Na-O anticorrelation and HB IX. Kinematics of the program clusters A link between systemic rotation and HB morphology?

We use accurate radial velocities for 1981 member stars in 20 Galactic globular clusters, collected within our large survey aimed at analyzing the Na-O anti-correlation, to study the internal kinematics of the clusters. We performed the first systematic exploration of the possible connections between cluster kinematics and the multiple populations phenomenon in GCs. We did not find any significant correlation between Na abundance and either velocity dispersion or systemic rotation. We searched for systemic rotation in the eight clusters of our sample that lack this analysis from previous works in the literature (NGC 2808, NGC5904, NGC6171, NGC6254, NGC6397, NGC6388, NGC6441, and NGC6838). These clusters are found to span a wide range of rotational amplitudes from similar to 0.0 km s(-1) (NGC6397) to similar to 13.0 km s(-1) (NGC6441). We found a significant correlation between the ratio of rotational velocity to central velocity dispersion (V-rot/sigma(0)) and the horizontal branch morphology parameter (B - R)/(B + R + V). The ratio Vrot/s0 is found to correlate also with metallicity, possibly hinting at a significant role for dissipation in the process of formation of globular clusters; V-rot is found to correlate well with (B - R)/(B + R + V), M-V, sigma(0), and [Fe/H]. All these correlations strongly suggest that systemic rotation may be intimately linked with the processes that led to the formation of globular clusters and the stellar populations they host.