The origin of the Gaussian initial mass function of old globular cluster systems

Abstract

Evidence favouring a Gaussian initial mass function for systems of old globular clusters 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 ε. Assuming that ε 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. Assuming instantaneous gas removal and a slope α≃−1.7 for the cloud mass spectrum, we evolve the derived cluster initial mass functions up to an age of 13 Gyr in a potential like that of the Milky Way. We obtain a good match to the Old Halo cluster mass function, with a present-day mass fraction of clusters in the halo of 2 per cent, as is observed, with mlow≃ 6 × 105 M⊙, mup≥ 5 × 106 M⊙, δ≃−2.9 and rc≃ 0.025, respectively, the lower and upper limits of the cloud mass range, the slope and the core of the power-law spectrum for the star formation efficiency. The steep slope δ means that most protoglobular clouds achieve too low a star formation efficiency to give rise to bound star clusters following gas removal. As a result, most newly formed stars are scattered into the field soon after their formation. Gas removal during star formation in massive clouds is thus likely the prime cause of the predominance of field stars in the Galactic halo. The shape of the present-day cluster mass function depends weakly on the underlying distribution of the star formation efficiency. Finally, we show that a Gaussian mass function for the protoglobular clouds with a mean log mG≃ 6.1–6.2 and an s.d. σ≲ 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.