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 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 ≤ M_ZAMS/ M_⊙ ≤ 125. In contrast, PISNe become effective only for moderately metal-poor (Z < 8.0 × 10^-3) VMSs. VMSs with m_ZAMS ≳ 220 M_⊙ and Z < 10^-3 do not undergo PISNe and form intermediate-mass BHs (with mass ≳200 M_⊙) via direct collapse.