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

## TL;DR

This paper updates the SEVN population synthesis code to model the evolution of very massive stars, including pair-instability supernovae, revealing their impact on black hole mass spectra and the formation of intermediate-mass black holes.

## Contribution

The paper introduces stellar evolution tracks for stars up to 350 M$_{igodot}$ and incorporates analytical models for PPISNe and PISNe into SEVN, advancing the simulation of massive star remnants.

## Key findings

- PPISNe favor the formation of black holes similar to GW150914.
- PISNe prevent remnants with masses between 60 and 120 M$_{igodot}$.
- VMSs with M$_{ ext{ZAMS}}$ > 220 M$_{igodot}$ and low metallicity form IMBHs via direct collapse.

## Abstract

Understanding the link between massive ($\gtrsim 30$ M$_{\odot{}}$) 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$_{\odot}$, 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 $M$_{\odot{}}$ 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 $Z=2.0\times 10^{-4}$ to $Z=2.0\times 10^{-2}$. 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$_{\odot{}}$. In particular, we find that PPISNe significantly enhance mass loss of metal-poor ($Z\leq 2.0\times 10^{-3}$) stars with ZAMS mass $60\leq $M$_{\mathrm{ZAMS}}/$M$_{\odot{}}\leq 125$. In contrast, PISNe become effective only for moderately metal-poor ($Z<8.0\times 10^{-3}$) VMSs. VMSs with M$_{\rm ZAMS}\gtrsim{}220$ M$_\odot$ and $Z<10^{-3}$ do not undergo PISNe and form intermediate-mass BHs (IMBHs, with mass $\gtrsim 200 $M$_{\odot{}}$) via direct collapse.