Not all stars form in clusters -- $Gaia$-DR2 uncovers the origin of OB
  associations
  Historically, it has often been asserted that most stars form in compact
clusters. In this scenario, present-day gravitationally-unbound OB associations
are the result of the expansion of initially gravitationally-bound star
clusters. However, this paradigm is inconsistent with recent results, both
theoretical and observational, that instead favour a hierarchical picture of
star formation in which stars are formed across a continuous distribution of
gas densities and most OB associations never were bound clusters. Instead they
are formed in-situ as the low-density side of this distribution, rather than as
the remnants of expanding clusters. We utilise the second $Gaia$ data release
to quantify the degree to which OB associations are undergoing expansion and,
therefore, whether OB associations are the product of expanding clusters, or
whether they were born in-situ, as the large-scale, globally-unbound
associations that we see today. We find that the observed kinematic properties
of associations are consistent with highly substructured velocity fields and
additionally require some degree of localised expansion from sub-clusters
within the association. While most present-day OB associations do exhibit low
levels of expansion, there is no significant correlation between radial
velocity and radius. Therefore, the large-scale structure of associations is
not set by the expansion of clusters, rather it is a relic of the molecular gas
cloud from which the association was formed. This finding is inconsistent with
a monolithic model of association formation and instead favours a hierarchical
model, in which OB associations form in-situ, following the fractal structure
of the gas from which they form.
