Merger Rate of Stellar Black Hole Binaries above the Pair-instability Mass Gap

In current stellar evolutionary models, the occurrence of pair-instability supernovae implies a lack of stellar black holes (BHs) with masses between about [60, 120] Mo, resulting in the presence of an upper-mass gap in the BH mass distribution. In this Letter, we propose a simple approach to describe 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 ≃[0.4, 7] yr-1 for LIGO/Virgo at design sensitivity and [10, 460] yr-1 for third-generation ground-based detectors, considering the most pessimistic and optimistic scenarios. The Laser Interferometer Space Antenna (LISA) can individually detect these binaries up to thousands of years from coalescence. The number of events merging in less than four years, which enable multiband observation in sequence, is expected to be in the range [1, 20]. While ET will detect all these events, LIGO/Virgo is expected to detect ≲50% of them. Finally, we estimate that the gravitational-wave background from unresolved sources in the LISA band may in principle be detected with a signal-to-noise ratio between ≃2.5 and ≃80.