The Effect of Age on the Grouping of Open Clusters: The Primordial Group
  Hypothesis
  The Primordial group hypothesis states that only young enough open clusters
(OCs) can be multiple, and old OCs are essentially single since the
gravitational interaction between OCs in primordial groups is very weak, and
the probability of gravitational capture of two unrelated OCs without
disruption is very low. We test such postulate through four different studies
using a manual search of Gaia EDR3 and extensive literature. First, we revisit
the work of de La Fuente Marcos & de La Fuente Marcos (2009), which states that
only ca. 40% of the OCs pairs are of primordial origin. However, no plausible
binary system among their proposed OC pairs having at least one member older
than 0.1 Gyr has been found. Second, we research among the youngest OCs (age <
0.01 Gyr) in Tarricq et al. (2021) and obtain that ca. 71% of them remain in
their primordial groups. Third, a similar study of the oldest OCs (age > 4 Gyr)
shows that they are essentially alone. Forth, the well-known case of the double
cluster in Perseus is shown also to accommodate the title hypothesis. A
simplified bimodal model allows retrieving the overall fraction of linked OCs
(around 12-16 %) from our results, assuming that young clusters remain
associated ~0.04 Gyr. The obtained results further support that OCs are born in
groups (Casado 2021).
