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 \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 .
Assuming instantaneous gas removal and a slope \alpha \simeq - 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 mass fraction of clusters in the halo of 2 \% , as is observed , with m _ { low } \simeq 6 \times 10 ^ { 5 } { M } _ { \odot } , m _ { up } \geq 5 \times 10 ^ { 6 } { M } _ { \odot } , \delta \simeq - 2.9 and r _ { c } \simeq 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 \delta 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 } 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 .