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

TL;DR

This study uses a homogeneous, high-resolution optical abundance dataset for 27 globular clusters to investigate the HEx ratio, the hydrostatic-to-explosive alpha-element abundance ratio, as a probe of the high-mass end of the early GC IMF. The HEx ratio is computed from hydrostatic elements ($[\mathrm{O/Fe}]$, $[\mathrm{Mg/Fe}]$) and explosive elements ($[\mathrm{Si/Fe}]$, $[\mathrm{Ca/Fe}]$, $[\mathrm{Ti/Fe}]$) and is evaluated for all stars and for the primordial component to mitigate multiple population effects, with $\mathrm{HEx}$ defined as $\frac{([\mathrm{O/Fe}]+[\mathrm{Mg/Fe}])/2}{([\mathrm{Si/Fe}]+[\mathrm{Ca/Fe}]+[\mathrm{Ti/Fe}])/3}$. The authors find that HEx declines with increasing metallicity and that using only the primordial component shifts the values closer to field stars; they also detect a declining $[\mathrm{O/Mg}]$ with $[\mathrm{Mg/H}]$, supporting a metallicity-dependent IMF lacking the most massive stars, and a mass-related trend emerges in extended samples. When contrasted with APOGEE results, the study confirms the general lack of a clear in situ vs accreted distinction in the HEx–$[\mathrm{Fe/H}]$ plane, while addressing specific outliers (e.g., M15) and clarifying M54/Sgr-core contamination effects. Overall, the work demonstrates that HEx is a robust diagnostic of the early, progenitor-rich phases of GC evolution and IMF variation across the Milky Way's building blocks, with implications for chemical evolution models.

Abstract

Galactic globular clusters (GCs) were born shortly after the Big Bang. For such old stellar systems the initial mass function (IMF) at the high mass regime can never be observed directly, because stars more massive than about 1 Mo have evolved since longtime. However, the hydrostatic to explosive alpha-element ratio (HEx ratio) offers a way to bypass the lack of observable high mass stars through the yields that massive stars released when exploding as supernovae, incorporated in the stars we presently 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 alpha-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 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 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 that analysis, the stars of the GC M 54 were probably confused with stars in the core of the Sagittarius dwarf galaxy, where the cluster is presently immersed.

Figures (7)

• Figure 1: Average abundance ratio [Na/H] as a function of metallicity for GC stars with primordial (P, red squares), intermediate (I, in blue), and extreme (E, green) composition in our GCs, superimposed to a reference sample of unpolluted field stars from Carretta (2013: grey open triangles).
• Figure 2: The ratio of the average of hydrostatic $\alpha-$elements O and Mg to the average of explosive $\alpha-$elements Si, Ca, and Ti (HEx ratio) for our sample of GCs. In the lower panel the ratio is computed using only stars of the unpolluted P component in each GC (see text). Blue and red symbols are for accreted and in situ GCs, respectively, grey empty circles are field stars from Gratton et al. (2003). The green square is for field stars in the core of Sgr dSph. A typical error is shown in both panels (average from all GCs).
• Figure 3: Distribution of metallicities for stars labelled as candidate members of NGC6715 in Schiavon et al. (2024), after the selection cuts from Horta and Ness (2025). The mean metallicity from APOGEE (Mészáros et al. 2020) for M 54 is indicated by the vertical red line.
• Figure 4: Abundance ratios of the hydrostatic (upper panel) and explosive (lower anel) $\alpha-$elements in the GCs of our extended sample, Blue and red points indicate accreted and in situ GCs. Black squares are disk GCs and green triangles are bulge GCs from literature. The Pearson's correlation coefficient and two-tailed probability are listed. Only Mg is used to represent the hydrostatic species in field stars.
• Figure 5: Abundance ratio [O/Mg] as a function of [Mg/H] for the extended sample of GCs. Symbols are as in Fig. \ref{['f:hydroexplo']}.