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, $Σ_{\rm LDR}$, and we compare the global spatial distributions using the $Λ_{\rm MSR}$ method. From a suite of twenty initially statistically identical simulations, 6/20 attain $\mathcal{R}_{\rm SSR} << 1$ $and$ $Σ_{\rm LDR} << 1$ $and$ $Λ_{\rm MSR} << 1$, 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 ($Σ_{\rm LDR} << 1$), but their global spatial distributions are indistinguishable ($Λ_{\rm MSR} = 1$) 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.

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