Global Stellar Budget for LIGO Black Holes

The binary black hole mergers observed by Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo gravitational-wave detectors pose two major challenges: (i) how to produce these massive black holes from stellar processes; and (ii) how to bring them close enough to merge within the age of the universe? We derive a fundamental constraint relating the binary separation and the available stellar budget in the universe to produce the observed black hole mergers. We find that less than or similar to 14% of the entire budget contributes to the observed merger rate of (30+30) M black holes, if the separation is around the diameter of their progenitor stars. Furthermore, the upgraded LIGO detector and third-generation gravitational-wave detectors are not expected to find stellar-mass black hole mergers at high redshifts. From LIGO's strong constraints on the mergers of black holes in the pair-instability mass gap (60-120 M), we find that less than or similar to 0.8% of all massive stars contribute to a remnant black hole population in this gap. Our derived separation-budget constraint provides a robust framework for testing the formation scenarios of stellar binary black holes.