The outskirts of globular clusters ( GCs ) simultaneously retain crucial information about their formation mechanism and the properties of their host galaxy .
Thanks to the advent of precision astrometry both their morphological and kinematic properties are now accessible .
Here we present the first dynamical study of the outskirts of the retrograde GC NGC3201 until twice its Jacobi radius ( < 100 pc ) , using specifically-selected high-quality astrometric data from Gaia DR2 .
We report the discovery of a stellar overdensity along the South-East/North-West direction that we identify as tidal tails .
The GC is characterized globally by radial anisotropy and a hint of isotropy in the outer parts , with an excess of tangential orbits around the lobes corresponding to the tidal tails , in qualitative agreement with an N -body simulation .
Moreover , we measure flat velocity dispersion profiles , reaching values of 3.5 \pm 0.9  km s ^ { -1 } until beyond the Jacobi radius .
While tidal tails could contribute to such a flattening , this high velocity dispersion value is in disagreement with the expectation from the sole presence of potential escapers .
To explain this puzzling observation , we discuss the possibility of an accreted origin of the GC , the presence of a dark matter halo – leftover of its formation at high redshift – and the possible effects of non-Newtonian dynamics .
Our study uncovers a new path for the study of GC formation and of the properties of the Milky Way potential in the era of precision astrometry .