The Fundamental Plane of Open Clusters

We utilize the data from the Apache Point Observatory Galactic Evolution Experiment-2 in the fourteenth data release of the Sloan Digital Sky Survey to calculate the line-of-sight velocity dispersion σ1D of a sample of old open clusters (aged older than 100 Myr) selected from the Milky Way open cluster catalog of Kharchenko et al. Together with their Ks band luminosity ${L}_{{K}_{s}}$, and the half-light radius rh of the most probable members, we find that these three parameters show significant pairwise correlations among each other. Moreover, a fundamental plane-like relation among these parameters is found for the oldest open clusters (aged older than 1 Gyr), ${L}_{{K}_{s}}\propto {\sigma }_{1{\rm{D}}}^{0.82\pm 0.29}\cdot {r}_{h}^{2.19\pm 0.52}$ with rms ∼ 0.31 mag in the Ks band absolute magnitude. The existence of this relation, which deviates significantly from the virial theorem prediction, implies that the dynamical structures of the old open clusters are quite similar, when survived from complex dynamical evolution to age older than 1 Gyr.