Global Stellar Budget for LIGO Black Holes

TL;DR

This paper establishes a fundamental constraint linking the stellar material available in the universe to the formation and merger rates of black holes observed by LIGO, highlighting limitations on high-redshift detections and the stellar origin of massive black holes.

Contribution

It introduces a novel separation-budget constraint that connects stellar resources to black hole merger rates, offering a new framework for testing binary black hole formation scenarios.

Findings

Only about 14% of the stellar budget contributes to observed 30 solar mass black hole mergers.

High-redshift stellar-mass black hole mergers are unlikely to be detected by current and future gravitational-wave detectors.

Less than 0.8% of massive stars produce black holes in the pair-instability mass gap.

Abstract

The binary black hole mergers observed by 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 $\lesssim 14\%$ of the entire budget contributes to the observed merger rate of $(30 + 30)~\mathrm{M}_\odot$ 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 ($60-120~\mathrm{M}_\odot$), we find that $\lesssim 0.8\%$ 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.