A Modified Initial Mass Function of the First Stars with Explodability Theory under Different Enrichment Scenarios

The most metal-poor stars record the earliest metal enrichment triggered by Population III stars. By comparing observed abundance patterns with theoretical yields of metal-free stars, physical properties of their first star progenitors can be inferred, including zero-age main-sequence mass and explosion energy. In this work, the initial mass distribution (IMF) of first stars is obtained from the largest analysis to date of 406 very metal-poor stars with the newest LAMOST/Subaru high-resolution spectroscopic observations. However, the mass distribution fails to be consistent with the Salpeter IMF, which is also reported by previous studies. Here we modify the standard power-law function with explodability theory. The mass distribution of Population III stars could be well explained by ensuring the initial metal enrichment to originate from successful supernova explosions. Based on the modified power-law function, we suggest an extremely top-heavy or nearly flat initial mass function with a large explosion energy exponent. This indicates that supernova explodability should be considered in the earliest metal enrichment process in the Universe.

💡 Research Summary

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This paper presents a comprehensive reconstruction of the initial mass function (IMF) of the first generation of stars (Population III) by incorporating supernova explodability theory and a dual‑enrichment scenario, using the largest high‑resolution spectroscopic sample of very metal‑poor (VMP) stars to date (406 objects). The authors begin by noting that traditional IMF assumptions—most notably the Salpeter power‑law (ξ ∝ M⁻²·³⁵)—fail to reproduce the mass distribution inferred from the abundance patterns of EMP/VMP stars. Moreover, recent theoretical work shows that not all massive metal‑free stars explode as core‑collapse supernovae (CCSNe); many collapse directly into black holes, creating “explosion‑failure islands” in mass space.

To address these issues, the study introduces two methodological innovations. First, it expands the enrichment model from a single supernova (mono‑enrichment) to a duo‑enrichment framework, allowing two independent Pop III supernovae to contribute to the observed chemical signature of each second‑generation star. Each supernova is assigned its own dilution factor, thereby capturing realistic inhomogeneous mixing in the early interstellar medium without over‑fitting limited abundance data. Second, the authors embed an explicit explodability parameter ζ(M) that equals 1 for masses that are theoretically capable of exploding and 0 for those that are not. This parameter is derived from a combination of compactness criteria (O’Connor & Ott 2011), the two‑parameter Ertl et al. (2016) condition, and metal‑free remnant‑mass limits (Zhang et al. 2008). Applying these constraints reduces the viable supernova model grid from ~17,600 to ~9,000 cases, dramatically tightening the parameter space.

The observational dataset combines LAMOST and Subaru high‑resolution spectra, selecting stars with