Open cluster dissolution rate and the initial cluster mass function in the solar neighbourhood. Modelling the age and mass distributions of clusters observed by Gaia

Abstract: Context. The dissolution rate of open clusters (OCs) and integration of their stars into the Milky Way's field population has been previously explored using their age distribution. With the advent of the Gaia mission, we have an exceptional opportunity to revisit and enhance these studies with ages and masses from high quality data. Aims. To build a comprehensive Gaia-based OC mass catalogue which, combined with the age distribution, allows a deeper investigation of the disruption experienced by OCs within the solar neighbourhood. Methods. Masses were determined by comparing luminosity distributions to theoretical luminosity functions. The limiting and core radii of the clusters were obtained by fitting the King function to their observed density profiles. We examined the disruption process through simulations of the build-up and mass evolution of a population of OCs which were compared to the observed mass and age distributions. Results. Our analysis yielded an OC mass distribution with a peak at $log(M)$ = 2.7 dex ($\sim 500 M_{\odot}$), as well as radii for 1724 OCs. Our simulations showed that using a power-law Initial Cluster Mass Function (ICMF) no parameters were able to reproduce the observed mass distribution. Moreover, we find that a skew log-normal ICMF provides a good match to the observations and that the disruption time of a $10^4 M{\odot}$ OC is $t_4^{tot} = 2.9 \pm 0.4$ Gyr. Conclusions. Our results indicate that the OC disruption time $t_4^{tot}$ is about twice longer than previous estimates based solely on OC age distributions. We find that the shape of the ICMF for bound OCs differs from that of embedded clusters, which could imply a low typical star formation efficiency of $\leq 20\%$ in OCs. Our results also suggest a lower limit of $\sim 60 M{\odot}$ for bound OCs in the solar neighbourhood.