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 and gravitational wave (GW) emission. The James Webb Space Telescope (JWST) has detected faint active galactic nuclei (AGNs) powered by accreting BHs with masses of ${M}_{\ifmmode\bullet\else\textbullet\fi{}}\ensuremath{\sim}{10}^{6--8}{M}_{\ensuremath{\bigodot}}$, revealing a previously unknown, abundant population of BHs. 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 (${M}_{\ifmmode\bullet\else\textbullet\fi{}}\ensuremath{\sim}{10}^{2\ensuremath{-}5}{M}_{\ensuremath{\bigodot}}$) formed in rare and overdense cosmic regions, and light seeds (${M}_{\ifmmode\bullet\else\textbullet\fi{}}\ensuremath{\sim}{10}^{1\ensuremath{-}3}{M}_{\ensuremath{\bigodot}}$) 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 $z\ensuremath{\sim}5$. 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 $\ensuremath{\lesssim}{10}^{\ensuremath{-}1}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$ for major mergers at $z\ensuremath{\ge}5$. However, the presence of light seeds increases the major merger rate by several orders of magnitude, which peaks at a total BH mass of $\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}{10}^{3}{M}_{\ensuremath{\bigodot}}$ over $5<z<10$ at a rate of $\ensuremath{\sim}30\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$. These events are detectable by future GW observatories such as the Laser Interferometer Space Antenna (LISA) and the pathfinder to DECi-hertz Interferometer Gravitational-wave Observatory (B-DECIGO). Precise sky localization and distance measurement of those GW events, with solid angle and luminosity distance uncertainties $\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Omega}}\mathrm{\ensuremath{\Delta}}\mathrm{log}{D}_{L}\ensuremath{\lesssim}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{deg}}^{2}$, will enable electromagnetic identification of mergers at $z\ensuremath{\ge}5$ and subsequent multimessenger follow-up observations.