Abundance Pattern Fitting with Bayesian Inference: Constraining First Stars' Properties and Their Explosion Mechanism with Extremely Metal-poor Stars

TL;DR

The paper develops a Bayesian abundance-fitting framework to constrain Pop III progenitor properties and explosion mechanisms using extremely metal-poor stars. By applying 1D NLTE corrections to key elements and using zero-metallicity CCSN yields with parameters M, E, and log f_mix, the authors quantify how observed abundances map to progenitor mass and explosion energy, while addressing grid-resolution biases. They find a robust mass–energy relation $E \propto M^{2}$ and identify two explodability islands in the ZAMS-mass distribution, which, combined with an explodability-aware IMF/EDF, yield exponents $\alpha_m=0.54$ and $\alpha_e=0.72$; these results are consistent with analogous findings at solar metallicity and support a non-monotonic explodability landscape. The study demonstrates that chemical abundance analysis offers a powerful, independent probe of the first stars and their supernova physics, highlighting the importance of homogeneous data and NLTE modeling for interpreting the early chemical enrichment of the Universe.

Abstract

The abundance patterns of extremely metal-poor stars preserve a fossil record of the Universe's earliest chemical enrichment by the supernova explosions from the evolution of first generation of stars, also referred to as Population III (or Pop III). By applying Bayesian inference to the analysis of abundance patterns of these ancient stars, this study presents a systematic investigation into the properties and explosion mechanism of Pop III stars. We apply NLTE corrections to enhance the reliability of abundance measurements, which significantly reduces the discrepancies in abundances between observations and theoretical yields for odd-Z elements, such as Na and Al. Our Bayesian framework also enables the incorporation of explodability and effectively mitigates biases introduced by varying resolutions across different supernova model grids. In addition to confirming a top-heavy ($α=0.54$) initial mass function for massive Pop III stars, we derive a robust mass--energy relation ($E\propto M^2$) of the first supernovae. These findings demonstrate that stellar abundance analysis provides a powerful and independent approach for probing early supernova physics and the fundamental nature of the first stars.

Figures (9)

• Figure 1: The abundances of EMP stars collected from FS, MMP and VMP 400 samples, which are represented as blue circles, orange squares and green triangles respectively. For FS samples, stars cataloged in different publications are distinguished by different brightness. The carbon abundance is corrected according to stellar evolution, while the sodium, magnesium and aluminum abundances are corrected for 1D NLTE effect. The typical observational uncertainties is on the order of $0.1\,\mathrm{dex}$. The dotted horizontal line in the carbon panel represents the division of CEMP of $\mathrm{[C/Fe]>0.7}$.
• Figure 2: Deviation of the measured abundances $\delta{\log\epsilon}$, which is defined as Equation \ref{['eqn:delta_logeps']}, as a function of surface gravity $\log g$ and their corresponding distributions. Target stars sourced from different samples are coded as the same in Figure \ref{['fig:abudist']}. Abundance deviation $\delta{\log\epsilon}$ caused by different atmospheric models mostly falls within the typical observational uncertainty of $0.1\,\mathrm{dex}$, represented as th horizontal dashed lines. However, the most significant deviations occur at the low surface gravity with $\log g<2$.
• Figure 3: The sensitivity of progenitor mass derivation for different elements. In each panel, the scattered points correspond to individual EMP stars from different samples, while the horizontal solid line and shaded regions indicate the 50th, 16th and 84th percentiles of the sensitivities. The sensitivity is expressed in the unit of $\mathrm{dex}^{-1}$.
• Figure 4: Distribution of the abundance residuals between predictions and observations over their corresponding observational uncertainties. The left (gray) and right (white) boxes represent the NLTE-corrected and LTE abundances from literature. Each box extends from the first to the third quartile of the corresponding abundance residuals, with an red solid line indicating the median value. Whiskers extend to the furthest abundance residuals lying within $1.5\times$ the IQRs from the boxes. The dashed horizontal lines signify the deviations of $1 \sigma$ and $3 \sigma$ of observational uncertainty.
• Figure 5: Deviation in progenitor mass caused by the non-detection (blue, left) and observational uncertainty (red, right) of each element, summarized in boxplots. The definition of boxes and whiskers follows that in Figure \ref{['fig:discpreancy_theory_observ']}. NLTE abundances are adopted for Na, Mg, and Al in this analysis.