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 clustermass function, that is, themass function of star clusterswhen effects of gas expulsion are over. We demonstrate that if the radii of cluster-forming gas cores are roughly constant over the coremass range, as supported by observations, then more massive cores undergo slower gas expulsion. Therefore, for a given star formation efficiency, moremassive cores retain a larger fraction of stars after gas expulsion. The initial cluster mass functionmay thus differ from the coremass function substantially, with the final shape depending on the star formation efficiency. Amassindependent star formation efficiency of 20% turns a power-law core mass function into a bell-shaped initial cluster mass function, while mass-independent efficiencies of order 40% preserve the shape of the core mass function. Subject headinggs: galaxies: star clusters — stars: formation — stellar dynamics