Asymptotic kinematics of globular clusters: The emergence of a Tully–Fisher relation

Abstract

ABSTRACT 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 $\sigma _{\infty }[\, \mathrm{km \, s}^{-1}]= 0.084^{+0.075}_{-0.040} (\mathrm{{\it M}/M}_{\odot })^{0.3 \pm 0.051}$, which is interesting to compare to the deep modified Newtonian dynamics (MOND) limit of $\sigma _{\infty } [\mathrm{km \, s}^{-1}]=0.2(\mathrm{{\it M}/M}_{\odot })^{0.25}$. 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.