Phase mixing due to the Galactic potential: steps in the position and velocity distributions of popped star clusters

As star clusters are expected to form with low star formation efficiencies, the gas in the cluster is expelled quickly and early in their development: the star cluster "pops." This leads to an unbound stellar system, evolving in the Galactic potential. Previous N-body simulations have demonstrated the existence of a stepped number density distribution of cluster stars after popping, both in vertical position and vertical velocity, with a passing resemblance to a Christmas tree. Using numerical and analytical methods, we investigate the source of this structure, which arises due to the phase mixing of the out-of-equilibrium stellar system, determined entirely by the background analytic potential. Considering only the vertical motions, we construct a theoretical model to describe the time evolution of the phase space distribution of stars in a Miyamoto-Nagai disk potential and a full Milky-Way type potential comprising bulge, halo and disk components, which is then compared with N-body simulations. Using our theoretical model, we investigate the possible observational signatures and the feasibility of detection.