Efficiencies of Low-Mass Star and Star Cluster Formation

Using a quantitative model for bipolar outflows driven by hydromagnetic protostellar winds, we calculate the efficiency of star formation assuming that available gas is either converted into stars or ejected in outflows. We estimate the efficiency of a single star formation event in a protostellar core, 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 consider the disruption of gas from a dense molecular clump in which a cluster of young stars is being born. In both cases, we present analytical formulae for the efficiencies that compare favorably against observations and, for clusters, against numerical simulations. We predict efficiencies in the range 30%-50% for the regions that form clusters of low-mass stars. In our 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 Msun.