A pressure dependence for bound and unbound clusters

Abstract

Hierarchical structure in gas and young stars produces clusters in high-density regions where the individual stellar orbits rapidly mix. For a fixed density at the onset of gas collapse (e.g. determined by changes in the ionization equilibrium and grain properties), the efficiency of star formation is automatically high in the high-density regions of giant molecular clouds. Thus, bound cluster formation follows somewhat trivially from hierarchical structure. The density where the efficiency is high enough to produce a bound cluster depends on the dispersion of the density probability distribution function (pdf), decreasing for higher dispersions and making bound cluster formation more likely. Similarly, the mass fraction of star formation in the form of bound clusters increases with the pdf dispersion. Because this dispersion is related to the turbulent Mach number, and also to the interstellar medium pressure and star-formation rate per unit volume, it follows that high-pressure or highly active regions tend to produce bound clusters, while low-pressure and inactive regions tend to produce stars in unbound associations.