On the self-enrichment scenario of galactic globular clusters: constraints on the IMF

Aims. Galactic globular cluster (GC) stars exhibit abundance patterns that are not shared by their field counterparts, e. g. the well-documented O-Na and Mg-Al anticorrelations. Recent spectroscopic observations of GC turnoff stars have provided compelling evidence that these abundance anomalies were already present in the gas from which the observed stars formed. A widely held hypothesis is that the gas was polluted by stars that were more massive (and evolving faster) than the presently observed low-mass stars. In the framework of this self-enrichment scenario for GCs, we present a new method of deriving the initial mass function (IMF) of the polluters, by using the O/Na abundance distribution. Methods. We focus on NGC 2808, a GC for which the largest sample of O and Na abundance determinations is presently available. We use the abundance distribution of [O/Na] to derive the amount of polluted material with respect to the original composition. We explore two scenarios in detail for the self-enrichment of the cluster, which differ by the assumptions made on the composition of the polluter ejecta. In each case we consider two classes of possible culprits: massive asymptotic giant branch (AGB) stars (4-9 M-circle dot) and winds of massive stars (WMS) in the mass range 10-100 M-circle dot. Results. We obtain upper limits for the slope of the IMF (assumed to be given by a power-law) of the stars initially more massive than the present turnoff mass. We also derive lower limits for the amount of stellar residues in NGC 2808. Conclusions. We find that the polluter IMF had to be much flatter than the presently observed IMFs in stellar clusters, which agrees with the results of two other GC IMF determination methods, which we also discuss. Likewise, we find that the present mass of the GC should be totally dominated by stellar remnants if the polluters were AGB stars, which is not the case if the culprits are WMS. We critically analyse the advantages and shortcomings of each potential polluter class and find the WMS scenario more attractive.