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

Using the L-Galaxies-BH semi-analytical model and Millennium simulations, this study reveals that the origins of overmassive and undermassive black holes are not uniform but depend on galaxy mass and redshift, arising from a complex interplay of enhanced merger histories, environmental stellar mass reduction, gravitational-wave recoils, and quiescent evolutionary paths.

The Gist

Imagine the universe as a giant, bustling city where every neighborhood (a galaxy) has a central mayor (a massive black hole). For a long time, astronomers thought there was a strict rulebook: the bigger the neighborhood, the bigger the mayor. If you had a huge city, you'd have a huge mayor; if you had a small village, you'd have a small mayor. This is the "scaling relation."

But recently, astronomers started finding "outliers." Some neighborhoods have mayors who are way too big for their town (Overmassive), while others have mayors who are surprisingly tiny for the size of their city (Undermassive).

This paper is like a detective story trying to figure out why these mismatches happen. The authors used a super-computer simulation (a digital universe) to track how these galaxies and their black hole mayors grow up over billions of years. They found that there isn't just one reason for the mismatch; it depends on the neighborhood's history and some dramatic cosmic events.

Here is the breakdown of the three main "culprits" behind these mismatches:

1. The "Overmassive" Mayors (Too Big for the Town)

Why do some black holes end up huge while their galaxies stay small? The paper identifies two main reasons:

• The "Bulge" Effect (High Redshift/Early Universe):
  In the early universe, some galaxies were like chaotic construction sites. They were constantly crashing into neighbors (mergers) and having internal riots (instabilities). This chaos acted like a super-funnel, dumping massive amounts of gas directly onto the black hole.

  • The Analogy: Imagine a black hole as a vacuum cleaner. Usually, it sucks up dust slowly. But in these chaotic early galaxies, someone kicked the "Turbo Mode" button. The black hole went into a feeding frenzy, eating gas faster than the speed of light allows (super-Eddington accretion). It grew huge very quickly, while the rest of the galaxy (the stars) hadn't caught up yet.
  • Result: A giant mayor in a town that is still under construction.

• The "Skinny" Effect (Low Redshift/Modern Universe):
  In the modern universe, some galaxies are actually too small for their black holes, not because the black hole grew too big, but because the galaxy got slimmed down.

  • The Analogy: Imagine a wealthy mayor living in a mansion. One day, a strong wind (gravity from a bigger neighbor) blows away the walls and the garden of the mansion, leaving only the mayor's office standing. The mayor is still the same size, but the "house" (the galaxy's stars) is now tiny.
  • Result: The black hole looks "overmassive" because the galaxy lost its stars, not because the black hole ate too much.

2. The "Undermassive" Mayors (Too Small for the Town)

Why do some huge galaxies have tiny black holes? The paper finds two main reasons here too:

• The "Eviction" (Gravitational Recoils):
  When two black holes merge, they don't just sit quietly. It's like two figure skaters spinning together and then letting go. The release of gravitational waves can act like a rocket kick, shooting the new, merged black hole out of the center of the galaxy.

  • The Analogy: Imagine the mayor gets kicked out of the town hall by a shockwave. The town hall is now empty! A new, smaller mayor (a black hole that was just visiting from a neighboring village) moves in to fill the spot. But this new mayor is small and hasn't had time to grow up with the town.
  • Result: A massive city with a tiny, new mayor who hasn't had time to "co-evolve" with the city. This happens mostly in massive galaxies.

• The "Quiet Life" (Low Mass Galaxies):
  In small, quiet galaxies, the black hole never got a chance to grow.

  • The Analogy: Imagine a small village where nothing ever happens. No parties, no construction, no visitors. The black hole is like a child who never got any food because the village was too quiet to bring in supplies. The village grew up (stars formed), but the black hole stayed a baby.
  • Result: A small town with a tiny mayor, simply because the town was too peaceful to feed the black hole.

The Big Picture

The paper concludes that the universe isn't following a single, simple rule. Instead, the relationship between a galaxy and its black hole is a messy, dynamic dance:

1. Environment matters: If a galaxy gets stripped of its stars by a neighbor, the black hole looks too big.
2. Violence matters: If a black hole gets kicked out of town by a merger, a tiny replacement moves in, making the black hole look too small.
3. History matters: If a galaxy has a wild, chaotic past, the black hole might have gorged itself and become a giant. If the galaxy had a boring, quiet life, the black hole stayed small.

In short: The "outliers" aren't mistakes; they are the result of different cosmic stories. Some black holes are giants because they had a wild youth; some are tiny because they were evicted or starved. The universe is a lot more chaotic and interesting than a simple rulebook suggests.

Technical Summary

1. Problem Statement

The co-evolution of galaxies and their central Massive Black Holes (MBHs) is typically characterized by tight scaling relations, most notably the correlation between MBH mass ($M_{BH}$) and host stellar mass ($M_*$). However, observational data reveals a population of outliers: overmassive MBHs (lying above the median relation) and undermassive MBHs (lying below it).

• Overmassive systems: Recent JWST observations at high redshift ($z > 5$) suggest MBHs can be orders of magnitude more massive than their hosts, challenging standard formation paradigms.
• Undermassive systems: These are observed in the local universe, often in pseudobulge-dominated galaxies or systems where MBH growth appears suppressed.
• The Gap: While various mechanisms (accretion efficiency, feedback, dynamical ejections) have been proposed, it remains unclear which physical processes dominate the formation of these outliers across different cosmic epochs and galaxy masses. Specifically, the interplay between environmental stripping, gravitational-wave (GW) recoils, and diverse fueling histories needs quantification.

2. Methodology

The authors utilize a state-of-the-art Semi-Analytical Model (SAM) called L-GalaxiesBH, built upon the Millennium suite of N-body simulations (Millennium and Millennium-II).

• Simulation Framework:

  • Merger Trees: The study employs a "grafting" technique (MS+Grafting) to combine the large cosmological volume of the Millennium simulation with the high mass resolution of Millennium-II. This allows for the statistical sampling of rare high-redshift systems while resolving low-mass galaxies.
  • Cosmology: $\Lambda$CDM cosmology with Planck 2014 parameters ($\Omega_m=0.315, \Omega_\Lambda=0.685, H_0=67.3$).

• Model Physics & Updates:

  • MBH Seeding: Implements four seed channels: Population III remnants ($\sim 100 M_\odot$), runaway stellar mergers ($\sim 10^3-10^4 M_\odot$), direct-collapse black holes ($\sim 10^5 M_\odot$), and merger-induced DCBHs.
  • Gas Accretion: Models both Eddington-limited and super-Eddington accretion triggered by high gas reservoirs and inflow rates following mergers or disc instabilities.
  • MBH Dynamics: Tracks the full dynamical evolution of MBH binaries from kiloparsec separations to coalescence, including dynamical friction, hardening, and GW emission.
  • Gravitational Recoils: Calculates kick velocities based on merger spin configurations (wet vs. dry mergers). If the kick exceeds the escape velocity, the MBH is ejected, and the model tracks its orbit and potential repopulation by a secondary MBH.
  • New Prescription (Gradual Stripping): Unlike previous models that assume instantaneous disruption of satellite galaxies, this model implements gradual stripping of stellar and cold-gas components based on the tidal radius ($R_t$). This allows for a continuous reduction of host stellar mass ($M_*$) while the MBH mass remains constant.

• Analysis Strategy:

  • The authors define five samples based on percentiles of the global $M_{BH}-M_*$ distribution: Median ($1\sigma$), Overmassive ($+2\sigma, +3\sigma$), and Undermassive ($-2\sigma, -3\sigma$).
  • They analyze the evolutionary pathways, merger histories, and environmental interactions of these specific populations across redshifts ($z=0$ to $z=6$).

3. Key Contributions & Results

A. Redshift Evolution of the Scaling Relation

• The global $M_{BH}/M_*$ ratio evolves significantly: rising from $\sim 5 \times 10^{-6}$ at $z \sim 6$ to $\sim 10^{-3}$ at $z \sim 2$, then declining to $\sim 2 \times 10^{-4}$ at $z=0$.
• Overmassive populations ($+2\sigma, +3\sigma$) follow this trend but with ratios 5–7 times higher. At $z > 3$, massive galaxies ($M_* > 10^{10} M_\odot$) in the $+3\sigma$ sample reach ratios of $\sim 0.1$, consistent with JWST observations.
• Undermassive populations ($-2\sigma, -3\sigma$) show little evolution, maintaining low ratios ($\sim 10^{-6}$ to $10^{-7}$).

B. Mechanisms Driving Overmassive MBHs

Two distinct pathways drive overmassive systems, dependent on redshift and mass:

1. Environmental Stripping (Low Redshift, $z < 3$):
   • Gradual stripping of satellite galaxies reduces the host's stellar mass ($M_*$) by factors of up to 8–9, while the MBH mass remains unchanged.
   • This shifts the system vertically in the $M_{BH}-M_*$ plane.
   • Limitation: This mechanism explains only $\sim 10\%$ of the overmassive population at low redshift and cannot explain overmassive MBHs at high redshift ($z > 3$) or in the $+2\sigma$ sample.
2. Enhanced Fueling Histories (All Redshifts):
   • Low Mass ($M_* < 10^9 M_\odot$): Driven by active merger histories (approx. 5x more interactions than average) leading to sustained growth.
   • High Mass ($M_* > 10^9 M_\odot$): Driven by a combination of frequent minor mergers and disc instabilities (DI).
   • Super-Eddington Accretion: Crucial for high-redshift overmassive MBHs. In the $+3\sigma$ sample at $z > 3$, $>50\%$ of MBHs experience super-Eddington episodes, often triggered by high gas inflows ($\dot{M}_{inflow} > 10 M_\odot/yr$) during mergers or DIs.

C. Mechanisms Driving Undermassive MBHs

Two primary channels create undermassive systems:

1. Gravitational Wave Recoils (High Mass, $M_* > 10^9 M_\odot$):
   • GW kicks eject the central MBH. The nucleus remains empty for a period (pairing phase) before a secondary MBH (from a past merger) sinks to the center.
   • The "Desynchronization" Effect: The sinking time is long (0.3 Gyr at $z \sim 5$ to 3 Gyr at $z \sim 1$). During this time, the host galaxy continues to grow, but the new central MBH is stalled. Consequently, the MBH never co-evolves with its new host, resulting in a permanently undermassive system.
   • This mechanism dominates undermassive populations in massive galaxies across all redshifts.
2. Quiescent Evolution (Low Mass, $M_* < 10^9 M_\odot$):
   • In low-mass galaxies, GW recoils are less frequent due to lower MBH occupation fractions.
   • Undermassive MBHs here arise from lack of activity: minimal merger history, negligible disc instabilities, and suppressed gas inflow. These MBHs remain close to their initial seed masses because they never receive sufficient fuel to grow.

4. Significance

• Unifying Framework: The paper demonstrates that outliers in the $M_{BH}-M_*$ relation are not the result of a single mechanism but arise from the interplay of environmental effects (stripping), dynamical processes (GW recoils), and fueling diversity (super-Eddington vs. quiescent growth).
• JWST Interpretation: The results provide a physical basis for the "heavy seed" or "super-Eddington" scenarios required to explain JWST's detection of massive MBHs in the early universe. The model confirms that super-Eddington accretion in high-redshift, merger-rich environments is a viable pathway for rapid MBH growth.
• Recoil Impact: The study quantifies the long-term impact of GW recoils, showing they are a primary driver of undermassive MBHs in massive galaxies, a factor often overlooked in scaling relation studies.
• Model Validation: The inclusion of gradual stripping and improved MBH dynamics allows the L-GalaxiesBH model to reproduce the scatter and specific sub-populations of the $M_{BH}-M_*$ relation across cosmic time, bridging the gap between theoretical predictions and multi-epoch observational data.

In conclusion, the paper establishes that the diversity of MBH populations is a natural outcome of hierarchical structure formation, where the relative importance of stripping, recoils, and accretion efficiency varies systematically with galaxy mass and cosmic time.