Evidence for feedback and stellar-dynamically regulated bursty star cluster formation: the case of the Orion Nebula Cluster
(abridged) A scenario for the formation of multiple co-eval populations separated in age by about 1 Myr in very young clusters (VYCs, ages less than 10 Myr) and with masses in the range 600-20000 Msun is outlined. It rests upon a converging inflow of molecular gas building up a first population of pre-main sequence stars. The associated just-formed O stars ionise the inflow and suppress star formation in the embedded cluster. However, they typically eject each other out of the embedded cluster within 10^6 yr, that is before the molecular cloud filament can be ionised entirely. The inflow of molecular gas can then resume forming a second population. This sequence of events can be repeated multiply. This model is applied to the Orion Nebula Cluster (ONC), in which three well-separated pre-main sequences in the color-magnitude diagram of the cluster have recently been discovered. The mass-inflow history is constrained using this model and the number of OB stars ejected from each population are estimated for verification using Gaia data. As a consequence of the proposed model, the three runaway O star systems, AE Aur, mu Col and iota Ori, are considered as significant observational evidence for stellar-dynamical ejections of massive stars from the oldest population in the ONC.