Orbital statistics of multiple systems formed from small-$N$ subclusters

We use numerical $N$-body experiments to explore the statistics of multiple systems formed in small-$N$ subclusters, i.e. the distributions of orbital semi-major axis, $a$, orbital eccentricity, $e$, mass ratio, $q$, mutual orbital inclination, $\theta$, and ejection velocity, $\upsilon_{\rm ej}$. The stars in a subcluster are evolved as if they are the fragmentation products of a single isolated prestellar core from which most of the natal gas has already been dispersed, and there are no correlations between the stars' initial positions and velocities. Two parameters are particularly important: the number of stars in the subcluster, $N$, and the fraction of kinetic energy in ordered rotation, $\alpha_{\rm rot}$. Increasing $N$ has the effect of systematically decreasing the semi-major axes of the tighter orbits, but has very little effect on the semi-major axes of the wider orbits. The main effect of $\alpha_{\rm rot}$ is to regulate the distribution of mutual orbital inclinations, with $\alpha_{\rm rot}\!\sim\!0.5$ producing a distribution of orbital inclinations for triple systems which is consistent with observed values. Triples frequently form in high-inclination orbits without the assistance of von Zeipel-Lidov-Kozai cycles. Our previous work demonstrated that subclusters with mass segregation, moderate rotation, and typically $N=4$ or 5 stars produced the best fit to the multiplicity statistics (proportions of singles, binaries, triples, etc.). Here we show that these parameters also reproduce the orbital statistics (distributions of orbital semi-major axis, $a$, orbital eccentricity, $e$, mass ratio, $q$, mutual orbital inclination, $\theta$, and ejection velocity, $\upsilon_{\rm ej}$). For the best-fit parameters, $21(\pm 1)\%$ of subclusters produce more than one multiple system.