🔭 astrophysics

Low-mass failed supernovae and the $10\,M_{\odot}$ peak in the merging black hole mass distribution

By analyzing 153 gravitational-wave events from the GWTC-4.0 catalog, this study confirms a distinct peak in the merging black hole mass distribution at $10\,M_{\odot}$ and a subsequent sharp drop in rates up to $\sim 16\,M_{\odot}$ , suggesting the existence of a separate subpopulation of black holes formed via low-mass failed supernovae.

Original authors: Isaac Legred, Jacob Golomb, Katerina Chatziioannou

Published 2026-04-03

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CC BY 4.0

Original authors: Isaac Legred, Jacob Golomb, Katerina Chatziioannou

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 black holes are the dancers. For a long time, scientists thought these dancers came in all sizes, following a smooth, predictable pattern: lots of small ones, fewer medium ones, and very few giant ones. It was like a gentle slope going down a hill.

But recently, when scientists listened to the "music" of the universe (gravitational waves), they noticed something strange. There was a massive crowd of dancers right around a specific weight—about 10 times the mass of our Sun. It was like a sudden, dense pile-up of people at a concert.

Even stranger, just a little bit heavier than that pile-up (between 12 and 16 solar masses), the dance floor suddenly went empty. It wasn't just a few fewer dancers; it was as if someone turned off the lights and told everyone in that specific weight range to go home.

This paper, written by Isaac Legred, Jacob Golomb, and Katerina Chatziioannou, tries to explain why this "pile-up" and this "empty zone" exist.

The Mystery: A Cliff in the Crowd

Think of the black hole masses like a staircase.

The 10 Solar Mass Step: There is a huge crowd of black holes here.
The 12–16 Solar Mass Gap: The stairs suddenly disappear. No one is standing here.
The Heavy Step: Above 16 solar masses, the stairs reappear, and people are dancing again.

Previous theories tried to explain the crowd at 10, but they couldn't explain why the stairs vanished completely in the middle.

The New Theory: The "Failed Explosion" Channel

The authors propose a new idea involving how stars die.

The Old Story:
Usually, when a massive star runs out of fuel, it explodes in a spectacular supernova. This explosion blows off the outer layers, leaving behind a smaller, dense core (a black hole). Think of it like a firework: it bursts, and the remaining spark is the black hole.

The New Story (The "Failed" Channel):
The paper suggests that for stars in a very specific weight range (around 10 solar masses), something goes wrong. Instead of exploding, the star just collapses silently. It's like a firework that runs out of powder and just crumples into a ball without making a sound.

Because this "silent collapse" happens so efficiently for stars of this specific size, it creates a huge pile-up of black holes right at that weight.

But here is the kicker: This "silent collapse" mechanism only works for that specific size.

If the star is slightly lighter, it explodes normally (leaving a smaller black hole).
If the star is slightly heavier (12–16 solar masses), the physics changes, and the "silent collapse" stops working. The star might explode, or it might not form a black hole at all in the way we expect.
If the star is much heavier (above 16), a different process takes over, creating the heavy black holes we see again.

So, the "gap" exists because the "silent collapse" factory shuts down, and the "normal explosion" factory hasn't started up yet.

The Evidence: Listening to the Dance Floor

The team analyzed data from 153 gravitational wave events (the "dances" they've recorded so far). They built a computer model that allowed for two different groups of black holes:

The "Failed" Group: The ones that collapsed silently around 10 solar masses.
The "Normal" Group: The heavier ones formed by other processes.

What they found:

The Crowd is Real: About 76% of the black holes they studied belong to that specific "10 solar mass" group.
The Gap is Likely: Their data strongly suggests that the dance floor is empty between 12 and 16 solar masses. While they can't say it's 100% empty (because they haven't listened long enough to be absolutely sure), the chance of it being empty is very high (about 88%).
Different Personalities: The black holes in the "10 solar mass" crowd spin differently and pair up differently than the heavy ones, confirming they are indeed two different groups with different origins.

The Big Picture Analogy

Imagine a bakery that makes cookies.

The 10g Cookies: The baker has a special machine that makes perfect 10g cookies very quickly. The bin is overflowing with them.
The 12g–16g Cookies: The machine breaks down for these sizes. The baker tries to make them by hand, but it's so difficult that almost no cookies get made. The bin is empty.
The 20g+ Cookies: The baker switches to a different, heavy-duty machine that makes giant cookies. The bin fills up again.

This paper is the baker realizing, "Ah, I have two different machines, and there's a weird gap in the middle where my current setup just doesn't work."

Why Does This Matter?

If this is true, it tells us that the universe isn't just a smooth, random distribution of black holes. It has structure. It suggests that the way stars die is much more complex than we thought. There are specific "rules" of physics that make certain sizes of stars collapse silently, while others explode or behave differently.

By finding this gap, we are essentially reading the "instruction manual" of how stars die, discovering that nature has very specific preferences for how it builds its heaviest objects.

1. Problem Statement

Gravitational-wave (GW) observations from the LIGO-Virgo-KAGRA (LVK) collaboration have revealed a distinct structure in the mass distribution of merging binary black holes (BBHs). Specifically:

There is a global maximum in the merger rate density near 10 M⊙.
The merger rate drops by approximately 1–2 orders of magnitude as primary mass ( $m_1$ ) increases from $\sim10$ M⊙ to $\sim15$ M⊙.
Previous studies using non-parametric models (e.g., Gaussian processes, splines) have struggled to confirm a sharp "gap" (zero merger rate) in the 12–16 M⊙ range, often finding only a suppression rather than a complete absence of events.
Theoretical models suggest that failed supernovae (failed-SNe)—where massive stars collapse directly into black holes without a visible explosion—could occur in a narrow mass range (around 10–14 M⊙) due to specific core compactness properties. However, standard population synthesis models often fail to reproduce the magnitude of the observed rate drop or the existence of a distinct gap.

The central question is whether the observed overdensity at 10 M⊙ and the subsequent rate suppression constitute a distinct astrophysical population (failed-SNe) separated from the higher-mass population by a genuine gap in the primary mass distribution.

2. Methodology

The authors propose a new parametric population model designed to explicitly test for a gap between low-mass and high-mass BBHs.

Data Source: The analysis utilizes 153 BBH events from the GWTC-4.0 catalog (false alarm rate < 1 yr⁻¹).
Model Architecture: The primary mass distribution is modeled as a mixture of two distinct subpopulations:
1. Failed-SN Subpopulation (FSN): Modeled as a truncated Gaussian distribution centered around 10 M⊙. This represents the hypothesized channel of direct collapse.
2. High-Mass Subpopulation (X): Modeled using either a Power Law + Peak (PLP) or a Broken Power Law (BPL).
Key Innovation (The Gap): Unlike previous models that forced the high-mass population to extend down to the minimum mass of the low-mass population, this model allows the minimum mass of the high-mass population ( $m_{min}^u$ ) to be distinct and higher than the maximum mass of the FSN population.
- A smooth "Planck taper" is applied to the high-mass population to define a turnover mass ( $m_{turn}$ ), representing the onset of the high-mass power law.
- If $m_{turn} > m_{max}^{FSN}$ , a gap exists where the merger rate is effectively zero.
Spin and Mass Ratio: The model allows the FSN and high-mass populations to have distinct mass ratio ( $q$ ) and effective spin ( $\chi_{eff}$ ) distributions, acknowledging that different formation channels may produce different pairing properties.
Statistical Framework: The authors use the gwpopulation framework with the nested sampler dynesty (via bilby) to infer hyperparameters. They employ marginalization over hyperparameters to generate posterior predictive distributions (PPD) for the differential merger rate.

3. Key Contributions

Explicit Gap Modeling: The paper introduces a flexible parametric model that does not assume continuity between the low-mass peak and the high-mass tail, explicitly testing for a "gap" in the primary mass distribution.
Subpopulation Differentiation: It demonstrates that allowing distinct spin and mass-ratio distributions for the low-mass (FSN) and high-mass populations significantly improves the fit to the data compared to models assuming a unified distribution.
Re-evaluation of the 10 M⊙ Peak: The study confirms that the 10 M⊙ peak is not merely the onset of a global power law but likely represents a separate astrophysical channel (failed-SNe) with a rate enhancement of orders of magnitude over the background.

4. Key Results

Using the 153 GWTC-4.0 events, the authors found:

Confirmation of the 10 M⊙ Peak:
- The peak is located at $9.95^{+0.53}_{-1.25}$ M⊙ with a standard deviation of $0.71^{+0.75}_{-0.35}$ M⊙.
- The peak merger rate density is $7.36^{+6.35}_{-3.11}$ M⁻¹⊙ yr⁻¹ Gpc⁻³.
Evidence for a Gap:
- The merger rate drops sharply after the peak. For primary masses in the range $m_1 \in (12.0, 16.1)$ M⊙, the rate is consistent with zero at the 90% credible level.
- The turnover mass (where the high-mass population begins) is inferred to be $16.21^{+3.81}_{-6.91}$ M⊙.
- There is an 88% probability that the turnover mass is greater than the effective maximum mass of the failed-SN population, indicating a separation (gap) rather than a continuous distribution.
Population Fractions:
- Approximately 76% of the observed BBH mergers belong to the failed-SN subpopulation.
Spin and Mass Ratio Differences:
- The failed-SN population exhibits a narrower effective spin distribution (peaked at $\sim0.05$ with $\sigma \sim 0.07$ ) compared to the high-mass population (peaked at $\sim0.04$ with $\sigma \sim 0.13$ ).
- The failed-SN population tends to have more asymmetric mass ratios (broader distribution) compared to the high-mass population.
Model Comparison:
- The model allowing for a gap (FSN + PLP) is strongly favored by the maximum likelihood ratio ( $\sim20$ ) over models that do not permit a gap, despite having more parameters.
- When compared to the standard GWTC-4.0 "2 power laws + 2 peaks" model, the gap model provides a better fit to the data, particularly in the 12–16 M⊙ range.

5. Significance and Implications

Astrophysical Origin: The results strongly support the hypothesis that the $\sim10$ M⊙ BBHs originate from a distinct formation channel involving failed supernovae (direct collapse) in a narrow range of Zero-Age Main Sequence (ZAMS) masses (likely $\sim12-14$ M⊙ for solar metallicity).
Stellar Evolution Constraints: The existence of a gap implies that stars in the $\sim12-16$ M⊙ range are uniquely prone to direct collapse without forming a black hole via a standard supernova, or that the resulting black holes are not efficiently formed in this specific mass window. This challenges simple core-compactness models and suggests complex dependencies on progenitor structure (e.g., entropy profiles).
Future Observations: The identification of a gap provides a clear target for future GW observing runs. Confirming the gap with higher statistics will be strong evidence for the existence of a separate low-mass population, fundamentally changing our understanding of massive star death and binary evolution.
Methodological Impact: The study highlights the importance of using parametric models with flexible gap definitions and distinct subpopulation properties, rather than relying solely on non-parametric smoothing which may obscure sharp features.

In conclusion, the paper provides robust statistical evidence that the low-mass end of the BBH mass distribution is dominated by a failed-supernova channel, creating a distinct peak at 10 M⊙ separated from the high-mass population by a significant gap in merger rates.