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A Possible Triple Formation Scenario of Binary Black Hole Merge With One In Pair-instability Supernova Mass Gap

This paper proposes an isolated hierarchical triple stellar evolution channel involving tidal synchronization-driven chemically homogeneous evolution and a subsequent triple common envelope phase to explain the origin of binary black hole mergers with high effective spins and primary masses within the pair-instability supernova mass gap, accounting for approximately 22% of the observed rate in this mass regime.

Original authors: Tian Huang, Xizhen Lu, Guoliang Lü, Chunhua Zhu, Sufen Guo, Helei Liu, Zhuowen Li, Zhijun Wang, Lei Li, Wei-Min Gu, Nurzada Beissen

Published 2026-07-08

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CC BY 4.0

Original authors: Tian Huang, Xizhen Lu, Guoliang Lü, Chunhua Zhu, Sufen Guo, Helei Liu, Zhuowen Li, Zhijun Wang, Lei Li, Wei-Min Gu, Nurzada Beissen

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 construction site where stars are born, live, and eventually die. Usually, when a massive star dies, it leaves behind a black hole. But there's a weird "forbidden zone" in the size of these black holes, called the Pair-Instability Supernova (PISN) Mass Gap.

Think of this gap like a "no-build zone" on a construction blueprint. Standard physics says that if a star is too big (between about 45 and 130 times the mass of our Sun), it shouldn't just collapse into a black hole. Instead, it should explode so violently that it completely blows itself apart, leaving nothing behind. So, finding a black hole in this size range is like finding a skyscraper built right in the middle of a "Do Not Build" zone. It shouldn't be there, yet our telescopes (LIGO) have spotted several of them.

This paper proposes a clever, three-part solution to explain how these "forbidden" black holes get built.

The Problem: The "Missing" Black Holes

Scientists have detected gravitational waves (ripples in space-time) from black holes colliding. Some of these collisions involve a primary black hole that is squarely in that forbidden "no-build" zone. Standard theories of how single stars or simple pairs of stars evolve can't explain how these massive objects survived without exploding.

The Solution: A Cosmic "Three-Person Dance"

The authors suggest that these black holes aren't born alone or in pairs, but in trios. They propose a specific evolutionary dance involving three stars that solves the mystery. Here is the step-by-step story:

1. The Tight Squeeze (Chemically Homogeneous Evolution)

Imagine two massive stars born very close together, holding hands so tightly they are practically touching. Because they are so close, they spin each other up like a figure skater pulling in their arms.

The Analogy: Think of them as two dancers spinning so fast that their insides get completely mixed up. In normal stars, the core burns fuel and the outer layers stay cool, but these two are spinning so fast that the hydrogen fuel is mixed throughout the whole star.
The Result: This "mixing" (called Chemically Homogeneous Evolution) prevents the stars from puffing up into giant, bloated balloons. Instead, they stay small and compact, burning their fuel efficiently. They skip the "giant" phase entirely and turn directly into tight pairs of black holes. Because they are so perfectly synchronized, they don't get kicked apart when they form.

2. The Third Wheel (The Tertiary Companion)

Now, imagine a third star hanging out nearby, orbiting the pair from a distance. This is the "third wheel" of the system.

The Analogy: Eventually, this third star grows old and starts to expand, like a balloon inflating. It gets so big that it bumps into the orbit of the inner pair.
The Result: This bumping triggers a chaotic event called a Triple Common Envelope. The third star's outer skin (its envelope) swallows the inner pair. It's like a giant, messy hug. As the inner pair swims through this gas, friction slows them down, causing them to spiral closer together.

3. The Grand Finale (The Merge)

The friction from the "hug" is so intense that it forces the inner pair of black holes to crash into each other very quickly.

The Outcome: They merge to form a single, super-massive black hole. Because the two original black holes were identical twins (same mass) and spinning in perfect sync, the crash is so smooth that the new black hole doesn't get kicked out of the system. It stays right there, perfectly positioned to be the "forbidden" black hole we see.

Why This Matters

The authors ran detailed computer simulations of this "trio dance." They found that:

It Works: This process naturally creates black holes in that forbidden size range.
It Fits the Data: The properties of the black holes created in their model (how heavy they are and how fast they spin) match the real data from events like GW190706 almost perfectly.
It's Not the Only Way: They calculate that this specific "trio" method explains about 22% of the observed "forbidden" black hole mergers. This is a huge chunk, but it leaves room for other methods (like stars crashing into each other in crowded star clusters) to explain the rest.

The Bottom Line

The paper argues that the universe has a secret shortcut. By having three stars interact in a specific way—two spinning so fast they stay small, and a third one forcing them to merge—we can build black holes that standard physics says shouldn't exist. It's a cosmic loophole that allows these massive giants to survive the explosion that usually destroys them.

Technical Summary: A Possible Triple Formation Scenario of Binary Black Hole Merge With One In Pair-instability Supernova Mass Gap

Problem Statement
Recent gravitational wave (GW) observations by LIGO-Virgo-KAGRA (LVK), including events such as GW170729, GW190620, GW190706, GW230107, GW230820, and GW230928, have identified binary black hole (BBH) mergers featuring primary black holes with masses squarely within the pair-instability supernova (PISN) mass gap ( $\sim 45 - 130 M_\odot$ ). These events also exhibit high effective spins. Standard isolated binary evolution models struggle to explain these systems because:

PISN Mechanism: Stars with helium core masses in this range are expected to undergo complete thermonuclear disruption via PISNe or pulsational PISNe (PPISNe), leaving no compact remnant.
Mass Transfer Constraints: Classical isolated binaries attempting to grow into this mass regime via super-Eddington accretion typically widen their orbits, preventing merger within a Hubble time.
Dynamical Limitations: While dynamical channels (e.g., dense star clusters, AGN disks) can populate the gap, they require exceptionally dense environments. Conversely, observational data indicates that a vast majority of massive stars (specifically $\sim 73\%$ of O-type stars) reside in hierarchical triple or higher-order systems, yet the isolated triple channel has not been fully explored for this specific mass regime.

Methodology
The authors propose an isolated hierarchical triple stellar evolution channel to explain these anomalies. The study utilizes the open-source numerical framework TSE (Triple Stellar Evolution), which integrates the MOBSE module for metallicity-dependent stellar winds and PISN physics. The methodology involves the following key physical mechanisms:

Chemically Homogeneous Evolution (CHE): In the tight inner binary, intense tidal synchronization drives rapid rotation, triggering efficient internal mixing. This allows stars to burn hydrogen into helium while remaining chemically homogeneous, bypassing the giant expansion phase and avoiding premature Roche-lobe overflow.
Triple Common Envelope (TCE): As the outer tertiary star evolves and expands, it fills its Roche lobe. If the mass transfer is dynamically unstable (governed by a critical mass ratio $q_c$ ), a TCE phase is triggered. The authors employ the SCATTER formalism, which is based on angular momentum conservation rather than energy conservation, to model the orbital decay and envelope ejection. This process rapidly shrinks the inner binary's orbit.
Natal Kicks and Spin: The model assumes low-metallicity environments ( $Z = 0.001$ ) to minimize wind mass loss. Black holes form via direct collapse (failed supernovae) with negligible natal kicks. Crucially, the inner binary is initialized with equal masses ( $q \approx 1$ ) and aligned spins (due to CHE and tidal locking). This symmetry results in zero gravitational recoil kick upon the first merger, preserving the system's dynamical integrity.
Cosmic Integration: The study calculates the volumetric merger rate by integrating over the cosmic star formation rate density (SFRD), metallicity distribution, and delay times, using a specific metallicity-dependent SFRD model.

Key Contributions and Results
The paper presents a detailed evolutionary pathway, specifically modeling the event GW190706, to demonstrate the viability of this channel:

Evolutionary Pathway:
- Initial State: A coplanar hierarchical triple with an inner binary of two $\sim 109 M_\odot$ stars (mass ratio $q=1$ ) and an outer tertiary of $\sim 108 M_\odot$ in a low-metallicity environment ( $Z=0.001$ ).
- Inner Evolution: Tidal forces induce CHE, transforming the inner stars into naked helium stars. They undergo PPISNe mass loss and direct collapse into two $\sim 38 M_\odot$ black holes.
- First Merger: The inner BBH merges rapidly due to GW radiation. Because of the equal mass and aligned spins, the merger produces a massive second-generation (2g) black hole ( $\sim 72.8 M_\odot$ ) with a dimensionless spin $\chi_{rem} \approx 0.686$ and zero recoil kick.
- TCE Phase: The outer tertiary evolves, fills its Roche lobe, and triggers a TCE. This shrinks the orbit between the new 2g black hole and the tertiary's helium core.
- Final Merger: The tertiary core also collapses into a black hole ( $\sim 39 M_\odot$ ) via direct collapse. The resulting asymmetric BBH ( $72.8 M_\odot + 39.3 M_\odot$ ) merges, reproducing the observed properties of GW190706 ( $m_1 \approx 74 M_\odot$ , $m_2 \approx 39 M_\odot$ , $\chi_{eff} \approx 0.28$ ).
Rate Calculation:
- The authors calculate the probability of forming such a system ( $P_{sys}$ ) by integrating over initial mass functions, triple fractions ( $f_{trip} \approx 0.73$ ), and orbital parameters. The resulting birth probability is $P_{sys} \approx 1.41 \times 10^{-9}$ .
- At a characteristic redshift of $z \approx 0.68$ , the model predicts a volumetric merger rate of $R_{triple} \approx 0.011 \text{ Gpc}^{-3} \text{ yr}^{-1}$ .
- Comparing this to the empirical rate derived from the LVK catalog for this mass/spin regime ( $R_{obs} \approx 0.050 \text{ Gpc}^{-3} \text{ yr}^{-1}$ ), the isolated hierarchical triple channel accounts for approximately 22% of the observed events.

Significance and Claims
The paper claims that primordial hierarchical triple interactions in isolated galactic fields are a highly efficient and fundamental astrophysical avenue for populating the PISN mass gap with highly spinning black holes.

Mechanism Validation: The study demonstrates that the combination of CHE (to bypass giant expansion) and TCE (to drive rapid coalescence) can naturally produce BBH mergers with primary masses in the forbidden PISN gap and high effective spins.
Quantitative Consistency: The model reproduces the specific mass and spin parameters of GW190706 and similar events without requiring exotic environments like AGN disks or dense clusters.
Complementary Role: The authors modestly claim that this channel explains a significant fraction (22%) of the observed population. This contribution is substantial enough to be a primary formation channel but leaves a necessary physical margin (the remaining ~78%) for alternative pathways, such as dynamical capture in dense clusters or AGN disks, avoiding overprediction.
Future Outlook: The paper suggests that future multi-band GW observations (combining ground-based detectors like Cosmic Explorer/Einstein Telescope with space-based interferometers like LISA) will be pivotal in detecting the tertiary companions and definitively confirming the demographics of these hierarchical systems.