Overmassive and Undermassive Massive Black Holes: The Role of Environment and Gravitational-Wave Recoils

Abstract

Understanding the connection between galaxy properties and their central massive black holes (MBHs) is key to unveiling their co-evolution. We use the ${\tt L{-}Galaxies{-} \it BH}$ semi-analytical model and the ${\tt Millennium}$ suite of simulations to investigate the physical origin of galaxies hosting overmassive and undermassive MBHs with respect to the $M_{\rm BH}-M_*$ relation, across stellar mass and cosmic time. We find that distinct evolutionary pathways drive different offsets from the scaling relation. Overmassive MBHs are primarily associated with galaxies that experienced enhanced merger history and secular activity. At $z\,{>}\,4$, this activity often leads to early, rapid MBH growth, frequently involving super-Eddington accretion episodes. At low redshift, a minority of overmassive systems ($20\%$) instead arise from environmental effects that reduce the stellar mass of the host, shifting galaxies above the relation without requiring additional MBH growth. Undermassive MBHs originate from two main channels. In massive galaxies, gravitational recoil following MBH mergers can eject the central MBH, temporarily leaving the galaxy without a nucleus. During this phase, MBHs coming from previous galaxy mergers can become the new central MBHs, but their masses remain below the expected ones from the scaling relation, as they never co-evolved with their new host galaxy. In low-mass galaxies ($M_*<10^9 M_\odot$), undermassive MBHs are more commonly linked to a quiescent evolutionary history, with limited mergers and weak secular processes that suppress an efficient MBH growth. We therefore conclude that outliers of the $M_{\rm BH}-M_*$ do not arise from a single mechanism, but from the interplay between environmental effects, gravitational recoils, and diverse MBH fueling histories, whose relative importance varies with galaxy mass and redshift.

Figures (9)

• Figure 1: $M_{\rm BH}\,{-}\,M_*$ plane at $z\,{=}\,0,1,3,5$. Different colors represent different populations. The results have been compared with the $z\,{\sim}\,0$ sample of Erwin2012 (squares) ReinesVolonteri2015 (diamonds) and Capuzzo2017 (circles), Ferre_Mateu2021 (pentagons) and Ramsden2026 (crosses). The $z\,{=}\,1$ and $z\,{=}\,3$ results presents the observational sample of Shu2020 (triangles) and the overmassive MBHs of Mezcua2023 and Mezcua2024, respectively. The $z\,{=}\,5$ results are compared with Maiolino2023 (circles), Harikane2023 (squares), Ding2023 (stars) and Lupi2024 (pentagons). At this redshift the black (grey) points correspond to $z\,{\geq}\,5$ ($z\,{\leq}\,5$). The horizontal line highlights $\,{\leq}\,10^4\, \,\mathrm{M_\odot}$, a mass range where electromagnetic information about the central MBH of the galaxy is expected to be undetectable by current observational facilities.
• Figure 2: Redshift evolution of the median $M_{\rm BH}/M_*$ ratio for the 5 different samples: ${+3\sigma}$ (red), ${+2\sigma}$ (coral), ${1\sigma}$ (orange), ${-2\sigma}$ (blue) and ${-3\sigma}$ (purple). Solid lines with circles represent the results for galaxies with $M_*\,{>}\,10^8\, \,\mathrm{M_\odot}$ while dashed lines with squares represent the same but for galaxies with $M_*\,{>}\,10^{10} \, \,\mathrm{M_\odot}$. The shaded areas correspond to the $16^{\rm th}\,{-}\,84^{\rm th}$ percentiles.
• Figure 3: Examples of evolutionary pathways for overmassive and undermassive MBHs. The upper panels show the galaxy merger trees, the middle panels illustrate the assembly of stellar mass and MBH mass, and the lower panels present the evolution of the ratio $M_{\rm BH}/M_*$. The first column corresponds to an overmassive MBH whose growth is driven by the gradual stripping of the host galaxy. The second column shows an undermassive MBH produced by a GW recoil event. The third column depicts an undermassive MBH resulting from a quiescent merger history, while the fourth column presents an overmassive MBH formed through an active merger history combined with a super-Eddington accretion episode.
• Figure 4: Upper panel: Redshift evolution of the fraction of galaxies that are undergoing a gradual stripping ($f_{\rm Satellite}$). Lower panel: Redshift evolution of the median fraction of stellar mass lost by galaxies due to gradual stripping ($f_{\rm Mass \, Stripped}$). In all panels, there are 5 different samples: ${+3\sigma}$ (red), ${+2\sigma}$ (coral), ${1\sigma}$ (orange), ${-2\sigma}$ (blue) and ${-3\sigma}$ (purple). The left column corresponds to galaxies with $10^{8} \,{<}\, M_* \,{<}\, 10^{9}\,\,\mathrm{M_\odot}$, the middle column to those with $10^{9} \,{<}\, M_* \,{<}\, 10^{10}\,\,\mathrm{M_\odot}$, and the right column to galaxies with $M_* \,{>}\, 10^{10}\,\,\mathrm{M_\odot}$.
• Figure 5: First panel: Redshift evolution of the fraction of galaxies that underwent an ejection of their central MBH due to GW recoils ($f_{\rm ejection}$). Second panel: Median time spent in the dynamical-friction phase ($t_{\rm DF}$) by MBHs that re-filled an empty galactic nucleus due to a GW ejection. Third panel: Redshift evolution of the median redshift at which the MBH was ejected from the center of the galaxy ($z_{\rm ejection}$). The color coding and mass dependence are the same as in Fig. \ref{['fig:StrippingEffect']}.