Stellar feedback in molecular clouds and its influence on the mass function of young star clusters

We investigate how the removal of interstellar material by stellar feedback limits the efficiency of star formation in molecular clouds and how this determines the shape of the mass function of young star clusters. In particular, we derive relations between the power-law exponents of the mass functions of the clouds and clusters in the limiting regimes in which the feedback is energy driven and momentum driven, corresponding to minimum and maximum radiative losses, and likely to bracket all realistic cases. We find good agreement between the predicted and observed exponents, especially for momentum-driven feedback, provided the protoclusters have roughly constant mean surface density, as indicated by observations of the star-forming clumps within molecular clouds. We also consider a variety of specific feedback mechanisms, concluding that H II regions inflated by radiation pressure predominate in massive protoclusters, a momentum-limited process when photons can escape after only a few interactions with dust grains. We show in this case that the star formation efficiency depends on the masses and sizes of the protoclusters only through their mean surface density, thus ensuring consistency between the observed exponents of the mass functions of the clouds and clusters. Our numerical estimate of this efficiency is also consistent with observations.