Do All Stars in the Solar Neighbourhood Form in Clusters?

We present a global study of low mass, young stellar object (YSO) surface densities (Sigma) in nearby (<500 pc) star forming regions based on a comprehensive collection of Spitzer Space Telescope surveys. We show that the distribution of YSO surface densities is a smooth distribution, being adequately described by a lognormal function from a few to 10(3) YSOs per pc(2), with a peak at similar to 22 stars pc(-2). The observed lognormal Sigma is consistent with predictions of hierarchically structured star-formation at scales below 10 pc, arising from the molecular cloud structures. We do not find evidence for multiple discrete modes of star-formation (e.g. clustered and distributed). Comparing the observed Sigma distribution to previous Sigma threshold definitions of clusters show that they are arbitrary. We find that only a low fraction (<26%) of stars are formed in dense environments where their formation/evolution (along with their circumstellar disks and/or planets) may be affected by the close proximity of their low-mass neighbours.