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

TL;DR

This paper interrogates the IMF of the first stars by leveraging 406 very metal-poor stars and a detailed abundance-fitting framework that incorporates Population III supernova yields and multi-enrichment scenarios. By enforcing explodability constraints via a baryonic remnant-mass maximum, the authors derive a mass distribution that favors an extremely top-heavy or nearly flat CCSN IMF with a sizable explosion-energy exponent, while PISN contributions carry large mass exponents. The work shows that standard Salpeter-like IMF models fail to capture observed abundance patterns and that explodability must be integrated into early-universe enrichment models to produce physically plausible progenitor distributions. The approach provides a pathway to refine theoretical explosion models with empirical metal-poor star data and suggests that future observations with broader elemental coverage will further constrain Population III star properties and their role in cosmic chemical evolution.

Abstract

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.

Figures (5)

• Figure 1: \ref{['fig:chisqr_abunum:a']} Comparison of the distributions of the $\chi^2_\mathrm{red}$ varying with the abundance number $N$, as well as histogram of $N$ in the upper panel. For a given $N$, the box extends from the first quartile to the third quartile of the corresponding $\chi^2_\mathrm{red}$, with an orange line indicating the median value. The whiskers extend to the furthest $\chi^2_\mathrm{red}$ lying within $1.5\times$ the IQR from the box. Outliers are represented by thin diamonds beyond the whiskers. The horizontal red dotted line at $\chi^2_\mathrm{red}=0.5$ signifies an over-fitting threshold. The distribution of the observed abundance number is shown in the upper panel. \ref{['fig:chisqr_abunum:b']} Same as Panel \ref{['fig:chisqr_abunum:a']}, but for the selected stars under duo-enrichment assumption.
• Figure 2: \ref{['fig:chisqr_abunum:a']} P-value distribution of K-S tests conducted on the selected stars. The red dashed line denotes the threshold value of $a=0.05$. \ref{['fig:chisqr_abunum:b']} Comparison between the good-fitting ratios of $100$ and $1000$ sampling times, along with the corresponding residual. The dotted lines are reference lines.
• Figure 3: Some examples of the resulting disturbed mass distributions for $100$ iterations. Twelve stars are randomly selected from the adopted samples. The hatched histograms represent the fitting results, with good/poor-fittings colored in blue/orange respectively. The solid/dotted black lines denote the fiducial results of the observed abundances for good/poor-fitting.
• Figure 4: Inferred progenitor mass distributions under \ref{['fig:chisqr_abunum:a']} mono-enrichment and \ref{['fig:chisqr_abunum:b']} duo-enrichment assumption, along with their best-fit IMFs and relative residuals based on different explodability constraints. The black circles with solid lines, red triangles with solid lines and brown dashed lines represent the best-fit standard power-law, explodability-modifying power-law distributions and combined log-normal power-law respectively. For detailed definition of parameters in legends, please refer to Section \ref{['subsec:std_pw']}-\ref{['subsubsec:explod_modify_dist']}.
• Figure 5: Baryonic remnant masses of different supernova models. The remnant maximum can be chosen between $1.94\ M_\odot$ and $2.35\ M_\odot$.