Spatial differences between stars and brown dwarfs: a dynamical origin?

We use $N$-body simulations to compare the evolution of spatial distributions of stars and brown dwarfs in young star-forming regions. We use three different diagnostics; the ratio of stars to brown dwarfs as a function of distance from the region's centre, $\mathcal{R}_{\rm SSR}$, the local surface density of stars compared to brown dwarfs, $\Sigma_{\rm LDR}$, and we compare the global spatial distributions using the $\Lambda_{\rm MSR}$ method. From a suite of twenty initially statistically identical simulations, 6/20 attain $\mathcal{R}_{\rm SSR} << 1$ $and$ $\Sigma_{\rm LDR} << 1$ $and$ $\Lambda_{\rm MSR} << 1$, indicating that dynamical interactions could be responsible for observed differences in the spatial distributions of stars and brown dwarfs in star-forming regions. However, many simulations also display apparently contradictory results - for example, in some cases the brown dwarfs have much lower local densities than stars ($\Sigma_{\rm LDR} << 1$), but their global spatial distributions are indistinguishable ($\Lambda_{\rm MSR} = 1$) and the relative proportion of stars and brown dwarfs remains constant across the region ($\mathcal{R}_{\rm SSR} = 1$). Our results suggest that extreme caution should be exercised when interpreting any observed difference in the spatial distribution of stars and brown dwarfs, and that a much larger observational sample of regions/clusters (with complete mass functions) is necessary to investigate whether or not brown dwarfs form through similar mechanisms to stars.