Modes of clustered star formation

Context. The recent realization that most stars form in clusters, immediately raises the question of whether star and planet formation are influenced by the cluster environment. The stellar density in the most prevalent clusters is the key factor here. Whether dominant modes of clustered star formation exist is a fundamental question. Using near-neighbour searches in young clusters, Bressert and collaborators claim this not to be the case. They conclude that - at least in the solar neighbourhood - star formation is continuous from isolated to densely clustered environments and that the environment plays a minor role in star and planet formation. Aims. We investigate under which conditions near-neighbour searches in young clusters can distinguish between different modes of clustered star formation. Methods. Model star clusters with different memberships and density distributions are set up and near-neighbour searches are performed. We investigate the influence of the combination of different cluster modes, observational biases, and types of diagnostic on the results. Results. We find that the specific cluster density profile, the relative sample sizes, the limitations of the observation, and the choice of diagnostic method decide, whether modelled modes of clustered star formation are detected by near-neighbour searches. For density distributions that are centrally concentrated but span a wide density range (for example, King profiles), separate cluster modes are only detectable under ideal conditions (sample selection, completeness) if the mean density of the individual clusters differs by at least a factor of similar to 65. Introducing a central cut-off can lead to an underestimate of the mean density by more than a factor of ten especially in high density regions. The environmental effect on star and planet formation is similarly underestimated for half of the population in dense systems. Conclusions. Local surface-density distributions are a very useful tool for single cluster analyses, but only for high-resolution data. However, in a simultaneous analysis of a sample of cluster environments, it is found that effects of superposition suppress characteristic features very efficiently and thus promote erroneous conclusions. While multiple peaks in the distribution of the local surface density in star forming regions imply the existence of different modes of star formation, the converse conclusion is impossible. Equally, a smooth distribution is no proof of continuous star formation, because such a shape can easily hide modes of clustered star formation.