Toward a Precision Measurement of Binary Black Holes Formation Channels Using Gravitational Waves and Emission Lines

The formation of compact objects—neutron stars, black holes, and supermassive black holes—and their connection to the chemical composition of galaxies is one of the central questions in astrophysics. We propose a novel data-driven, multi-messenger technique to address this question by exploiting the inevitable correlation between gravitational waves and atomic/molecular emission-line signals. For a fiducial probability distribution function $p({t}_{d})\propto {t}_{d}^{-\kappa }$ of time delays, this method can provide a measurement of the minimum delay time of 0.5 Gyr and a power-law index of κ = 1 with a standard deviation of 0.12 (and 0.45) and 0.06 (and 0.34), respectively, from five years of LIGO–Virgo–KAGRA observations in synergy with SPHEREx line intensity mapping (and DESI emission-line galaxies). Such measurements will provide data-driven, multi-messenger constraints on the delay time distribution which is currently not well known.