Variations in stellar clustering with environment: Dispersed star formation and the origin of faint fuzzies

The observed increase in star formation efficiency with average cloud density, from several percent in whole giant molecular clouds to similar to 30% or more in cluster-forming cores, can be understood as the result of hierarchical cloud structure if there is a characteristic density at which individual stars become well defined. Also in this case, the efficiency of star formation increases with the dispersion of the density probability distribution function (PDF). Models with lognormal PDFs illustrate these effects. The difference between star formation in bound clusters and star formation in loose groupings is attributed to a difference in cloud pressure, with higher pressures forming more tightly bound clusters. This correlation accounts for the observed increase in the clustering fraction with star formation rate and with the observation of scaled OB associations in low-pressure environments. Faint fuzzie'' star clusters, which are bound but have low densities, can form in regions with high Mach numbers and low background tidal forces. The proposal by Burkert, Brodie & Larsen that faint fuzzies form at large radii in galactic collisional rings satisfies these constraints.