Very massive stars, pair-instability supernovae and intermediate-mass black holes with the sevn code

Understanding the link between massive (30 M_) stellar black holes (BHs) and their progenitor stars is a crucial step to interpret observations of gravitational-wave events. In this paper, we discuss the final fate of very massive stars (VMSs), with zero-age main sequence (ZAMS) mass $>150$ M_, accounting for pulsational pair-instability supernovae (PPISNe) and for pair-instability supernovae (PISNe). We describe an updated version of our population synthesis code SEVN, in which we added stellar evolution tracks for VMSs with ZAMS mass up to $350 $M_ and we included analytical prescriptions for PPISNe and PISNe. We use the new version of SEVN to study the BH mass spectrum at different metallicity Z, ranging from Z=2.0× 10⁻⁴ to Z=2.0× 10⁻². The main effect of PPISNe and PISNe is to favour the formation of BHs in the mass range of the first gravitational-wave event (GW150914), while they prevent the formation of remnants with mass 60 - 120 M_. In particular, we find that PPISNe significantly enhance mass loss of metal-poor (Z≤ 2.0× 10⁻³) stars with ZAMS mass 60≤MZAMS/M_≤ 125. In contrast, PISNe become effective only for moderately metal-poor (Z<8.0× 10⁻³) VMSs. VMSs with MZAMS220 M_ and Z<10⁻³ do not undergo PISNe and form intermediate-mass BHs (IMBHs, with mass 200M_) via direct collapse.