Off-center black hole seed formation? Implications for high and low redshift massive black holes

TL;DR

This study evaluates how off-center formation of light MBH seeds alters the cosmic evolution of MBHs and MBHBs by implementing wandering seeds in the L-GalaxiesBH framework on Millennium merger trees. PopIII remnants form off-center while other seeds seed at galactic centers, leading to delayed mass growth and altered high-redshift demographics; two-phase gas accretion governs MBH growth, with dynamical-friction delays shaping MBHB assembly. The main findings show a strong suppression of $M_{ m BH}>10^5 M_\odot$ MBHs and a reduced high-$z$ quasar LF for the Off-center model, plus a redshift-dependent shift in the MBH–galaxy scaling relation and a pronounced reduction of high-$z$ MBHB mergers with a compensating boost at low redshift. These effects lessen by $z o0$ for larger galaxies, while JWST's overmassive MBH population remains compatible with both models; importantly, LISA could distinguish off-center seeding via altered IMRI-rich low-$z$ merger rates and mass-ratio distributions, though degeneracies with other growth processes may arise.

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 centers 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-center 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 use the $\texttt{L-Galaxies}{\it BH}$ semi-analytical model, which includes multiple seed formation mechanisms, with light Population III remnants being the most significant contributors. To incorporate off-center formation, we modify the model to track the initial seed location, the sinking timescales toward the galactic center, and any growth during this phase. The results indicate that seed formation occurring away from the galactic center has a negligible impact on the MBH population at $z<1$, but causes significant differences at higher redshifts. Particularly, the abundance of $10^5 M_{\odot}$ MBHs at $z>4$ can be up to 2-10 times smaller compared to a nuclear seed formation model. Quasar luminosity functions with $\rm L_{bol}>10^{44} \rm erg/s$ are similarly affected, although they still align with observational constraints. The 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 $z \sim 2$ for galaxies $>10^{11} M_{\odot}$, and by $z=0$ for smaller galaxies. Notably, the overmassive MBH population recently unveiled by JWST is still present in the model, suggesting they can form independently of the seed dynamics. Finally, the merging rate of MBHs within LISA sensitivity band is strongly impacted. Specifically, there is a suppression of events at high-$z$ and an enhancement at low-$z$.

Figures (9)

• Figure 1: Redshift evolution of the number density of newly formed seeds predicted by L-GalaxiesBH when run on top of the Millennium-II merger trees. Red, blue and green lines correspond to the PopIII remnants, RSM and DCBH seeds, respectively.
• Figure 2: Upper panels: Black hole mass function (BHMF) at $z\,{=}\,0,1,2,3,4,5, 6$ and $7$. The results correspond to the L-GalaxiesBH SAM run on the Millennium merger trees after applying the grafting methodology presented in Section \ref{['sec:EMT']}. The $z\,{=}\,0$ observations correspond to Shankar2013, Shen2020 and LiepoldAndMa2024. Blue and orange lines represent the Fiducial and Off-center model predictions. Shaded areas correspond to the Poisson error. Lower panels: Ratio between the predictions of the Off-center and Fiducial models. The horizontal gray lines are placed at $1,2, 5$.
• Figure 3: Upper panels: Quasar luminosity function at $z\,{=}\,0.5,2,3,5,6$ and $7$ predicted by the Fiducial (blue) and Off-center (orange) model. The results of L-GalaxiesBH are presented for the Millennium trees with the grafting methodology. Shaded areas correspond to the the Poisson error. Observational data corresponds to Shen2020Lacy2015Kokorev2024Greene2024Matthee2024Akins2024 and BarlowHall2025. Lower panels: Ratio between the predictions of the Off-center and Fiducial models. The horizontal grey lines are placed at $0.5,1,2$ and $5$ to guide the eye.
• Figure 4: Scaling relations at predicted by L-GalaxiesBH applied in the Millennium trees with the grafting methodology. Left panel: Median black hole mass ($\rm M_{BH}$) at fixed stellar mass ($\rm M_{Stellar}$). The shaded areas correspond to the percentile $\rm 16^{th}\,{-}\,84^{th}$. Blue color represents the results for the Fiducial model while orange corresponds to the Off-center one. Central and right panels:$\rm M_{BH} \,{-}\, M_{Stellar}$ plane for MBHs with $\rm L_{bol}\,{>}\,10^{44} erg/s$. As shown, that population far beyond the $\rm 16^{th}\,{-}\,84^{th}$ percentiles. The observational constraints are: $z\,{=}\,0$Erwin2012 (squares) ReinesVolonteri2015 (diamonds) and Capuzzo2017 (circles); $z\,{=}\,2$Shu2020 (pentagons) and at $z\,{\geq}\,5$Maiolino2023 (circles), Harikane2023 (squares) and Ding2023 (stars).
• Figure 5: Fraction of mass acquired by the MBH via gas accretion. While the left panels represent the entire MBH population divided in mass bins, the right panel is restricted to active MBHs, divided in different bolometric luminosities. Orange and blue lines represent the results for Fiducial and Off-center one. Shaded areas correspond to the $\rm 16^{th}\,{-}\,84^{th}$ percentiles of the distribution.