Constraints on the early growth of massive black holes from the PTA and JWST with

Recent pulsar timing array (PTA) results provide strong evidence of a stochastic gravitational wave background (sGWB), consistent with a population of merging massive black holes (MBHs) at z<1. Meanwhile, JWST observations at z>5 suggest a higher number density of accreting MBHs than previously estimated. Together with constraints from local MBHs and high-z quasars, these findings offer a unique opportunity to test MBH seeding and early growth models. We explored this using L-Galaxies BH , a new extension of the galaxy formation model L-Galaxies , developed to explicitly model all stages of MBH evolution, including seeding, accretion, and binary dynamics. To take advantage of both the high resolution of the MillenniumII and the large volume of the Millennium simulations, we ran L-Galaxies BH on the former and used its outputs as initial conditions for the latter, via our ``grafting'' method. We find that reproducing the number density of high-z active MBHs observed by JWST requires either a heavy seed formation rate that is significantly higher than that predicted by current theoretical models (≳ 0.01 ^ Mpc -3 at z ∼ 10) or a widespread formation of light seeds undergoing multiple phases of super-Eddington accretion. Furthermore, matching the amplitude of the PTA sGWB signal requires nearly all galaxies with stellar masses M_ * > 10^9 M_⊙ to host central MBHs by z Given the extreme heavy seed densities required to satisfy both PTA and JWST constraints, our results favor a scenario in which MBHs originate from light seeds that grow rapidly and efficiently in the early Universe. This work demonstrates the power of combining multimessenger data with physical models to probe the origins and evolution of MBHs across cosmic time.