Stellar Yields of Rotating First Stars. II. Pair Instability Supernovae and Comparison with Observations

Abstract

Recent theory predicts that a first star is born with a massive initial mass of $\gtrsim$ 100 $M_\odot$. Pair instability supernova (PISN) is a common fate for such a massive star. Our final goal is to prove the existence of PISN and thus the high mass nature of the initial mass function in the early universe by conducting {\it abundance profiling}, in which properties of a hypothetical first star is constrained by metal-poor star abundances. In order to determine reliable and useful abundances, we investigate the PISN nucleosynthesis taking both rotating and non-rotating progenitors for the first time. We show that the initial and CO core mass ranges for PISNe depend on the envelope structures: non-magnetic rotating models developing inflated envelopes have a lower-shifted CO mass range of $\sim$ 70--125 $M_\odot$, while non-rotating and magnetic rotating models with deflated envelopes have a range of $\sim$ 80--135 $M_\odot$. However, we find no significant difference in explosive yields from rotating and non-rotating progenitors, except for large nitrogen production in non-magnetic rotating models. Furthermore, we conduct the first systematic comparison between theoretical yields and a large sample of metal-poor star abundances. We find that the predicted low [Na/Mg] $\sim$ $-1.5$ and high [Ca/Mg] $\sim$ $0.5$--$1.3$ abundance ratios are the most important to discriminate PISN signatures from normal metal-poor star abundances, and confirm that no currently observed metal-poor star matches with the PISN abundance. Extensive discussion on the non-detection is finally made.