Global survey of star clusters in the Milky Way VIII. Cluster formation and evolution

Context. We consider tidal masses and ages of Milky Way open clusters, as well as a simple model of their distribution. This model is presented as part of the Milky Way Star Cluster (MWSC) survey. Aims. Our aim is to investigate the space of model parameters and the correspondence between modelled and observed twodimensional (2D) cluster age-mass distributions. Methods. The model for cluster evolution is comprised of a two-section cluster initial mass function, constant cluster formation rate, and a mass loss function. This mass loss function represents a supervirial phase after sudden expulsion of the remaining gas, cluster mass loss due to stellar evolution and gradual cluster dissolution driven by internal dynamics and the Galactic tidal field. We constructed different estimators of model fitness based on χ 2-statistics, the Kullback-Leibler divergence (KLD) and a maximumlikelihood approach, taking into account the uncertainty of our observed cluster parameters. Using these estimators and Markov chain Monte Carlo (MCMC) sampling, we obtained best-fit values and posterior distributions for a selection of model parameters. Results. The KLD returned a superior model compared to the other statistics, because it also reproduced the low-density regions of the observed cluster age-mass distribution. The cluster initial mass function is well constrained and we find a clear signature of an enhanced cluster mass loss in the first 50 Myr. Deviations from a constant cluster formation rate could not be determined due to its strong degeneracy with the shape of the cluster mass loss function. In the KLD best model, clusters lose 72% of their initial mass in the violent relaxation phase, after which cluster mass loss slows down, allowing for a relatively low rate of cluster formation of 0.088 M ⊙ kpc −2 Gyr −1. The observed upper limit of cluster ages at approx. 5 Gyr is reflected in the model by a very shallow lifetimemass relation for clusters with initial masses above 1000 M ⊙. The application of the model to an independent cluster sample based on Gaia DR3 data yielded similar results except for a systematic shift in typical age and higher number densities. Conclusions. We conclude that the observed cluster age-mass distribution is compatible with a constant cluster formation rate. Strong correlations between model parameters reflect a sensitive dependence of the cluster age-mass distribution not just on the formation rate and initial mass function, but the details of cluster mass loss and dissolution in particular. The enhanced number of young massive clusters observed requires an early violent relaxation phase of strong mass loss. The cluster age limit cannot be fully explained by an initial mass cutoff.