# Merger rate of stellar black hole binaries above the pair instability mass gap

## TL;DR

This paper models the merger rate of stellar black hole binaries with masses above the pair instability gap, predicting detection rates for current and future gravitational wave observatories and exploring the potential for multi-band observations.

## Contribution

It introduces a fiducial model for black holes beyond the pair instability mass gap, incorporating cosmic star formation and metallicity evolution, and estimates merger rates and detection prospects.

## Key findings

- Detection rate for LIGO/Virgo: 0.4 to 7 per year.
- Third-generation detectors could observe 10 to 460 per year.
- LISA can detect these binaries up to thousands of years from coalescence.

## Abstract

In current stellar evolutionary models, the occurrence of pair instability supernovae implies the lack of stellar black holes (BHs) with masses between about $[60, \, 120] \, \rm{M}_\odot$, resulting in the presence of an upper mass gap in the BH mass distribution. In this Letter, we develop a fiducial model describing BHs beyond the pair instability gap, by convolving the initial mass function and star formation rate with the metallicity evolution across cosmic time. Under the ansatz that the underlying physics of binary formation does not change beyond the gap, we then construct the cosmic population of merging BH binaries. The detection rate of BH binaries with both mass components above the gap, is found to range between $\simeq [0.4,\,7] \, \rm{yr}^{-1}$ for LIGO/Virgo at design sensitivity and $[10, \, 460] \, \rm{yr}^{-1}$ for third-generation ground based detectors, considering the most pessimistic and optimistic scenarios. LISA can detect individually these binaries up to thousands of years from coalescence. The number of events merging in less than four years, which enable multi-band observation in sequence, is expected in the range $[1, \, 20]$. While ET will detect all these events, LIGO/Virgo is expected to detect $\lesssim 50\%$ of them. Finally, we estimate that the gravitational-wave background from unresolved sources in the LISA band may be in principle detected with a signal-to-noise ratio between $ \simeq 2.5$ and $\simeq 80$.