On encounter rates in star clusters

Abstract: Close encounters between stars in star forming regions are important as they can perturb or destroy protoplanetary discs, young planetary systems, and stellar multiple systems. We simulate simple, viralised, equal-mass $N$-body star clusters and find that both the rate and total number of encounters between stars varies by factors of several in statistically identical clusters due to the stochastic/chaotic details of orbits and stellar dynamics. Encounters tend to rapidly `saturate' in the core of a cluster, with stars there each having many encounters, while more distant stars have none. However, we find that the fraction of stars that have had at least one encounter within a particular distance grows in the same way (scaling with crossing time and half-mass radius) in all clusters, and we present a new (empirical) way of estimating the fraction of stars that have had at least one encounter at a particular distance.