The Origin of the Gaussian Initial Mass Function of Old Globular Cluster Systems

[Abridged] Evidence favouring a Gaussian initial globular cluster mass function has accumulated over recent years. We show that an approximately Gaussian mass function is naturally generated from a power-law mass distribution of protoglobular clouds by expulsion from the protocluster of star forming gas due to supernova activity, provided that the power-law mass distribution shows a lower-mass limit. As a result of gas loss, the gravitational potential of the protocluster gets weaker and only a fraction of the newly formed stars is retained. The mass fraction of bound stars ranges from zero to unity, depending on the local star formation efficiency $\epsilon$. Assuming that $\epsilon$ is independent of the protoglobular cloud mass, we investigate how such variations affect the mapping of a protoglobular cloud mass function to the resulting globular cluster initial mass function. A truncated power-law cloud mass spectrum generates bell-shaped cluster initial mass functions, with a turnover location mostly sensitive to the lower limit of the cloud mass range. We also show that a Gaussian mass function for the protoglobular clouds with a mean ${\rm log}m_G \simeq 6.1-6.2$ and a standard deviation $\sigma \lesssim 0.4$ provides results very similar to those resulting from a truncated power-law cloud mass spectrum, that is, the distribution function of masses of protoglobular clouds influences only weakly the shape of the resulting globular star cluster initial mass function. The gas removal process and the protoglobular cloud mass-scale dominate the relevant physics. Moreover, gas removal during star formation in massive clouds is likely the prime cause of the predominance of field stars in the Galactic halo.