[KBK2014] N1256 , the SIMBAD biblio

NGC 4372 is a poorly studied old, very metal-poor globular cluster (GC) located in the inner Milky Way halo. We present the first in-depth study of the kinematic properties and derive the structural parameters of NGC 4372 based on the fit of a Plummer profile and a rotating, physical model. We explore the link between internal rotation to different cluster properties and together with similar studies of more GCs, we put these in the context of globular cluster formation and evolution. We present radial velocities for 131 cluster member stars measured from high-resolution FLAMES/GIRAFFE observations. Their membership to the GC is additionally confirmed from precise metallicity estimates. We build a velocity dispersion profile and a systemic rotation curve using this kinematic data set. Additionally, we obtain an elliptical number density profile of NGC 4372 based on optical images using a Markov chain Monte Carlo fitting algorithm. From this, we derive the cluster's half-light radius and ellipticity as r_h=3.44'±0.04' and ε=0.08±0.01. Finally, we give a physical interpretation of the observed morphological and kinematic properties of this GC by fitting an axisymmetric, differentially rotating, dynamical model. Our results show that NGC 4372 has an unusually high ratio of rotation amplitude to velocity dispersion (1.2 vs. 4.5km/s) for its metallicity. This puts it in line, however, with two other exceptional, very metal-poor GCs: M 15 and NGC 4590. We also find a mild flattening of NGC 4372 in the direction of its rotation. Given its old age, this suggests that the flattening is indeed caused by the systemic rotation rather than tidal interactions with the Galaxy. Additionally, we estimate the dynamical mass of the GC M_dyn=2.0±0.5x10⁵M_☉ based on the dynamical model, which constrains the mass-to-light ratio of NGC 4372 between 1.4 and 2.3 M_☉/L_☉, representative of an old, purely stellar population.