g_{SI}(r) = g_{3D}(r) + g_{2D}(r)$ with $g_{2D}(r) = sqrt(G alpha) sqrt(M_D(r)) / r$ and uses morphology and environment proxies to connect to observed dynamics. Through ~40,000 simulated galaxies and an MCMC-style analysis, it shows that morphology–environment correlations can reproduce the radial-acceleration relation and suppress apparent EFE, challenging the interpretation of ChaE et al.'s claims. The results indicate that current observational data do not decisively support an EFE and highlight convergence issues in prior MCMC analyses, underscoring the need for more robust tests of GR self-interaction versus MOND-like behavior.

Abstract

We examine the claimed observations of a gravitational external field effect (EFE) reported in Chae et al. We show that observations suggestive of the EFE can be interpreted without violating Einstein's equivalence principle, namely from known correlations between morphology, environment and dynamics of galaxies. While Chae et al's analysis provides a valuable attempt at a clear test of Modified Newtonian Dynamics, an evidently important topic, a re-analysis of the observational data does not permit us to confidently assess the presence of an EFE or to distinguish this interpretation from that proposed in this article.

Figures (4)

• Figure 1: Left: Radial acceleration relation for 40,000 simulated galaxies, color coded for bulge-to-total mass ratios $\mu$. Three different populations are shown, two of which are the edge cases of bulge-dominated (red line) and disk-dominated (blue line) galaxies (both subsamples contain 2% of the total population), while the green line shows the remaining average population. Right: Distribution of bulge-to-total mass ratio, $\mu$, for the same galaxies, also color-coded. The shape of the distribution comes from our enforcement of realistic combinations of galaxy parameters. Vertical dashed lines delineate the three populations. We use the 2D-gravity effective coupling value $\alpha=2.3\times 10^{-10}~{\rm m/s^2}$.
• Figure 2: Total acceleration $g_{\rm SI}$ versus that expected from the baryonic matter and Newtonian gravity, $g_{\rm 3D}$. The colors correspond to the average number of satellite galaxies per bin within 200 kpc. The number of satellite galaxies were calculated by applying Eq. (\ref{['JKR_1-1']}) to the bulge-to-total ratios of modeled galaxies. The similarity between Fig. \ref{['fig:g_vs_Nsat_1']} and Fig. \ref{['fig:2pop']} arises from both figures using the same 40,000 simulated galaxies and the strong relationship between the bulge-to-total mass ratio $\mu$ and the satellite galaxy population, as given by Eq. (\ref{['JKR_1-1']}).
• Figure 3: Relationship between the total baryonic mass and the asymptotic velocity $V_\infty$ using the model in Eq. (\ref{['GRSI_IF-1']}). A slope slightly smaller than 4 is consistent with baryonic Tully-Fisher relation. A value of $\alpha=2.3\times 10^{-10}~{\rm m/s^2}$ is used.
• Figure 4: Results for the dimensionless parameters in the parameter vector and their error margins (1, 2 and 3$\sigma$) from the MCMC analysis by chae_2020 and in our evaluation, both using the $\nu_{\rm C20}$ model, Eq. \ref{['eq:nu-model-c20']}. The results from our analysis are given both for the likelihood build from $\chi^2$, Eq. \ref{['eq:chi2']}, (red) and $\hat{\chi}^2$, Eq. \ref{['eq:chi2-new']} (green). The estimated parameters are shown by the light green, red and black lines, respectively and the green, orange and blue regions give the respective error margins. In the first three panels, we show the products $\hat{D}\Upsilon_D$, $\hat{D}\Upsilon_B$, $\hat{D}\Upsilon_G$, respectively, as the mass-to-light rations $\Upsilon$ are degenerate with $\hat{D}$. Note that $\hat{D}\Upsilon_B$ can only be determined for galaxies with non-vanishing $V_B$. The two bottom panels give the results for the inclination $i$ and the external field parameter $e$.