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.