The Structure, Dynamics and Star Formation Rate of the Orion Nebula
  Cluster
  The spatial morphology and dynamical status of a young, still-forming stellar
cluster provide valuable clues on the conditions during the star formation
event and the processes that regulated it. We analyze the Orion Nebula Cluster
(ONC), utilizing the latest censuses of its stellar content and membership
estimates over a large wavelength range. We determine the center of mass of the
ONC, and study the radial dependence of angular substructure. The core appears
rounder and smoother than the outskirts, consistent with a higher degree of
dynamical processing. At larger distances the departure from circular symmetry
is mostly driven by the elongation of the system, with very little additional
substructure, indicating a somewhat evolved spatial morphology or an expanding
halo. We determine the mass density profile of the cluster, which is well
fitted by a power law that is slightly steeper than a singular isothermal
sphere. Together with the ISM density, estimated from average stellar
extinction, the mass content of the ONC is insufficient by a factor $\sim 1.8$
to reproduce the observed velocity dispersion from virialized motions, in
agreement with previous assessments that the ONC is moderately supervirial.
This may indicate recent gas dispersal. Based on the latest estimates for the
age spread in the system and our density profiles, we find that, at the
half-mass radius, 90% of the stellar population formed within $\sim 5$-$8$
free-fall times ($t_{\rm ff}$). This implies a star formation efficiency per
$t_{\rm ff}$ of $\epsilon_{\rm ff}\sim 0.04$-$0.07$, i.e., relatively slow and
inefficient star formation rates during star cluster formation.
