2020MNRAS.491..272H

Using a recent homogeneous sample of 40 high-quality velocity dispersion profiles for Galactic globular clusters, we study the regime of low gravitational acceleration relevant to the outskirts of these systems. We find that a simple empirical profile having a central Gaussian component and a constant large-radius asymptote, σ[?], accurately describes the variety of observed velocity dispersion profiles. We use published population synthesis models, carefully tailored to each individual cluster, to estimate mass-to-light ratios from which total stellar masses, M, are inferred. We obtain a clear scaling, reminiscent of the galactic Tully-Fisher relation of σ _{[?]}[ km s^{-1}]= 0.084^{+0.075}_{-0.040} ({M/M}_{☉ })^{0.3 ± 0.051}, which is interesting to compare to the deep modified Newtonian dynamics (MOND) limit of σ _{[?]} [km s^{-1}]=0.2({M/M}_{☉ })^{0.25}. Under a Newtonian interpretation, our results constitute a further restriction on models where initial conditions are crafted to yield the outer flattening observed today. Within a modified gravity scheme, because the globular clusters studied are not isolated objects in the deep MOND regime, the results obtained point towards a modified gravity where the external field effect of MOND does not appear, or is significantly suppressed.