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tokens: distribution. 3 In reality, the whole structure moves on the same short dynamical time-scale of equation ( 1 ) and hence the effective surface density is much reduced if the system as a whole begins to re-expand. We suspected that the choice of fixed initial density may be the reason for the undetectable shift of the peak on Fig. 8 . Our choice of initial conditions implies that the system size R o M 1/3 ; had we chose instead to use an empirical relation such as R o M 1/5 for stellar clusters (Larsen 2004 ), we would have found a scaling of E s / E s a 3 N 7/5 . The same rise in N as before would have produced a shift from 40 to 6.5au in the peak of the distribution, and this is still too large to go undetected. 5 EXTREME TIGHT AND WIDE BINARIES As mentioned in Section 3.2 , Bate ( 2012 ) has found several examples of binaries reducing their separation over time through stellar encounters, from 10au down to 0.5au. Tighter systems were hindered by numerical resolution issues. The regularized treatment of close encounters (which allows us to integrate up to machine precision) of the code nbody 6 means that the same collisional process will be at play in the calculations that we have performed. Since no binaries with semimajor axis a shorter than 1au were inserted in the initial conditions, we focus first on the statistics of binaries that evolved to a 1au. In the second part of this section, we will explore the formation and the evolution of very wide ( a 10 4 au) binaries, many of which end up loosely bound to the stellar cluster as a whole. 5.1 Tight binaries Several binaries with a 1au were detected at the end of the low-density simulations. By comparison, almost none developed in the high-density runs. Their properties are summarized in the left-hand panel of Fig. 10 . The data are taken from N 20k runs but similar statistics were obtained for the other setups. The top row shows the binarys mass as a function of semimajor axis, while the bottom row on that figure graphs the distance of their barycentre to the centre of the cluster. Open circles denote binaries that already existed at t = 0, and became tighter over time, while filled circles are new binaries that formed in the course of the simulation. Inspection of these new, tight binaries shows that both of their components were part of binaries originally inserted in the system. Thus all new tight binaries shown on Fig. 10 are the results of strong binarybinary interactions leading to splitting or exchange. (None of the original binaries that survived to the end of the simulation had a 1/2au.) Figure 10. Left-hand panels: total binary mass (top) and distance to centre of the cluster (bottom) versus the semimajor axis for binaries tighter than 1au at the end of the simulation. Right-hand panels: same layout for binaries wider than 10 4 au. The greyed area in the top panels shows the 90percent probability range of a binary total mass from random pairing given the present IMF. The red