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.