3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR 3: Its Relation to Cluster Dynamics

We analyze the 3D morphology and kinematics of 13 open clusters (OCs) located within 500 pc of the Sun, using Gaia EDR 3 and kinematic data from the literature. Members of OCs are identified using the unsupervised machine-learning method StarGO, using five parameters (X, Y, Z, muα cosδ muδ). The OC sample covers an age range of 25 Myr to 2.65 Gyr. We correct the asymmetric distance distribution that is due to parallax error using Bayesian inversion. The uncertainty in the corrected distance for a cluster at 500 pc is 3.0-6.3 pc, depending on the intrinsic spatial distribution of its members. We determine the 3D morphology of the OCs in our sample and fit the spatial distribution of stars within the tidal radius in each cluster with an ellipsoid model. The shapes of the OCs are well described with oblate spheroids (NGC 2547, NGC 2516, NGC 2451A, NGC 2451B, and NGC 2232), prolate spheroids (IC 2602, IC 4665, NGC 2422, Blanco 1, and Coma Berenices), or triaxial ellipsoids (IC 2391, NGC 6633, and NGC 6774). The semimajor axis of the fitted ellipsoid is parallel to the Galactic plane for most clusters. Elongated filament-like substructures are detected in three young clusters (NGC 2232, NGC 2547, and NGC 2451B), while tidal-tail-like substructures (tidal tails) are found in older clusters (NGC 2516, NGC 6633, NGC 6774, Blanco 1, and Coma Berenices). Most clusters may be supervirial and expanding. N-body models of rapid gas expulsion with a star formation efficiency of ≈1/3 are consistent with clusters more massive than 250 M o˙, while clusters less massive than 250 M o˙ tend to agree with adiabatic gas expulsion models. Only five OCs (NGC 2422, NGC 6633, NGC 6774, Blanco 1, and Coma Berenices) show clear signs of mass segregation.