Orbits and vertical height distribution of 4006 open clusters in the Galactic disk using Gaia DR3

Open clusters (OCs) in the Galaxy are excellent probes for tracing the structure and evolution of the Galactic disk. We present an updated catalog of parameters for 1,145 OCs, estimated using the Gaia DR3 data earlier listed in Cantat-Gaudin et al. (2020). This sample is complemented by 3,677 OCs from the catalog by Hunt & Reffert (2023). Using the Galaxy potential and the space velocities, orbits of 4,006 OCs were computed. We provide a catalog with orbital parameters such as eccentricity, perigalactic and apogalactic distance, and the maximum vertical height traced by OCs from the Galactic disk. The OCs were found to be distributed between 5-16 kpc from the Galactic center, with older OCs showing a radially extended distribution. The low number of old OCs in the inner Solar circle region likely suggests their destruction in this area. We derive a quantitative expression for the dependency of the maximum vertical height (Z_max) OCs can reach with the cluster's age and Galactocentric radius for the first time. The young and intermediate-age OCs show similar values of Z_max till 9 kpc, with the latter group having higher values beyond. OCs older than 1 Gyr show larger values of Z_max at all Galactocentric radii and significantly larger values beyond 9 kpc. Higher values of Z_max are found in the third Galactic quadrant, suggesting a link between these higher values and the Galactic warp. This sample shows that young OCs are also involved in the diagonal ridge formation in the solar neighborhood.