Collinder 135 and UBC 7: A Physical Pair of Open Clusters
  Given the closeness of the two open clusters Cr 135 and UBC 7 on the sky, we
investigate the possibility of the two clusters to be physically related. We
aim to recover the present-day stellar membership in the open clusters
Collinder 135 and UBC 7 (300 pc from the Sun), to constrain their kinematic
parameters, ages and masses, and to restore their primordial phase space
configuration. The most reliable cluster members are selected with our
traditional method modified for the use of Gaia DR2 data. Numerical simulations
use the integration of cluster trajectories backwards in time with our original
high order Hermite4 code \PGRAPE. We constrain the age, spatial coordinates and
velocities, radii and masses of the clusters. We estimate the actual separation
of the cluster centres equal to 24 pc. The orbital integration shows that the
clusters were much closer in the past if their current line-of-sight velocities
are very similar and the total mass is more than 7 times larger the mass of the
determined most reliable members. We conclude that the two clusters Cr 135 and
UBC 7 might very well have formed a physial pair, based on the observational
evidence as well as numerical simulations. The probability of a chance
coincidence is only about $2\%$.
