On the mass function of star clusters

Clusters that form in total 10(3) less than or similar to N less than or similar to 10(5) stars (type II clusters) lose their gas within a dynamical time as a result of the photoionizing flux from O stars. Sparser (type I) clusters get rid of their residual gas on a time-scale longer or comparable to the nominal crossing time and thus evolve approximately adiabatically. This is also true for massive embedded clusters (type III) for which the velocity dispersion is larger than the sound speed of the ionized gas. On expelling their residual gas, type I and III clusters are therefore expected to lose a smaller fraction of their stellar component than type II clusters. We outline the effect this has on the transformation of the mass function of embedded clusters (ECMF), which is directly related to the mass function of star cluster-forming molecular cloud cores, to the 'initial' MF of bound gas-free star clusters (ICMF). The resulting ICMF has, for a featureless power-law ECMF, a turnover near 10(4.5) M-. and a peak near 10(3) M-.. The peak lies close to the initial masses of the Hyades, Praesepe and Pleiades clusters. We also find that the entire Galactic population II stellar spheroid can be generated if star formation proceeded via embedded clusters distributed like a power-law MF with exponent 0.9 less than or similar to beta less than or similar to 2.6.