The formation of multiples in small-<i>N</i> subclusters

ABSTRACT 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 $\mu _{_{N}}\sim 4.8$ and standard deviation $\sigma _{_N}\sim 2.4$. This fit is obtained when $\sim 50~{{\ \rm per\ cent}}$ of the subcluster’s internal kinetic energy is invested in ordered rotation and $\sim 50~{{\ \rm per\ cent}}$ 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. $N\!=\!1\,\,{\rm or}\,\,2$), very similar values ($N\!=\!4.3\pm 0.4$ and $N\!=\!4.5\pm 1.9$) have been derived previously by completely independent routes, and seem inescapable when the observed distribution of multiplicities is taken into account.