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.