Stars mostly form in groups consisting of a few dozen to several ten thousand members. For 30 years, theoretical models provide a basic concept of how such star clusters form and develop: they originate from the gas and dust of collapsing molecular c
louds. The conversion from gas to stars being incomplete, the left over gas is expelled, leading to cluster expansion and stars becoming unbound. Observationally, a direct confirmation of this process has proved elusive, which is attributed to the diversity of the properties of forming clusters. Here we take into account that the true cluster masses and sizes are masked, initially by the surface density of the background and later by the still present unbound stars. Based on the recent observational finding that in a given star-forming region the star formation efficiency depends on the local density of the gas, we use an analytical approach combined with mbox{N-body simulations, to reveal} evolutionary tracks for young massive clusters covering the first 10 Myr. Just like the Hertzsprung-Russell diagram is a measure for the evolution of stars, these tracks provide equivalent information for clusters. Like stars, massive clusters form and develop faster than their lower-mass counterparts, explaining why so few massive cluster progenitors are found.
Direct N-body calculations are presented of the early evolution of exposed clusters to quantify the influence of gas expulsion on the time-varying surface brightness. By assuming that the embedded OB stars drive out most of the gas after a given time
delay, the change of the surface brightness of expanding star clusters is studied. The influence of stellar dynamics and stellar evolution is discussed. The growth of the core radii of such models shows a remarkable core re-virialisation. The decrease of the surface mass density during gas expulsion is large and is only truncated by this re-virialisation process. However, the surface brightness within a certain radius does not increase noticeably. Thus, an embedded star cluster cannot reappear in observational surveys after re-virialisation. This finding has a bearing on the observed infant mortality fraction.
We investigate the impact of the star formation efficiency in cluster forming cores 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. Assuming a constant fo
rmation 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 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. We describe model aspects which are still to be worked out before achieving this goal.
We explore how the expulsion of gas from star-cluster forming cloud-cores due to supernova explosions affects the shape of the initial cluster mass function, that is, the mass function of star clusters when effects of gas expulsion are over. We demon
strate that if the radii of cluster-forming gas cores are roughly constant over the core mass range, as supported by observations, then more massive cores undergo slower gas expulsion. Therefore, for a given star formation efficiency, more massive cores retain a larger fraction of stars after gas expulsion. The initial cluster mass function may thus differ from the core mass function substantially, with the final shape depending on the star formation efficiency. A mass-independent star formation efficiency of about 20 per cent turns a power-law core mass function into a bell-shaped initial cluster mass function, while mass-independent efficiencies of order 40 per cent preserve the shape of the core mass function.
We present new results on the evolution of the mass function of the globular cluster system of the Milky Way, taking the effect of residual gas expulsion into account. We assume that gas embedded star clusters start with a power-law mass function wit
h slope beta=2. The dissolution of the clusters is then studied under the combined influence of residual gas expulsion driven by energy feedback from massive stars, stellar mass-loss, two-body relaxation and an external tidal field. The influence of residual gas expulsion is studied by applying results from a large grid of N-body simulations computed by Baumgardt & Kroupa (2007). In our model, star clusters with masses less than 10^5 M_sun lose their residual gas on timescales much shorter than their crossing time and residual gas expulsion is the main dissolution mechanism for star clusters, destroying about 95% of all clusters within a few 10s of Myr. We find that in this case the final mass function of globular clusters is established mainly by the gas expulsion and therefore nearly independent of the strength of the external tidal field, and that a power-law mass function for the gas embedded star clusters is turned into a present-day log-normal one. Another consequence of residual gas expulsion and the associated strong infant mortality of star clusters is that the Galactic halo stars come from dissolved star clusters. Since field halo stars would come mainly from low-mass, short-lived clusters, our model provides an explanation for the observed abundance variations of light elements among globular cluster stars and the absence of such variations among the halo field stars.
