The Fundamental Plane of Open Clusters
  We utilize the data from the Apache Point Observatory Galactic Evolution
Experiment-2 (APOGEE-2) in the fourteenth data release of the Sloan Digital Sky
Survey (SDSS) to calculate the line-of-sight velocity dispersion $\sigma_{1D}$
of a sample of old open clusters (age larger than 100\,Myr) selected from the
Milky Way open cluster catalog of Kharchenko et al. (2013). Together with their
$K_s$ band luminosity $L_{K_s}$, and the half-light radius $r_{h}$ of the most
probable members, we find that these three parameters show significant pairwise
correlations among each other. Moreover, a fundamental plane-{\it like}
relation among these parameters is found for the oldest open clusters (age
older than 1\,Gyr), $L_{K_s}\propto\sigma_{1D}^{0.82\pm0.29}\cdot
r_h^{2.19\pm0.52}$ with $rms \sim\, 0.31$\,mag in the $K_s$ 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.
