Temperature-resolved sensitivities of 56Ni production to helium-burning reactions in pair-instability supernovae

We propose a temperature-resolved Monte Carlo (MC) approach to identify the temperature ranges in which low-energy helium-burning reaction rates most strongly affect nucleosynthesis in very massive stars that undergo pair-instability supernovae (PISNe). By performing MC simulations of PISNe, we quantify how temperature-dependent variations in key helium-burning reaction rates, i.e., the triple-α and ¹² C(α ,γ )¹⁶ O rates, influence ⁵⁶Ni synthesis. Thousands of stellar evolution calculations using MESA reveal that both the ¹² C(α ,γ )¹⁶ O and triple-α reactions exhibit their strongest sensitivity at T 2.5 × 10⁸\, K, but with opposite correlation signs. We show that this temperature corresponds to the regime in which the ratio of the sampled rate multipliers is most clearly imprinted on the pre-carbon-burning C/O composition. This demonstrates that PISN nucleosynthesis can probe helium-burning reaction rates in specific low-temperature regimes.