The puzzle of metallicity and multiple stellar populations in the globular clusters in Fornax

All models for the formation of multiple populations in globular clusters (GCs) imply an initial mass of the systems several times greater than the present mass. A recent study of the dwarf spheroidal galaxy Fornax, where the low-metallicity ([Fe/H] less than or similar to -2) stars contained in GCs appear to account for similar to 20 per cent of the total number, seems to constrain the initial mass of the four low-metallicity GCs in Fornax to be at most a factor of 5-6 greater than their present mass. We examine the photometric data for Fornax clusters, focusing our attention on their horizontal branch (HB) colour distribution and, when available, on the fraction and period distribution of RR Lyrae variables. Based on our understanding of the HB morphology in terms of varying helium content (and red giant mass-loss rate) in the context of multiple stellar generations, we show that the clusters F2, F3 and F5 must contain substantial fractions of second-generation stars (similar to 54-65 per cent). On the basis of a simple chemical evolution model we show that the helium distribution in these clusters can be reproduced by models with cluster initial masses ranging from values equal to similar to 4 to similar to 10 times greater than the current masses. Models with a very short second-generation star formation episode can also reproduce the observed helium distribution but require greater initial masses up to about 20 times the current mass. While the lower limit of this range of possible initial GC masses is consistent with those suggested by observations of the low-metallicity field stars, we also discuss the possibility that the metallicity scale of field stars (based on Ca ii triplet spectroscopy) and the metallicities derived for the clusters in Fornax may not be consistent with each other. In this case, observational constraints would allow greater initial cluster masses. Two interesting hypotheses are needed in order to reproduce the HB morphology of the clusters F2, F3 and F5. (i) The first-generation HB stars all lie at 'red' colours; that is, they populate only the RR Lyraes and the red HB region. According to this interpretation, the low-metallicity stars in the field of Fornax, populating the HB at colours bluer than the blue side [(V - I)(0) less than or similar to 0.3 or (B - V)(0) less than or similar to 0.2] of the RR Lyraes, should be second-generation stars born in the clusters. A preliminary analysis of available colour surveys of Fornax field provides a fraction similar to 20 per cent of blue HB stars, in the low-metallicity range. (ii) The mass loss from individual second-generation red giants is a few per cent of a solar mass larger than the mass loss from first-generation stars.