2025A&A...703A.215S

Very massive stars (VMSs, M_★ ≥ 100 M_⊙) play a crucial role in several astrophysical processes. At low metallicity, they might collapse directly into black holes or end their lives as pair-instability supernovae. Recent observational results set an upper limit of 0.7 yr^–1 Gpc^–3 on the rate density of pair-instability supernovae in the nearby Universe. However, most theoretical models predict rates exceeding this limit. In this work, we computed new VMS tracks with the MESA code and used them to analyze the evolution of the (pulsational) pair-instability supernova rate density across cosmic time. We show that stellar-wind models accounting for the transition between optically thin and thick winds yield a pair-instability supernova rate of ℛ_PISN ∼ 0.1 Gpc^–3 yr^–1 at redshift ɀ ∼ 0, which is about two orders of magnitude lower than our previous models. We find that the main contribution to the pair-instability supernova rate comes from stars with metallicities of Z ∼ 0.001 - 0.002. Stars with higher metallicities cannot enter the pair-instability supernova regime, even if their zero-age main-sequence mass is up to 500 M_⊙. The main reason is that VMSs enter the regime for optically thick winds during the main sequence at metallicities as low as Z ∼ 4 × 10^–4. This enhances the mass-loss rate, quenching the growth of the He core and thus preventing the onset of pair-instability in later evolutionary stages. This result highlights the critical role of mass loss in shaping the final fate of very massive stars and the rate of pair-instability supernovae.