Homogeneous abundance ratios of hydrostatic and explosive α-elements in globular clusters from high-resolution optical spectroscopy

Galactic globular clusters (GCs) were born shortly after the Big Bang. For these old stellar systems, the initial mass function (IMF) in the high-mass regime can never be observed directly, because stars more massive than about 1 M_⊙ have evolved since for a long time. However, the hydrostatic to explosive α-element ratio (HEx ratio) offers a way to bypass the lack of observable high-mass stars through the yields that massive stars released when they exploded as supernovae, which is incorporated in the stars we currently observe in GCs. The HEx ratio measures the percentage of high-mass stars over the total number of stars exploding as supernovae, and it is an efficient probe of the ephemeral first phases of the GC evolution. We exploited a recently completed survey to assemble a dataset of very homogeneous abundances of α-elements in 27 GCs from Fe/H ∼ -2. 4 to ∼ -0. 3 dex. In agreement with previous results from APOGEE, we confirm that the HEx ratio is indistinguishable for GCs that formed in situ and accreted in the Galaxy, and that this ratio decreases with increasing metallicity. However, we posit that this trend is better explained by a metallicity-dependent IMF that is deficient in the highest-mass stars at high metallicity, as corroborated by the declining O/Mg ratio as a function of the Mg/H ratio. At odds with the previous analysis based on APOGEE data, we detect an anti-correlation of HEx ratio with both present-day and initial GC masses. Finally, we hypothesise that in the analysis of APOGEE data, the stars of the GC M 54 were probably confused with stars in the core of the Sagittarius dwarf galaxy, in which the cluster is currently immersed.