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 lognormal 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)similar to 4.8 and standard deviation sigma(N)similar to 2.4. This fit is obtained when similar to 50 per cent of the subcluster's internal kinetic energy is invested in ordered rotation and similar to 50 per cent in isotropic Maxwellian velocities. There is little dependence on other factors, for example mass segregation or the rotation law. While such high values of N are at variance with the lower values often quoted (i.e. N=1or2), very similar values (N=4.3 +/- 0.4 and N=4.5 +/- 1.9) have been derived previously by completely independent routes, and seem inescapable when the observed distribution of multiplicities is taken into account.