On the spatial distributions of stars and gas in numerical simulations of molecular clouds

We compare the spatial distribution of stars which form in hydrodynamical simulations to the spatial distribution of the gas, using the $\mathcal{Q}$-parameter. The $\mathcal{Q}$-parameter enables a self-consistent comparison between the stars and gas because it uses a pixelated image of the gas as a distribution of points, in the same way that the stars (sink particles in the simulations) are a distribution of points. We find that, whereas the stars have a substructured, or hierarchical spatial distribution ($\mathcal{Q} \sim 0.4 - 0.7$), the gas is dominated by a smooth, concentrated component and typically has $\mathcal{Q} \sim 0.9$. We also find no statistical difference between the structure of the gas in simulations that form with feedback, and those that form without, despite these two processes producing visually different distributions. These results suggest that the link between the spatial distributions of gas, and the stars which form from them, is non-trivial.