Roche volume filling of star clusters in the Milky Way

We examine the ratios $r_h/r_J$ of projected half-mass and Jacobi radius as well as $r_t/r_J$ of tidal and Jacobi radius for open and globular clusters in the Milky Way using data of both observations and simulations. We applied an improved calculation of $r_J$ for eccentric orbits of globular clusters. A sample of 236 open clusters of Piskunov et al. within the nearest kiloparsec around the Sun has been used. For the Milky Way globular clusters, data are taken from the Harris catalogue. We particularly use the subsample of 38 Milky Way globular clusters for which orbits have been integrated by Dinescu et al. We aim to quantify the differences between open and globular clusters and to understand, why they form two intrinsically distinct populations. We find under certain assumptions, or, in other words, in certain approximations, (i) that globular clusters are presently Roche volume underfilling and (ii) with at least $3σ$ confidence that the ratio $r_h/r_J$ of half-mass and Jacobi radius is $3 - 5$ times larger at present for an average open cluster in our sample than for an average globular cluster in our sample and (iii) that a significant fraction of globular clusters may be Roche volume overfilling at pericentre with $r_t > r_J$. Another aim of this paper is to throw light on the underlying theoretical reason for the existence of the van den Bergh correlation between half-mass and galactocentric radius.