Off-centre black hole seed formation: Implications for high- and low-redshift massive black holes

Recent studies show that light seeds of black holes, which grow into massive black holes (MBHs) over time, often struggle to remain at the centres of their birthplaces in high-redshift galaxies, limiting their ability to accrete gas and merge with other black holes. In this work, we investigate how off-centre formation of the first seeds affects the evolution of the MBH and massive black hole binary (MBHB) populations over cosmic history. To this end, we used the L-Galaxies BH semi-analytical model, which includes multiple seed formation mechanisms, with light Population III remnants being the most significant contributors. To incorporate off-centre formation, we modified the model to track the initial seed location, the sinking timescales towards the galactic centre, and any growth during this phase. Our results indicate that seed formation occurring away from the galactic centre has a negligible impact on the MBH population at z < 1, but causes significant differences at higher redshifts. In particular, the abundance of > 10 5 M ⊙ MBHs at z > 4 can be 2–10 times smaller than in a nuclear seed formation model. Quasar luminosity functions with L bol > 10 44 erg/s are similarly affected, although they continue to align with observational constraints. Off-centre formation also alters the galaxy-MBH mass relation. At z > 5, the amplitude of the relation can be up to 2 dex smaller than in nuclear seed models. These differences fade by z ∼ 2 for galaxies > 10 11 M ⊙ , and by z = 0 for less massive galaxies. Notably, the overmassive MBH population recently unveiled by JWST is still present in the model, suggesting that these objects can form independently of the seed dynamics. Finally, the merging rate of MBHs within the LISA sensitivity band is strongly impacted. Specifically, there is a suppression of events at high- z and an enhancement at low- z .