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

¹ Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
² INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
³ Como Lake Center for AstroPhysics, University of Insubria, 22100 Como, Italy
⁴ Institut d’Astrophysique de Paris, Sorbonne Université, CNRS, UMR 7095, 98 bis bd Arago, 75014 Paris, France
⁵ Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047 Selargius (CA), Italy
⁶ Donostia International Physics Centre (DIPC), Paseo Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
⁷ IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain

^⋆ Corresponding author: david.izquierdovillalba@unimib.it

Received: 7 August 2025
Accepted: 17 September 2025

Abstract

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-GalaxiesBH 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 > 10⁵ M_⊙ MBHs at z > 4 can be 2–10 times smaller than in a nuclear seed formation model. Quasar luminosity functions with L_bol > 10⁴⁴ 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 > 10¹¹ 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.