The formation of multiples in small-$N$ subclusters

We explore the relative percentages of binary systems and higher-order multiples that are formed by pure stellar dynamics, within a small subcluster of $N$ stars. The subcluster is intended to represent the fragmentation products of a single isolated core, after most of the residual gas of the natal core has dispersed. Initially the stars have random positions, and masses drawn from a log-normal distribution. For low-mass cores spawning multiple systems with Sun-like primaries, the best fit to the observed percentages of singles, binaries, triples and higher-order systems is obtained if a typical core spawns on average between $N=$ 4.3 and 5.2 stars, specifically a distribution of $N$ with mean $\mu_{_{N}}\sim4.8$ and standard deviation $\sigma_{_N}\sim2.4$. This fit is obtained when $\sim 50\%$ of the subcluster's internal kinetic energy is invested in ordered rotation and $\sim 50\%$ in isotropic Maxwellian velocities. There is little dependence on other factors, for example mass segregation or the rotation law. Whilst such high values of $N$ are at variance with the lower values often quoted (i.e. $N=$ 1 or 2), very similar values ($N=4.3\pm0.4$ and $N=4.5\pm1.9$) have been derived previously by completely independent routes, and seem inescapable when the observed distribution of multiplicities is taken into account.