Properties of star clusters - II. Scaleheight evolution of clusters

Until now, it has been impossible to observationally measure how star cluster scaleheight evolves beyond 1 Gyr as only small samples have been available. Here, we establish a novel method to determine the scaleheight of a cluster sample using modelled distributions and Kolmogorov-Smirnov tests. This allows us to determine the scaleheight with a 25 per cent accuracy for samples of 38 clusters or more. We apply our method to investigate the temporal evolution of cluster scaleheight, using homogeneously selected sub-samples of Kharchenko et al. (MWSC), Dias et al. (DAML02), WEBDA, and Froebrich et al. (FSR). We identify a linear relationship between scaleheight and log(age/yr) of clusters, considerably different from field stars. The scaleheight increases from about 40 pc at 1 Myr to 75 pc at 1 Gyr, most likely due to internal evolution and external scattering events. After 1 Gyr, there is a marked change of the behaviour, with the scaleheight linearly increasing with log(age/yr) to about 550 pc at 3.5 Gyr. The most likely interpretation is that the surviving clusters are only observable because they have been scattered away from the mid-plane in their past. A detailed understanding of this observational evidence can only be achieved with numerical simulations of the evolution of cluster samples in the Galactic disc. Furthermore, we find a weak trend of an age-independent increase in scaleheight with Galactocentric distance. There are no significant temporal or spatial variations of the cluster distribution zero-point. We determine the Sun's vertical displacement from the Galactic plane as Z(circle dot) = 18.5 +/- 1.2 pc.