Towards 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 its connection to the chemical composition of the 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 the power-law index $\kappa =1$ with a standard deviation $0.12$ (and $0.45$) and $0.06$ (and $0.34$), respectively from five years of LIGO-Virgo-KAGRA observation 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.