We examine various implications from a dynamical and chemical model of globular clusters (GCs), which successfully reproduces the observed abundance patterns and the multiple populations of stars in these systems assuming chemical enrichment from fast rotating massive stars. Using the model of Decressin et al. (2007) we determine the ratio between the observed, present-day mass of globular clusters and their initial stellar mass as a function of the stellar initial mass function (IMF). We also compute the mass of low-mass stars ejected, and the amount of hydrogen ionising photons emitted by the proto globular clusters. Typically, we find that the initial masses of GCs must be ~8-10 times (or up to 25 times, if second generation stars also escape from GCs) larger than the present-day stellar mass. The present-day Galactic GC population must then have contributed to approximately 5-8% (10-20%) of the low-mass stars in the Galactic halo. We also show that the detection of second generation stars in the Galactic halo, recently announced by different groups, provides a new constraint on the GC initial mass function (GCIMF). These observations appear to rule out a power-law GCIMF, whereas they are compatible with a log-normal one. Finally, the high initial masses also imply that GCs must have emitted a large amount of ionising photons in the early Universe. Our results reopen the question on the initial mass function of GCs, and reinforce earlier conclusions that old GCs could have represented a significant contribution to reionise the inter-galactic medium at high redshift.
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