The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters - V. Constraints on formation scenarios

We build on the evidence provided by our Legacy Survey of Galactic globular clusters (GC) to submit to a crucial test four scenarios currently entertained for the formation of multiple stellar generations in GCs. The observational constraints on multiple generations to be fulfilled are manifold, including GC specificity, ubiquity, variety, predominance, discreteness, supernova avoidance, p-capture processing, helium enrichment and mass budget.We argue that scenarios appealing to supermassive stars, fast rotating massive stars and massive interactive binaries violate in an irreparable fashion two or more among such constraints. Also the scenario appealing to asymptotic giant branch (AGB) stars as producers of the material for next generation stars encounters severe difficulties, specifically concerning the mass budget problem and the detailed chemical composition of second-generation stars.We qualitatively explore ways possibly allowing one to save the AGB scenario, specifically appealing to a possible revision of the cross-section of a critical reaction rate destroying sodium, or alternatively by a more extensive exploration of the vast parameter space controlling the evolutionary behaviour of AGB stellar models. Still, we cannot ensure success for these efforts and totally new scenarios may have to be invented to understand how GCs formed in the early Universe.