Binary stars in young clusters: models versus observations of the Trapezium Cluster

The frequency of low-mass pre-main sequence binary systems is significantly lower in the Trapezium Cluster than in Taurus-Auriga. We investigate if this difference can be explained through stellar encounters in dense clusters. To this effect, a range of possible models of the well observed Trapezium Cluster are calculated using Aarseth's direct N-body code, which treats binaries accurately. The results are confronted with observational constraints. The range of models include clusters in virial equilibrium, expanding clusters as a result of instantaneous mass loss, as well as collapsing clusters. In all cases the primordial binary proportion is larger than 50 per cent, with initial period distributions as observed in Taurus-Auriga and the Galactic field. It is found that the expanding model, with an initial binary population as in the Galactic field, is most consistent with the observational constraints. This raises the possibility that the primordial group of OB stars may have expelled the cluster gas roughly 50 000 yr ago. The cluster's bulk expansion rate is thus a key observable that needs to be determined. The other models demonstrate that the rapidly decreasing binary proportion, its radial dependence and the form of the period distribution, together with structural and kinematical data, are very useful diagnostics on the present and past dynamical state of a young cluster. In particular, kinematical cooling from the disruption of wide binaries is seen for the first time.