The cosmic rate of pair-instability supernovae

Pair-instability superno vae (PISNe) hav e crucial implications for man y astrophysical topics, including the search for v ery massiv e stars, the black hole mass spectrum, and galaxy chemical enrichment. To this end, we need to understand where PISNe are across cosmic time, and what are their fa v ourable galactic environments. We present a new determination of the PISN rate as a function of redshift, obtained by combining up-to-date stellar evolution tracks from the PARSEC and FRANEC codes, with an up-to-date semi-empirical determination of the star formation rate and metallicity evolution of star-forming galaxies throughout cosmic history. We find the PISN rate to exhibit a huge dependence on the model assumptions, including the criterion to identify stars unstable to pair production, and the upper limit of the stellar initial mass function. Remarkably, the interplay between the maximum metallicity at which stars explode as PISNe, and the dispersion of the galaxy metallicity distribution, dominates the uncertainties, causing a similar to seven-orders-of-magnitude PISN rate range. Furthermore, we show a comparison with the core-collapse supernova rate, and study the properties of the fa v ourable PISN host galaxies. According to our results, the main contribution to the PISN rate comes from metallicities between similar to 10(-3) and 10(-2) , against the common assumption that views very low metallicity, Population III stars as e xclusiv e or dominant PISN progenitors. The strong dependencies we find offer the opportunity to constrain stellar and galaxy evolution models based on possible future (or the lack of) PISN observations.