On the formation rate of galactic clusters in clouds of various masses

Abstract

The formation rate of galactic clusters is estimated to be 2.5 +- 1 x 10/sup -7/ kpc/sup -2/ yr/sup -1/ from published tables of cluster positions and ages. OB associations form at about the same rate, so most clusters could form in giant molecular clouds, along with the associations. This result leads to a serious problem with the fate of star formation in low-mass clouds. The space density of low-mass clouds is so high, and the cluster formation rate is so low, that low-mass clouds must seldom form bound clusters even though they have enough mass to do so. The formation of a cluster depends on the efficiency of star formation in the cloud, and this efficiency depends on the relative mass of stars that have formed by the time a sufficiently luminous star destroys the cloud. Thus the formation of a bound cluster depends on the formation order of stars of various masses. We assume that this formation order is random and estimate the cluster formation probability for clouds of various masses with Monte Carlo simulations. Critical efficiencies for bound cluster formation are also calculated, including cloud support from magnetic fields. The results suggest that at least 10% ofmore » low-mass clouds should form bound clusters. Consequently, either the cluster formation time per low-mass cloud exceeds 10/sup 8/ yr, or such clouds avoid forming clusters even when their star formation efficiencies are high. If the formation order of stars is not random, but high-mass stars form after low-mass stars, then the probability of forming a bound cluster, and the mean formation time per low-mass cloud, are even larger. Implications of these results are discussed; in particular, the observed cluster luminosity function can be reproduced by the model.« less