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Globular cluster stars show chemical abundance patterns typical of hot‐CNO processing, and photometric evidence for the presence of multiple populations. Lithium is easily destroyed by proton capture in stellar environments, so determining its abundance may be crucial to discriminate among different models proposed to account for the origin of the gas from which the multiple populations form. In order to reproduce the observed O–Na anticorrelation and other patterns typical of multiple populations, the formation of second‐generation stars must occur from the nuclearly processed stellar ejecta, responsible for the chemical anomalies,  diluted  with pristine gas having the composition of first‐generation stars. This gas is a remnant of the first phases of star formation, or it has been re‐accreted on the cluster core after the end of the Type II supernova explosions. As a consequence, the lithium abundance in the unprocessed gas – which is very likely to be equal to the lithium abundance emerging from the big bang – affects the lithium chemical patterns among the cluster stars. This paper focuses on a scenario in which processed gas is provided by asymptotic giant branch (AGB) stars. We examine the predictions of this scenario for the lithium abundances of multiple populations. We study the role of the non‐negligible lithium abundance in the ejecta of massive AGB stars [   A  (   Li   )  ∼   2], and, at the same time, we explore how our models can constrain the extremely large – and very model dependent – lithium yields predicted by recent super‐AGB models. We show that the super‐AGB yields may be tested by examining the lithium abundances in a large set of blue main‐sequence stars in ω Cen and/or NGC 2808. In addition, we examine the different model results obtained by assuming for the pristine gas either the big bang abundance predicted by the standard models [   A  (   Li   )  =  2.6  --  2.7   ] or the abundance detected at the surface of Population II stars [   A  (   Li   )  =  2.2  --  2.3   ], and we show that, once a chemical model is well constrained by a comparison with the observations, the O–Li distribution could perhaps be used to shed light on the primordial lithium abundance.

Models for the lithium abundances of multiple populations in globular clusters and the possible role of the big bang lithium