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

Recent theory predicts that first stars are born with a massive initial mass of ≳100 M _⊙. Pair-instability supernova (PISN) is a common fate for such massive stars. Our final goal is to prove the existence of PISNe and thus the high-mass nature of the initial mass function in the early universe by conducting 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 nonrotating progenitors for the first time. We show that the initial and CO core mass ranges for PISNe depend on the envelope structures: nonmagnetic rotating models developing inflated envelopes have a lower shifted CO mass range of ∼70-125 M _⊙, while nonrotating and magnetic rotating models with deflated envelopes have a range of ∼80-135 M _⊙. However, we find no significant difference in explosive yields from rotating and nonrotating progenitors, except for large nitrogen production in nonmagnetic 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] ∼ -1.5 and high [Ca/Mg] ∼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. An extensive discussion on the nondetection is presented.