Globular clusters are useful to test the validity of Newtonian dynamics in the low acceleration regime typical of galaxies, without the complications of non-baryonic dark matter. Specifically, in absence of disturbing effects, e.g. tidal heating, their velocity dispersion is expected to vanish at large radii. If such behaviour is not observed, and in particular if, as observed in elliptical galaxies, the dispersion is found constant at large radii below a certain threshold acceleration, this might indicate a break down of Newtonian dynamics. To minimise the effects of tidal heating in this paper we study the velocity dispersion profile of two distant globular clusters, NGC 1851 and NGC 1904. The velocity dispersion profile is derived from accurate radial velocities measurements, obtained at the ESO 8m VLT telescope. Reliable data for 184 and 146 bona fide cluster star members, respectively for NGC 1851 and NGC 1904, were obtained. These data allow to trace the velocity dispersion profile up to ~2r0, where r0 is the radius at which the cluster internal acceleration of gravity is a0 = 10e-8 cm/s/s. It is found that in both clusters the velocity dispersion becomes constant beyond ~r0. These new results are fully in agreement with those found for other five globular clusters previously investigated as part of this project. Taken all together, these 7 clusters support the claim that the velocity dispersion is constant beyond r0, irrespectively of the specific physical properties of the clusters: mass, size, dynamical history, and distance from the Milky Way. The strong similarly with the constant velocity dispersion observed in elliptical galaxies beyond r0 is suggestive of a common origin for this phenomenon in the two class of objects, and might indicate a breakdown of Newtonian dynamics below a0.
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