Efficiencies of low-mass star and star cluster formation

Using a quantitative model for bipolar outflows driven by hydromagnetic pro tostellar winds, we calculate the efficiency of star formation assuming tha t available gas is either converted into stars or ejected in outflows. We e stimate the efficiency of a single star formation event in a protostellar c ore, finding 25%-70% for cores with various possible degrees of flattening. The core mass function and the stellar initial mass function have similar slopes because the efficiency is not sensitive to its parameters. We then c onsider the disruption of gas from a dense molecular clump in which a clust er of young stars is being born. In both cases, we present analytical formu lae for the efficiencies that compare favorably against observations and, f or clusters, against numerical simulations. We predict efficiencies in the range of 30%-50% for the regions that form clusters of low-mass stars. In o ur model, star formation and gas dispersal happen concurrently. We neglect the destructive effects of massive stars : our results are therefore upper limits to the efficiency in regions more massive than about 3000 M-..