Kinematic Signatures of Subvirial Initial Conditions in Young Clusters

Motivated by kinematic observations of young embedded clusters, this paper explores possible kinematic signatures produced by asphericity and departures from initial virial equilibrium in these systems. Specifically, the kinematic quantity that is measured and calculated in this study is the distribution of the line-of-sight velocities as a function of position along the cluster. Although clusters are found within a wide range of sizes, we focus on the regime with stellar membership N ~ 10³. The gravitational potential of these young clusters is dominated by the gas, and the geometry of the gas distribution is generalized to include axisymmetric (and triaxial) forms. With this loss of symmetry, the kinematic results thus depend on viewing angle. This work also considers the stars to begin their trajectories with subvirial speeds, as indicated by observations of core motions in such clusters. Our results determine the conditions necessary for the kinematic signature to display interesting structure, i.e., a nonspherical potential, a viewing angle that is not along one of the principal axes, and subvirial starting conditions. We characterize the effects on this signature due to projection angle, initial stellar velocities, cluster elongation, and star formation efficiency. Finally, we compare our theoretical results to recent kinematic observations of the Orion Nebula Cluster; we find that the observations can be explained provided that the cluster is nonspherical, starts with subvirial initial velocities, and is not viewed along a principal axis.