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Accretion-Driven Evolution of Compact-Object Populations in Gas-Rich Environments and the Origin of Massive Gravitational-Wave Sources

This paper proposes a continuity-equation framework demonstrating that gas accretion acts as a mass-space transport process that, depending on the accretion rate's mass dependence, can either diverge or converge compact-object populations, thereby naturally explaining the origin of massive gravitational-wave sources and the observed high-mass tails in merger catalogs.

Original authors: Mor Rozner, Alejandra Rosselli-Calderon, Enrico Ramirez-Ruiz

Published 2026-06-29✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Mor Rozner, Alejandra Rosselli-Calderon, Enrico Ramirez-Ruiz

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a vast, cosmic factory floor filled with heavy objects (black holes and neutron stars) floating in a thick, swirling soup of gas. For a long time, scientists thought these objects just grew a little bit if they happened to bump into some gas, but their overall "family tree" of sizes stayed mostly the same.

This paper proposes a new, dynamic way to look at that factory. The authors suggest that the gas isn't just a snack; it's a transport system that actively shuffles these objects around, changing the entire population's size distribution in predictable ways.

Here is the breakdown of their findings using simple analogies:

1. The "Growth Rule" Determines the Outcome

The core idea is that how fast an object grows depends on how heavy it already is. The authors call this the "growth rule," and it comes in three main flavors, like different rules for a game:

The "Rich Get Richer" Rule (Divergent Evolution): If the rule is that heavier objects grow much faster than light ones (like a snowball rolling down a hill that gets bigger and picks up speed), the population splits apart. You end up with a few massive giants and a sea of small ones. This creates a "long tail" of super-heavy objects that wouldn't exist otherwise.
The "Leveling" Rule (Convergent Evolution): If the rule is that lighter objects grow faster than heavy ones (like a small plant catching up to a big tree because it has more room to grow), the population bunches together. Everyone ends up being roughly the same size, squeezing the distribution into a narrow range.
The "Fair Share" Rule (Self-Similar Evolution): If everyone grows at the exact same percentage rate (like a photo being zoomed in), the shape of the population stays the same, just shifted to be heavier overall.

2. The Gas is the Conveyor Belt

The paper argues that in gas-rich environments (like the disks around supermassive black holes), the gas acts like a conveyor belt in a warehouse.

Objects don't just sit there and get heavier; they are transported through "mass space."
Because the "speed" of this transport depends on the object's mass, the whole crowd shifts and reshapes itself over time.
This explains why we are seeing some incredibly massive black holes merging (like the event GW231123 mentioned in the paper). They aren't necessarily born that way; they were "shipped" to that massive size by the gas conveyor belt.

3. The "Dance Partner" Effect (Binary Systems)

Many of these objects are in pairs (binaries), dancing around each other. The paper looks at how gas affects these couples:

Scenario A: Dancing Apart (Isolated Accretion): If the two partners are far apart, the heavier one grabs the gas faster. This makes the heavy one even heavier and the light one relatively lighter. The pair becomes more unequal, like a dance where one partner grows huge and the other stays small.
Scenario B: Dancing Together (Collective Accretion): If the pair is close enough, they create a shared "wake" in the gas (like two boats moving close together creating a shared wave). In this case, the gas gets funneled toward the lighter partner. This helps the smaller partner catch up, driving the pair toward having equal mass. It's like a dance where the music helps the smaller partner grow until they are the same size as their partner.

4. What This Means for Gravitational Waves

When these objects eventually crash into each other, they create gravitational waves (ripples in space-time). The authors show that the "gas conveyor belt" leaves a fingerprint on these ripples:

The High-Mass Tail: We see a few extremely heavy mergers that are hard to explain with normal star death. The paper suggests these are the result of the "Rich Get Richer" gas rule.
The Equal Masses: If we see many mergers where the two objects are almost the same size, it might be a sign that they were in a "Collective Accretion" environment where the gas helped the smaller one catch up.

Summary

The paper claims that gas-rich environments act as a mass-shaping machine. They don't just add weight; they actively sort and redistribute the population of black holes. Depending on the specific physics of the gas, they can either create a few cosmic giants, squeeze everyone into a similar size, or pair up objects to make them equal. This provides a natural explanation for the heaviest black hole mergers we are currently detecting.

Technical Summary: Accretion-Driven Evolution of Compact-Object Populations in Gas-Rich Environments

Problem Statement
The origin of the most massive gravitational-wave (GW) sources, particularly black holes (BHs) exceeding the pair-instability mass gap (e.g., GW231123 with component masses $\approx 137 M_\odot$ and $103 M_\odot$ ), remains uncertain. While hierarchical mergers and gas-assisted growth have been proposed, a general framework connecting the physical mechanisms of gas accretion to the statistical reshaping of entire compact-object populations is lacking. Specifically, it is unclear how sustained gas accretion in environments like Active Galactic Nucleus (AGN) disks alters the mass function and binary mass-ratio distributions beyond simply increasing individual object masses.

Methodology
The authors develop a general framework treating population evolution as a transport problem in mass space, governed by a continuity equation.

Continuity Equation Framework: The evolution of the mass function $p(m, t)$ is derived from the conservation of objects, where $p(m, t) = p_0(m_0) |dm_0/dm|$ . The Jacobian $|dm_0/dm|$ is determined by the underlying growth law.
Growth Laws: The accretion rate is parameterized as $\dot{m} = k m^\beta e^{-t/\tau_{gas}}$ $\overset{m}{˙} = k m^{β} e^{- t / τ_{g a s}}$ , where $\beta$ $β$ dictates the mass dependence. The authors analyze three physically motivated regimes:
- Bondi-Hoyle-Lyttleton (BHL): $\beta = 2$ (divergent evolution).
- Hill Accretion: $\beta = 2/3$ (convergent evolution).
- Eddington-Limited: $\beta = 1$ (self-similar evolution).
Analytical and Numerical Models:
- Analytical solutions are derived for initial power-law distributions to characterize asymptotic mass functions.
- Monte Carlo population simulations ( $5 \times 10^6$ realizations) track the evolution of binary populations initialized with a Salpeter-like power law plus a Gaussian component ( $5-50 M_\odot$ ).
- Binary evolution models consider two regimes: independent accretion (where components accrete separately) and collective accretion (where overlapping accretion radii create a common wake, enhancing secondary accretion based on hydrodynamic simulations).
GW Merger Rates: The merger rate distribution $\Gamma_{merge}(t)$ is calculated by integrating the evolved mass and separation distributions over the binary population, accounting for gravitational-wave inspiral timescales.

Key Contributions and Results

Mass Space Transport: The paper demonstrates that accretion acts as a transport mechanism that reshapes the mass function based on $\beta$ $β$ .
- $\beta > 1$ (Divergent): Massive objects grow disproportionately faster, naturally generating extended high-mass tails and broadening the distribution.
- $\beta < 1$ (Convergent): Lower-mass objects grow relatively faster, compressing the population toward a narrower mass range.
- $\beta = 1$ (Self-similar): The distribution preserves its shape while shifting to higher masses.
Binary Mass-Ratio Evolution: The evolution of the mass ratio $q = m_2/m_1$ $q = m_{2} / m_{1}$ depends critically on how gas is partitioned:
- Independent Accretion: If components accrete independently, the more massive component grows preferentially (for $\beta > 1$ ), driving $q$ toward zero and deepening mass asymmetries.
- Collective Accretion: In compact binaries with overlapping accretion radii, hydrodynamic effects create a common wake that channels gas to the lower-mass companion. This enhances the secondary's growth rate, driving $q$ toward unity ( $q \approx 1$ ).
GW Population Signatures:
- Sustained gas accretion produces merger populations with extended high-mass tails, offering a pathway to form massive mergers like GW231123 without requiring hierarchical mergers.
- Mixed populations (containing both accreting and non-accreting binaries) naturally generate multi-component merger distributions, where the relative amplitude of high-mass peaks traces the fraction of systems embedded in long-lived gas reservoirs.
- The model predicts that gas-rich environments can populate parameter space regions (high mass, equal mass ratios) that are difficult to access via stellar evolution alone.

Significance and Claims
The paper claims to establish a direct connection between the statistical properties of compact-object populations and the gaseous environments in which they evolve. The authors argue that gas-rich environments should not be viewed merely as sites where mergers occur, but as "transport media" that continuously reshape populations.

Interpretation of Observations: The framework suggests that the high-mass tails and specific mass-ratio distributions observed in GW catalogs are cumulative imprints of accretion-driven evolution.
Mechanism for Massive Sources: It provides a natural mechanism for forming massive black hole mergers through sustained accretion in regimes where $\beta > 1$ (such as BHL accretion in AGN disks).
Universality: While motivated by AGN disks, the authors assert that the qualitative behavior (divergent vs. convergent evolution based on $\beta$ ) applies broadly to any gas-rich environment capable of sustaining compact-object accretion, including proto-clusters and dense stellar systems.

The authors note that their treatment isolates accretion-driven transport, neglecting feedback, magnetic spin evolution, and complex binary dynamics, which they identify as necessary for future quantitative refinement. However, they maintain that the qualitative consequence of differential accretion reshaping populations is robust.

1. The "Growth Rule" Determines the Outcome

2. The Gas is the Conveyor Belt

3. The "Dance Partner" Effect (Binary Systems)

4. What This Means for Gravitational Waves

Summary

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