Most open clusters follow the radial acceleration relation (RAR) and the baryonic Tully-Fisher relation (BTFR)

TL;DR

This study finds that most open clusters in the Milky Way follow the radial acceleration relation and baryonic Tully-Fisher relation, supporting modified gravity theories like MOND at parsec scales.

Contribution

First comprehensive analysis of open clusters showing their adherence to RAR and BTFR, providing evidence for low-acceleration dynamics within the Milky Way.

Findings

Approximately 90% of clusters follow the RAR with significant scatter.

Best-fitting acceleration scale consistent with MOND predictions.

Massive clusters align with Newtonian expectations.

Abstract

We test whether parsec-scale stellar systems in the Milky Way follow the galactic radial acceleration relation (RAR) or the baryonic TullyFisher relation (BTFR). We analyse 5646 Gaia DR3 open clusters from the Hunt \& Reffert catalogue. Observed accelerations are derived from velocity dispersions and characteristic radii, and baryonic accelerations from stellar masses and characterisitc radii. The clusters are placed on the RAR and BTFR planes and compared with Newtonian and MOND expectations. Approximately 90 per cent of open clusters (those with $N_\star \leq 250$) lie close to the RAR, albeit with significant scatter. In a first-of-its-kind test, a smaller fiducial sample is consistent with a best-fitting acceleration scale $g_\dagger \approx 1.2 \times 10^{-10}\ \mathrm{m\,s^{-2}} \pm 0.5$ dex, compatible with canonical MOND values. More massive clusters approach the Newtonian virial expectation. No correlations are found between RAR residuals and galactocentric radii, distance to the Galactic disk midplane, age, or morphology. Tidal effects and unresolved binaries are insufficient to reproduce the observations without fine-tuning. Interpreted within a MOND framework, the alignment of most open clusters with the RAR and BTFR suggests that low-acceleration dynamics operate on parsec scales within the Milky Way. This implies that the Galactic gravitational field is not smooth on these scales and may include regions where the total gravitational acceleration falls below $a_0$, partially mitigating the external field effect, thereby motivating higher-resolution modelling of the Galactic potential and informing other small-scale gravity tests within the Galaxy.