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

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.

Figures (5)

• Figure 1: The four regimes of MOND, based on figure one of 2022Symm...14.1331B.
• Figure 2: Comparison of observed kinetic accelerations, $g_{\mathrm{obs}}$, and Newtonian virial equilibrium accelerations, $g_{\mathrm{bar}}$ for the inferred masses, velocity dispersions and radii for the 3618 open clusters after our quality cuts from the HR134 catalogue. The colour number density shading gives the position of the 3251 $N_{\star}\leq 250$ clusters which accurately trace the galactic RAR relation given by the solid curve. The solid squares show the 145 most massive $N_{\star}\geq 500$ clusters, mostly tracing the Newtonian virial expectations, while the dots give the positions of the 222 intermediate mass $250 \leq N_{\star} \leq 500$ clusters, filling the region in between the two previous populations.
• Figure 3: Same data as shown in Fig. \ref{['Fig_Main_plot']} but only for the smallest $N_{\star} \leq 250$ clusters. The thin dotted line gives the resulting fit to these clusters to eq. \ref{['rar_eq']}, yielding an optimal fit acceleration scale almost identical to the standard $a_{0}$ value of MOND, which in turn results in the galactic RAR given by the solid curve. The equivalent fit using the fiducial $N_{\star}<250$ sub-sample with CMD quality$>75\%$ clusters actually coincides with this solid curve.
• Figure 4: Open clusters with $N\star<250$ compared to the baryonic Tully-Fisher relation. The error bars indicate the $1\sigma$ spread of the data for each mass bin. The dotted lines are the systematic uncertainty expected due to the presence of unresolved binary contamination, as modelled by HR134. Other data included: galaxy groups 2019PhRvD..99d4041M2022AA...662A..57M, rotating galaxies 2021MNRAS.507.5820D2019MNRAS.484.3267L2021AJ....162..202M; dwarf galaxies 2021AJ....162..202M; weak lensing 2024ApJ...969L...3M.
• Figure 5: Residuals with respect to the radial acceleration relation for our main $N_\star\leq250$ open cluster sample, plotted against various independent cluster characteristics.