Abstract:
The fundamental plane (FP) is a scaling relation among effective radius, central velocity dispersion and average surface brightness of spherical dynamical systems, which is expected to be originated from the virial equilibrium of their members. Observations show that two kind of old and (relatively) isolated dynamical systems (age > 10 giga-year (Gyr)) both have FP: 1) elliptical galaxies (mass of ~10^12 solar masses), and 2) globular clusters (mass of 10^6 solar masses). Open clusters are the lower-mass counterparts of globular clusters, with masses are in the range of 100–104  solar masses. On the contrary to globular clusters, which are isolated in the remote halo of Milky Way without much perturbation, open clusters reside in the crowded plane of the Milky Way. They are subjected to strong tidal disturbance, such as disk shock, spiral arm passage, molecular cloud encounter, which increase the internal cluster energy, and consequently lead to their expansion and disruption. Many studies have suggested a typical survival timescale of 200 million-year (Myr) for open clusters and only 3% of the known open clusters have ages above 1 Gyr. Besides, the velocity dispersion of open clusters is at the order of 0.5-1 km/s, which requires spectroscopy of very high resolution. Therefore, their FP is not been studied or investigated in the past, due to the complexity of their dynamical evolution and the difficulty in obtaining precise velocity dispersion. We are motivated to extend the FP study to open clusters and quantify their dynamical status.  We select a sample of old open clusters (aged older than 1 Gyr) from the Milky Way open cluster catalog,  and make use of the data from the Apache Point Observatory Galactic Evolution Experiment-2 in the fourteenth data release of the Sloan Digital Sky Survey. For the first time, we establish a fundamental plane among cluster parameters, the line-of-sight velocity dispersion σ1D, Ks band luminosity LKs, and the half-light radius rh. 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.