Detailed analysis of open clusters: a mass function break and evidence of a fundamental plane

We derive photometric, structural and dynamical evolution-related parameters of 11 nearby open clusters with ages in the range 70 Myr to 7 Gyr and masses in the range $\approx400$ \ms to $\approx5 300$ \ms. We search for relations of structural and evolutionary parameters with age and Galactocentric distance. The main results for the present sample are: {\em (i)} cluster size correlates both with age and Galactocentric distance; {\em (ii)} because of size and mass scaling, core and limiting radii, and core and overall mass correlate; {\em (iii)} massive ($\rm m\geq1 000$ \ms) and less-massive clusters follow separate correlation paths on the plane core radius and overall mass; {\em (iv)} MF slopes of massive clusters are restricted to a narrow range, while those of the less-massive ones distribute over a wider range. Core and overall MF flattening is related to the ratio ($\tau$) of age to relaxation time. For large values of $\tau$ the effects of large-scale mass segregation and low-mass stars evaporation can be observed in the MFs. In this sense, $\tau$ appears to characterize the evolutionary state of the clusters. We conclude that appreciable slope flattenings in the overall MFs of the less-massive clusters take $\sim6$ times longer to occur than in the core, while in the massive clusters they take a time $\sim13$ times longer. We investigate cluster parameters equivalent to those determining the fundamental plane of ellipticals. These parameters are: overall mass, projected mass density and core radius. We conclude that in the present sample there is evidence of a fundamental plane.