Gravitational Wave Forecasts Constrained by JWST AGN Observations for Early Massive Black Hole Mergers

Massive black holes (BHs) grow by gas accretion and mergers, observable through electromagnetic (EM) and gravitational wave (GW) emission. The James Webb Space Telescope (JWST) has detected faint active galactic nuclei (AGNs), revealing an abundant population of accreting BHs with masses of $M_\bullet\sim 10^{6-8}~M_\odot$. This mass range overlaps with the detection scopes of space-based GW interferometers and approaches the upper bounds of the predicted mass of seed BHs. We model BH mass assembly in light of the new JWST findings to investigate their formation channels and predict merger events. Two types of seed BHs are considered: heavy seeds ($M_\bullet\sim 10^{2-5}~M_\odot$) formed in rare and overdense cosmic regions, and light seeds ($M_\bullet\sim 10^{1-3}~M_\odot$) formed as stellar remnants in less massive dark-matter halos. The BHs grow through episodic accretion and merger events, which we model by fitting the AGN luminosity function to observational data including JWST-identified AGNs at $z\sim 5$. We find that heavy seeds alone struggle to explain quasars and faint JWST-selected AGNs simultaneously, requiring the more abundant light seeds. The observed merger rate of BHs from heavy seeds alone is limited to $\lesssim 10^{-1}~{\rm yr}^{-1}$ for major mergers at $z\geq5$. However, the presence of light seeds increases the major merger rate by several orders of magnitude, which peaks at a total BH mass of $M_\bullet\simeq 2\times 10^3~M_\odot$ over $5<z<10$ at a rate of $\sim 30~{\rm yr}^{-1}$. These events are detectable by future GW observatories such as the Laser Interferometer Space Antenna (LISA). Precise sky localization and distance measurement of those GW events, with solid angle and luminosity distance uncertainties $\Delta\Omega\Delta\log D_L\lesssim 10^{-4}~\rm deg^2$, will enable EM identification of mergers at $z\geq5$ and multi-messenger follow-up observations.