3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR3
  II: Hierarchical Star Formation Revealed by Spatial and Kinematic
  Substructures
  We identify members of 65 open clusters in the solar neighborhood using the
machine-learning algorithm StarGO based on Gaia EDR3 data. After adding members
of twenty clusters from previous studies (Pang et al. 2021a,b; Li et al. 2021)
we obtain 85 clusters, and study their morphology and kinematics. We classify
the substructures outside the tidal radius into four categories: filamentary
(f1) and fractal (f2) for clusters $<100$ Myr, and halo (h) and tidal-tail (t)
for clusters $>100$ Myr. The kinematical substructures of f1-type clusters are
elongated; these resemble the disrupted cluster Group X. Kinematic tails are
distinct in t-type clusters, especially Pleiades. We identify 29 hierarchical
groups in four young regions (Alessi 20, IC 348, LP 2373, LP 2442); ten among
these are new. The hierarchical groups form filament networks. Two regions
(Alessi 20, LP 2373) exhibit global "orthogonal" expansion (stellar motion
perpendicular to the filament), which might cause complete dispersal.
Infalling-like flows (stellar motion along the filament) are found in UBC 31
and related hierarchical groups in the IC 348 region. Stellar groups in the LP
2442 region (LP 2442 gp 1-5) are spatially well-mixed but kinematically
coherent. A merging process might be ongoing in the LP 2442 subgroups. For
younger systems ($\lesssim30$ Myr), the mean axis ratio, cluster mass and
half-mass radius tend to increase with age values. These correlations between
structural parameters may imply two dynamical processes occurring in the
hierarchical formation scenario in young stellar groups: (1) filament
dissolution and (2) sub-group mergers.
