When Efficient Star Formation Drives Cluster Formation

We investigate the impact of the star formation efficiency in cluster-forming-cores (i.e. local SFE) on the evolution of the mass in star clusters over the age range 1-100Myr, when star clusters undergo their infant weight-loss/mortality phase. Our model builds on the N -body simulation grid of Baumgardt & Kroupa (2007). Assuming a constant formation rate of gas-embedded clusters and a weak tidal field, we show that the ratio between the total mass in stars bound to the clusters over that age range and the total mass in stars initially formed in gas-embedded clusters is a strongly increasing function of the averaged local SFE, with little influence from any assumed core mass-radius relation. Our results suggest that, for young starbursts with estimated tidal field strength and known recent star formation history, observed cluster-to-star mass ratios, once corrected for the undetected clusters, constitute promising probes of the local SFE, without the need of resorting to gas mass estimates. Similarly, the mass ratio of stars which remain in bound clusters at the end of the infant mortality/weight-loss phase (i.e. age & 50Myr) depends sensitively on the mean local SFE, although the impacts of the width of the SFE distribution function and of the core mass-radius relation require more careful assessment in this case. Following the recent finding by Bastian (2008) that galaxies form, on the average, 8% of their stars in bound clusters regardless of their star formation rate, we raise the hypothesis that star formation in the present-day Universe is characterized by a near-universal distribution for the local SFE. A related potential application of our model consists in tracing the evolution of the local SFE over cosmological lookback times by comparing the age distribution of the total mass in star clusters to that in field stars in galaxies where field stars can be resolved and age-dated. We describe model aspects which are still to be worked out before achieving this goal. Subject headings: galaxies: star clusters — galaxies: evolution — galaxies: starburst — stars: formation — stellar dynamics