Wide binaries are rare in open clusters
  The population statistics of binary stars are an important output of star
formation models. However populations of wide binaries evolve over time due to
interactions within a system's birth environment and the unfolding of wide,
hierarchical triple systems. Hence the wide binary populations observed in star
forming regions or OB associations may not accurately reflect the wide binary
populations that will eventually reach the field. We use Gaia DR2 data to
select members of three open clusters, Alpha~Per, the Pleiades and Praesepe and
to flag cluster members that are likely unresolved binaries due to
overluminosity or elevated astrometric noise. We then identify the resolved
wide binary population in each cluster, separating it from coincident pairings
of unrelated cluster members. We find that these clusters have an average wide
binary fraction in the 300-3000\,AU projected separation range of
2.1$\pm^{0.4}_{0.2}$\% increasing to 3.0$\pm^{0.8}_{0.7}$\% for primaries with
masses in the 0.5-1.5\,$M_{\odot}$ range. This is significantly below the
observed field wide binary fraction, but shows some wide binaries survive in
these dynamically highly processed environments. We compare our results with
another open cluster (the Hyades) and two populations of young stars that
likely originated in looser associations (Young Moving Groups and the
Pisces-Eridanus stream). We find that the Hyades also has a deficit of wide
binaries while the products of looser associations have wide binary fractions
at or above field level.
