When efficient star formation drives cluster formation

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 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 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.

The shape of the initial cluster mass function: what it tells us about the local star formation efficiency

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 demonstrate 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.

The poorly constrained cluster disruption time-scale in the Large Magellanic Cloud

We use Monte-Carlo simulations, combined with homogeneously determined age and mass distributions based on multi-wavelength photometry, to constrain the cluster formation history and the rate of bound cluster disruption in the Large Magellanic Cloud (LMC) cluster system. We evolve synthetic star cluster systems formed with a power-law initial cluster mass function (ICMF) of spectral index $alpha =-2$ assuming different cluster disruption time-scales. For each of these disruption time-scales we derive the corresponding cluster formation rate (CFR) required to reproduce the observed cluster age distribution. We then compare, in a Poissonian $chi^2$ sense, model mass distributions and model two-dimensional distributions in log(mass) vs. log(age) space of the detected surviving clusters to the observations. Because of the bright detection limit ($M_V^{rm lim} simeq -4.7$ mag) above which the observed cluster sample is complete, one cannot constrain the characteristic disruption time-scale for a $10^4$ M$_odot$ cluster, $t_4^{rm dis}$ (where the disruption time-scale depends on cluster mass as $t_{rm dis} = t_4^{rm dis} (M_{rm cl} / 10^4 {rm M}_odot)^0.62$), to better than $t_4^{rm dis} ge 1$ Gyr. We conclude that the CFR has increased from 0.3 clusters Myr$^{-1}$ 5 Gyr ago, to a present rate of $(20-30)$ clusters Myr$^{-1}$. For older ages the derived CFR depends sensitively on our assumption of the underlying CMF shape. If we assume a universal Gaussian ICMF, then the CFR has increased steadily over a Hubble time from $sim 1$ cluster Gyr$^{-1}$ 15 Gyr ago to its present value. If the ICMF has always been a power law with a slope close to $alpha=-2$, the CFR exhibits a minimum some 5 Gyr ago, which we tentatively identify with the well-known age gap in the LMCs cluster age distribution.