The Low Detection Rate of Pair-instability Supernovae and the Effect of the Core Carbon Fraction

The pair-instability supernova (PISN) is a common fate of very massive stars (VMSs). Current theory predicts initial and CO core mass ranges for PISNe of ∼140-260 and ∼65-120 M _o, respectively, for stars that are not much affected by the wind mass loss. The corresponding relative event rate between PISNe and core-collapse supernovae is estimated to be ∼1% for the present-day initial mass function. However, no confident PISN candidate has been detected so far, despite more than 1000 supernovae being discovered every year. We investigate the evolution of VMSs with various core carbon-to-oxygen ratios for the first time by introducing a multiplication factor to the ¹²C(α, γ)¹⁶O reaction rate. We find that a less massive VMS with a high X(C)/X(O) develops shell convection during the core carbon-burning phase, with which the star avoids the pair-creation instability. The second result is the high explodability for a massive VMS; i.e., a star with high X(C)/X(O) explodes with a smaller explosion energy. Consequently, the initial and CO core mass ranges for PISNe are significantly increased. Finally, a PISN with high X(C)/X(O) yields a smaller amount of ⁵⁶Ni. Therefore, PISNe with high X(C)/X(O) are much rarer and fainter. This result advances the first theory to decrease the PISN event rate by directly shifting the CO core mass range.