A systematic method to identify runaways from star clusters produced from single-binary interactions: A case study of M67

One hypothesis for runaway stars (RSs) is that they are ejected from star clusters with high velocities relative to the cluster center-of-mass motion. There are two competing mechanisms for their production: supernova-based ejections in binaries, where one companion explodes, leaves no remnant, and launches the other companion at the instantaneous orbital velocity, and the disintegration of triples (or higher-order multiples), which produces a recoiled runaway binary (RB) and an RS. We search for RS candidates using data from the Gaia DR3 survey with a focus on triple disintegration since in this case the product is always a binary and a single star that should be moving in opposite directions. We created a systematic methodology to look for candidate RS-RB runaway pairs produced from the disintegration of bound three-body systems formed from single-binary interactions based on momentum conservation and causality. The method we use is general and can be applied to any cluster with a 5D kinematic data set. We used our criteria to search for these pairs in a 150 pc circular field of view surrounding the open cluster M67, which we used as a benchmark cluster to test the robustness of our method. Our results reveal only one RS-RB pair that is consistent with all of our selection criteria out of an initial sample of $10^8$ pairs.