🔭 astrophysics

Twin Peaks: Resolving Features in the Binary Black Hole Mass Function with COSMIC-METISSE

This study utilizes a new grid of MESA stellar tracks paired with the COSMIC-METISSE population synthesis framework to demonstrate how uncertainties in wind-driven mass loss and convective boundary mixing significantly influence the binary black hole mass function, potentially creating a "twin peak" structure near $10M_\odot$ driven by mass ratio reversal or merging into a single peak, while also causing a six-fold variation in merger rates.

Original authors: Duncan B. Maclean, Poojan Agrawal, Katelyn Breivik, and Alexandra G. Guerrero, Michael Zevin, Mathieu Renzo, Carl L. Rodriguez

Published 2026-06-30

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CC BY 4.0

Original authors: Duncan B. Maclean, Poojan Agrawal, Katelyn Breivik, and Alexandra G. Guerrero, Michael Zevin, Mathieu Renzo, Carl L. Rodriguez

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 or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic dance floor where massive stars are born, live, and eventually die. Sometimes, two of these stars are born together as partners. If they survive their dramatic lives without crashing into each other immediately, they can eventually collapse into black holes and continue dancing until they finally merge, sending ripples through space-time called gravitational waves.

This paper is like a massive, high-tech simulation lab. The authors, Duncan Maclean and his team, wanted to understand why the black holes we detect look the way they do. Specifically, they are trying to solve a mystery about the "weight" of these black holes. When we look at the data from our gravitational wave detectors (like LIGO), we see a bump in the number of black holes around 10 times the mass of our Sun. But is that a single bump, or is it two bumps hiding underneath each other?

Here is how they cracked the code, explained simply:

1. The Problem: The "Recipe" is Unclear

To predict how these stars dance and die, scientists use computer models. Think of these models as recipes for stellar evolution. However, for a long time, these recipes had some missing ingredients or vague instructions. Two specific "ingredients" were the biggest sources of confusion:

The Wind: Massive stars blow off material like a giant hair dryer. How strong is this wind? Does it strip the star naked, or does it leave a fluffy coat?
The Mixing: Inside a star, hot gas churns like a boiling pot. Sometimes, this churning spills over the edges of the "pot" (the core) and mixes with the cooler gas outside. How much mixing happens?

The authors realized that if you change these two "ingredients" in your recipe, you get very different results.

2. The Experiment: Cooking with New Ingredients

The team built a massive library of new "recipes" (stellar tracks) using a super-accurate cooking simulator called MESA. They didn't just use the old, standard recipes. They tested four different versions:

Standard: The old-school wind and mixing rules.
New Winds: Using the latest observations to make the "hair dryer" effect more accurate.
New Mixing: Using a newer theory about how the star's interior churns (called "convective penetration").
The Combo: Using both the new wind and new mixing rules.

They then fed these recipes into a fast-forward machine called COSMIC-METISSE. This machine simulates millions of binary star systems, fast-forwarding them through billions of years to see which ones survive to become merging black holes.

3. The Big Discovery: The "Twin Peaks"

When they looked at the results, they found a fascinating pattern in the mass of the black holes.

The Mystery: The data showed a peak around 10 solar masses.
The Reveal: In most of their models, this wasn't just one peak. It was actually two peaks right next to each other: one around 8 solar masses and another around 13 solar masses.

They call this the "Twin Peaks" (a nod to the famous TV show, though the paper uses it to describe two distinct groups of black holes).

Why are there two peaks?
It comes down to a dramatic plot twist in the stars' lives called Mass Ratio Reversal (MRR).

Imagine two partners, Star A (the big one) and Star B (the smaller one).
In some cases, Star A gets so hungry it eats Star B's mass, or Star B steals mass from Star A.
If Star B steals enough mass, Star B becomes the bigger partner, and Star A becomes the smaller one. This is the "reversal."
The team found that the 13 solar mass black holes mostly come from these "reversal" stories. The 8 solar mass ones come from stories where the original big star stayed the big star.

4. The "Mass Ratio" Clue

The paper also looked at the relationship between the two black holes in a pair. They found that the heavier black holes (the 13 solar mass ones) tend to have a partner that is about 70% of their size (a ratio of 0.7). This matches what real-world detectors are seeing!

5. The "Magic" Combination

Here is the most interesting part:

When they used the old recipes, the two peaks (8 and 13) were clearly separate.
When they used the new wind and mixing rules together, something magical happened: the two peaks merged into one single, smooth hill right around 9 or 10 solar masses.

This single hill looked exactly like the data we see from the real universe. It suggests that the real universe might be using these "new" physics rules.

6. The Catch: The Rate Problem

While the "New Winds + New Mixing" model got the shape of the black hole masses perfect, it had one big problem: it predicted too many black holes merging. It said there should be about 4 to 6 times more mergers happening in the universe than we actually see.

The authors suggest this might be because their model is too "optimistic" about how often stars survive a dangerous phase called the "Common Envelope" (where two stars get tangled up in a giant cloud of gas). If we tweak that part, the numbers might match perfectly.

Summary

Think of this paper as a team of astronomers trying to tune a radio.

The Static: We see a signal (black hole masses), but it's fuzzy.
The Tuning: They adjusted the "wind" and "mixing" knobs on their simulation.
The Result: When they turned both knobs to the "New" setting, the static cleared up, and the signal (the mass distribution) matched the real world perfectly, revealing that the "Twin Peaks" of black hole masses are likely just one smooth feature in reality.

The paper concludes that to truly understand how black holes are born and die, we need to keep refining these stellar "recipes," specifically how stars lose mass and how their insides mix.

Problem Statement
Gravitational wave (GW) observations from the LVK collaboration have revealed specific features in the binary black hole (BBH) population, notably a global peak in the primary mass spectrum near $10 M_\odot$ and a feature in the mass ratio distribution at $q \approx 0.7$ . While population synthesis models based on isolated binary evolution can reproduce these populations, their predictive power is limited by uncertainties in the underlying stellar physics. Specifically, standard rapid population synthesis codes often rely on fitting formulae (Single Star Evolution, or SSE) that may not accurately capture the effects of varying stellar winds and convective boundary mixing (CBM) across a wide range of metallicities. These uncertainties propagate significantly into binary evolution outcomes, such as mass transfer stability, common envelope (CE) formation, and the final remnant masses.

Methodology
The authors present a new grid of stellar tracks computed with the open-source code MESA (release r24.08.1), spanning metallicities $10^{-3} \le Z/Z_\odot \le 7$ and masses up to $300 M_\odot$ . The grid includes 85 mass points for hydrogen-rich stars and 42 for naked helium stars. The authors vary two key stellar physics parameters:

Wind-driven mass loss: Comparing standard prescriptions (Vink et al. 2001; Jager & v. d. Hucht 1988) against newer, observationally calibrated fits (Krticka et al. 2025; Decin et al. 2023).
Convective Boundary Mixing (CBM): Comparing standard exponential overshooting (Herwig 2000) against a convective penetration model (Johnston et al. 2024).

These MESA tracks are interpolated using METISSE (Method of Interpolation for Single Stellar Evolution) and fed into the rapid population synthesis code COSMIC. This pipeline, termed COSMIC-METISSE, allows for the generation of synthetic merging BBH populations in the local Universe ( $z < 0.2$ ) while systematically varying the input stellar physics. The study employs a "pessimistic" CE scenario where donors lacking a core-envelope boundary are assumed to merge, though "optimistic" scenarios are also tested for comparison.

Key Results

The "Twin Peaks" at $10 M_\odot$ : In most model variations (Standard, New Winds, New CBM), the primary mass spectrum exhibits two distinct sub-populations flanking the $10 M_\odot$ $10 M_{⊙}$ peak: one at $\approx 8 M_\odot$ $\approx 8 M_{⊙}$ and another at $\approx 13 M_\odot$ $\approx 13 M_{⊙}$ .
- The $\approx 8 M_\odot$ peak is dominated by systems that do not undergo Mass Ratio Reversal (MRR).
- The $\approx 13 M_\odot$ peak is dominated by systems that do undergo MRR. These MRR systems preferentially form from progenitors with initial mass ratios $q_{ZAMS} \gtrsim 0.5$ and result in final mass ratios clustering around $q \approx 0.7$ .
Sensitivity to Stellar Physics: The "New Winds & CBM" model, which combines weaker winds and convective penetration, merges these two sub-populations into a single peak near $9 M_\odot$ . This occurs because the specific combination of physics allows high-metallicity binaries to survive the CE phase and undergo MRR, shifting the MRR population to lower masses where it overlaps with the non-MRR population.
Merger Rates: The choice of stellar physics dramatically affects the predicted local merger rate. Models using convective penetration (New CBM and New Winds & CBM) predict rates of $\approx 120\text{--}168 \text{ Gpc}^{-3}\text{yr}^{-1}$ , roughly 4–6 times higher than models using standard overshooting ( $\approx 25 \text{ Gpc}^{-3}\text{yr}^{-1}$ ). This increase is driven by the modulation of the CE channel; convective penetration delays the second Roche lobe overflow, allowing more systems to survive the CE phase and merge within a Hubble time.
Metallicity Dependence: Standard and New Winds models produce merging BBHs predominantly at very low metallicities ( $Z \lesssim 0.01 Z_\odot$ ). In contrast, the New Winds & CBM model produces a significant sub-population of mergers at solar and supersolar metallicities, contributing to the single peak near $10 M_\odot$ .
Mass Ratio Correlation: The models reproduce the observed feature at $q \approx 0.7$ , which is strongly linked to MRR events. An anticorrelation is observed between primary mass and mass ratio for MRR systems, where higher primary masses preferentially undergo MRR and settle at $q \approx 0.7$ .

Significance and Claims
The paper claims that the "twin peaks" observed in the BBH mass function are not necessarily distinct astrophysical populations but rather a resolution of two sub-populations (MRR and non-MRR) whose relative strength and location are highly sensitive to stellar wind and CBM prescriptions. The authors demonstrate that:

Interpolation is critical: Using interpolated MESA tracks via METISSE allows for a more direct study of how stellar physics uncertainties propagate to binary populations compared to traditional SSE fitting formulae.
Stellar physics drives rates: Variations in CBM and wind treatments can alter the predicted BBH merger rate by a factor of $\approx 6$ , primarily by modulating the efficiency of the common envelope channel.
Reconciling with Observations: While no single model perfectly recovers both the LVK local merger rate and the redshift evolution simultaneously, the "New Winds & CBM" model (when normalized to the observed rate) produces a primary mass spectrum and mass ratio distribution that aligns notably well with the GWTC-5 PixelPop posterior, particularly regarding the $10 M_\odot$ peak and the $q \approx 0.7$ feature.

The authors conclude that resolving the specific features of the BBH mass function requires precise constraints on massive star evolution, particularly regarding wind mass loss and convective boundary mixing, and that future work must address uncertainties in the cosmic star formation history and CE formation mechanisms.