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

Understanding the link between massive (>= 30M circle dot) 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 circle dot, 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 350M circle dot 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 x 10(-4) to 2.0 x 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 60-120M circle dot . In particular, we find that PPISNe significantly enhance mass-loss of metal-poor (Z = 2.0 x 10(-3)) stars with ZAMS mass 60 <= M-ZAMS/M circle dot = 125. In contrast, PISNe become effective only for moderately metal-poor (Z < 8.0 x 10(-3)) VMSs. VMSs with mZAMS >= 220 M circle dot and Z < 10(-3) do not undergo PISNe and form intermediate-mass BHs (with mass >= 200M circle dot) via direct collapse.