Approximately 10 per cent of star clusters are found in pairs, known as binary clusters. We propose a mechanism for binary cluster formation; we use N-body simulations to show that velocity substructure in a single (even fairly smooth) region can cause binary clusters to form. This process is highly stochastic and it is not obvious from a region's initial conditions whether a binary will form and, if it does, which stars will end up in which cluster. We find the probability that a region will divide is mainly determined by its virial ratio, and a virial ratio above 'equilibrium' is generally necessary for binary formation. We also find that the mass ratio of the two clusters is strongly influenced by the initial degree of spatial substructure in the region.

We use N-body simulations to probe the early phases of the dynamical evolution of star-forming regions and focus on mass and velocity distributions of unbound stars. In this parameter space study, we vary the initial virial ratio and degree of spatial and kinematic substructure and analyse the fraction of stars that become unbound in two different mass classes (above and below 8 M ⊙ ). We find that the fraction of unbound stars differs depending on the initial conditions. After 10 Myr, in initially highly subvirial, substructured simulations, the high-mass and lower-mass unbound fractions are similar at ∼23 per cent. In initially virialised, substructured simulations, we find only ∼16 per cent of all high-mass stars are unbound, whereas ∼37 per cent of all lower-mass stars are. The velocity distributions of unbound stars only show differences for extremely different initial conditions. The distributions are dominated by large numbers of lower-mass stars becoming unbound just above the escape velocity of ∼3 km s −1 with unbound high-mass stars moving faster on average than lower-mass unbound stars. We see no high-mass runaway stars (velocity > 30 km s −1 ) from any of our initial conditions and only an occasional lower-mass runaway star from initially subvirial/substructured simulations. In our simulations, we find a small number of lower-mass walkaway stars (with velocity 5-30 km s −1 ) from all of our initial conditions. These walkaway stars should be observable around many nearby star-forming regions with Gaia.

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We present a new method of analysing and quantifying velocity structure in star forming regions suitable for the rapidly increasing quantity and quality of stellar position-velocity data. The method can be applied to data in any number of dimensions, does not require the centre or characteristic size (e.g. radius) of the region to be determined, and can be applied to regions with any underlying density and velocity structure. We test the method on a variety of example datasets and show it is robust with realistic observational uncertainties and selection effects. This method identifies velocity structures/scales in a region, and allows a direct comparison to be made between regions.

The kinematic structure of the Cygnus OB2 association is investigated. No evidence of expansion or contraction is found at any scale within the region. Stars that are within ∼0.5 pc of one another are found to have more similar velocities than would be expected by random chance, and so it is concluded that velocity substructure exists on these scales. At larger scales velocity substructure is not found. We suggest that bound substructures exist on scales of ∼0.5 pc, despite the region as a whole being unbound. We further suggest that any velocity substructure that existed on scales > 0.5  pc has been erased. The results of this study are then compared to those of other kinematic studies of Cygnus OB2.