The spatial distribution of star formation in the solar neighbourhood: do all stars form in dense 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 in the solar neighbourhood is a smooth distribution, being adequately described by a lognormal function from a few to 10(3) YSOs pc(-2), with a peak at similar to 22 stars pc(-2) and a dispersion of sigma(log10) (Sigma) similar to 0.85. We do not find evidence for multiple discrete modes of star formation (e. g. clustered and distributed). Comparing the observed surface density distribution to previously reported surface density threshold definitions of clusters, we find that the fraction of stars in clusters is crucially dependent on the adopted definitions, ranging from 40 to 90 per cent. However, we find that only a low fraction (< 26 per cent) of stars are formed in dense environments where their formation/evolution (along with their circumstellar discs and/or planets) may be affected by the close proximity of their low-mass neighbours.