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We determine the mass functions (MFs) and the dynamical parameters of 15nearby open clusters (OCs) using the unprecedented data set of the Gaia EarlyData Release 3. We select the members of each cluster by combining thephotometric (colour and magnitude) and astrometric (parallax and propermotions) parameters of stars, minimizing the contamination from Galactic fieldinterlopers. By comparing the observed distribution of stars along the clustermain sequence with the best-fitting synthetic population, we find thepresent-day MF and the binary fraction of the OCs, along with their dynamicalparameters like mass, half-mass radius, and half-mass relaxation time. We foundthat the global present-day MF of OCs are consistent with a single power-lawfunction, $F(m)\propto m^\alpha$, with slopes $-3<\alpha<-0.6$ including bothsubsolar, $0.2<m/\text{M}_\odot<1$, and supersolar mass regimes. A significantcorrelation between the MF-slope and the ratio of age to half-mass relaxationtime is evidenced, similarly to the same conclusion already observed amongGalactic globular clusters. However, OCs evolve along different tracks incomparison with the globular clusters, possibly indicating primordialdifferences in their initial mass function (IMF). The comparison with MonteCarlo simulations suggests that all the analysed OCs could have been born withan IMF with slope $\alpha_{\text{IMF}}<-2.3$. We also show that the lessevolved OCs have a MF consistent with that of the solar neighbourhood,indicating a possible connection between the dissolution of OCs and theformation of the Galactic disc.

The family pictures of our neighbours: investigating the mass function and dynamical parameters of nearby open clusters