Gravity or turbulence V: Star forming regions undergoing violent
  relaxation
  Using numerical simulations of the formation and evolution of stellar
clusters within molecular clouds, we show that the stars in clusters formed
within collapsing molecular cloud clumps exhibit a constant velocity dispersion
regardless of their mass, as expected in a violent relaxation processes. In
contrast, clusters formed in turbulence-dominated environments exhibit an {\it
inverse} mass segregated velocity dispersion, where massive stars exhibit
larger velocity dispersions than low-mass cores, consistent with massive stars
formed in massive clumps, which in turn, are formed through strong shocks. We
furthermore use Gaia EDR3 to show that the stars in the Orion Nebula Cluster
exhibit a constant velocity dispersion as a function of mass, suggesting that
it has been formed by collapse within one free-fall time of its parental cloud,
rather than in a turbulence-dominated environment during many free-fall times
of a supported cloud. Additionally, we have addressed several of the criticisms
of models of collapsing star forming regions: namely, the age spread of the
ONC, the comparison of the ages of the stars to the free-fall time of the gas
that formed it, the star formation efficiency, and the mass densities of clouds
vs the mass densities of stellar clusters, showing that observational and
numerical data are consistent with clusters forming in clouds undergoing a
process of global, hierarchical and chaotic collapse, rather than been
supported by turbulence.
