Very Massive Stars and Their Compact Remnants

At the end of carbon burning, very massive stars (VMSs, Mstar > 100 Msun) can efficiently produce electron-positron pairs in their core, triggering an instability that leads either to the ejection of a fraction of their mass in multiple pulsations (pulsational pair-instability supernova) or to their complete destruction (pair-instability supernova). Despite the robust theoretical framework pair-instability theory is grounded in, we still do not have any unquestionable detection of a pair-instability supernova. Thus far, VMS modellers have implemented wind models, that could have under-estimated the mass-loss rate. As a consequence, the predicted maximum metallicity at which stars are expected to enter the pair-instability regime might be excessively high. In this Thesis, I studied the evolution of very massive stars with a new model for radiation-driven stellar winds, focusing on low metallicities, to obtain an accurate prediction for the pair-instability supernova rate density. To this purpose, I modelled the evolution of very massive stars using the stellar evolution code MESA. I modelled them as single stars and binary systems, following episodes of mass transfer. I then used my models to produce stellar tracks for the rapid population synthesis code SEVN, which is optimized to simulate several millions of single and binary stars per day, probing the parameter space of pair-instability supernovae. Finally, I modelled the evolution of the pair-instability supernova rate as function of redshift, by combining my population synthesis models with a metal-dependent cosmic star formation rate history.