Dynamical evolution of the open clusters with different star formation efficiencies and orbital parameters

Open star clusters are dynamic systems whose evolution is critically influenced by initial conditions such as star formation efficiency and orbital parameters. Understanding their dissolution mechanisms provides insight into stellar population dynamical mixing in the Milky Way. We aim to investigate the dynamical evolution and dissolution of initially non-virialised open clusters by examining how different global star formation efficiencies and orbital characteristics impact the cluster longevity and structural changes. We followed the evolution of the clusters up to their dissolution time on the basis of our calculations. We compare our open cluster dynamical evolutionary models with the observed open clusters in our Galaxy's solar vicinity. Using high-order direct N-body simulations, we modelled cluster evolution across different Galactic orbits, systematically varying initial star formation efficiencies to comprehensively explore dissolution mechanisms. Our simulations reveal that open clusters typically survive approximately ten orbital periods, with cluster lifetime being strongly dependent on global star formation efficiency and only marginally influenced by orbital eccentricity. We estimate gas expulsion timescales of 0.9 Myr, with initial supernova explosions efficiently removing gaseous components from the cluster. The expected lifetime of the cluster (in units of orbital periods) strongly depends on the cluster global star-formation efficiency and only slightly on the orbital eccentricities of the cluster. The theoretical models demonstrate a remarkable agreement of the Roche-volobe filling parameter with the recent observed Gaia DR3 cluster catalogues in the solar vicinity. By incorporating a mixed sample of clusters with varying star formation efficiencies, we provide a more nuanced understanding of open cluster evolution in the Galactic disc.