The impact of mass loss on star cluster formation - I. Analytical results

We study analytically the disruptive effect of instantaneous gas removal from a cluster containing O stars. We set up an iterative calculation based on the stellar velocity distribution function to compute the fraction of stars that remain bound once the cluster has ejected the gas and is out of equilibrium. We show that the stellar bound fraction is a function of the initial cluster distribution function as well as the star-formation efficiency, e, taken constant throughout the cluster. The case of the Plummer sphere is dealt with in greater detail, where we find that up to ≃50 per cent of the stars may remain bound when e assumes values <1/2, contrary to expectations derived from the virial theorem. The fraction of bound stars is expressed algebraically for polytropic distribution functions.