Global survey of star clusters in the Milky Way -- VII. Tidal parameters and mass function

We built Galactic open star cluster mass functions (CMFs) for different age sub-samples in the wider solar neighbourhood. We present a simple cluster formation and evolution model to reproduce the main features of the CMFs. We used an unbiased sample of 2227 clusters of the Milky Way Star Cluster (MWSC) catalogue, which occupy the heliocentric cylinders with magnitude-dependent completeness radii of 1-5 kpc. We derived tidal masses of clusters with an accuracy of 70%. Our cluster formation and evolution model is based on the cluster initial mass function, the cluster formation rate, cluster mass loss due to stellar evolution and the clusters' dynamical evolution in the Galactic tidal field. The obtained tidal masses have been added to the MWSC catalogue. A general CMF (GCMF), built for all cluster ages around the Sun, extends over four decades in mass. The high-mass slope is +1.14. The CMFs for different age groups show the same high-mass slopes, while the low-mass slope is flat for the youngest sub-sample and about -0.7 for the others. The sub-samples inside and outside the solar Galactocentric radius are consistent with the GCMF, once the exponential decline of the Galactic disc density is taken into account. The model suggests star formation with low efficiency of 15%, where 10% of stars remain bound in a cluster after gas expulsion and violent relaxation. The cluster formation rate required to reproduce the observed age-mass-distribution is 0.4 solar masses per square pc and Gyr. The obtained high-mass slope of the GCMF for the wide solar neighbourhood is similar to slopes determined in nearby galaxies. The MWSC catalogue supports models with low star-formation efficiency, where 90% of stars are lost quickly after gas expulsion. The cluster formation rate corresponds to open clusters' contribution to the stellar content of the thin disc of 30%.