Binary Evolution Can Mimic the Pair-Instability Mass Gap in Black Hole Mergers

This study demonstrates that efficient mass transfer in binary systems can naturally produce a black hole mass distribution mimicking the pair-instability mass gap, suggesting that observed features in gravitational-wave data may arise from binary evolution rather than solely from pair-instability supernovae.

The Gist

The Big Mystery: The "Black Hole Weight Limit"

Imagine you are a detective looking at a pile of heavy weights (Black Holes) found by gravitational wave detectors (like LIGO). Recently, scientists noticed something strange: there seem to be no black holes between roughly 45 and 130 solar masses (one solar mass is the mass of our Sun — about 2 × 10³⁰ kilograms, or 330,000 times the mass of Earth).

This missing zone is called the "Pair-Instability Mass Gap."

The Traditional Theory (The "Explosion" Explanation):
Most scientists think this gap exists because of a cosmic safety valve. If a star gets too heavy (between 45 and 130 solar masses), it doesn't just collapse into a black hole. Instead, it gets so hot inside that it explodes completely, blowing itself apart. It's like a pressure cooker that gets so hot the lid blows off, leaving nothing behind to become a black hole. Therefore, no black holes should exist in that weight range.

The New Twist:
Astronomer Aleksandra Olejak says, "Wait a minute. Maybe we don't need an explosion to explain the missing weights. Maybe it's just how black holes are born in pairs."

The New Theory: The "Tug-of-War" Analogy

Olejak suggests that the "missing" black holes aren't missing because they exploded. They are missing because of a specific dance between two stars before they die.

Imagine two stars as siblings in a tug-of-war, but instead of pulling a rope, they are trading mass (stuff).

1. The First Swap (The Big Brother gives to the Little Brother):

   • Star A is the big, strong sibling. Star B is smaller.
   • Star A starts to expand and spills its "stuff" onto Star B.
   • The Crucial Part: In this new theory, Star B is a very greedy sibling. It catches more than half of what Star A gives it.
   • The Result: Star B suddenly becomes the heavy hitter! Star A is left skinny and weak. They have swapped roles.

2. The Second Swap (The Little Brother tries to give back):

   • Now, the new big star (Star B) expands and tries to give stuff back to the skinny Star A (which has already turned into a black hole).
   • The Problem: The black hole has a "full stomach." It can only eat so fast (like a speed limit). It can't swallow all the stuff Star B is dumping on it. Most of the stuff flies away into space.
   • The Result: The skinny black hole (Star A) stays skinny. It never gets enough food to grow into the "forbidden zone" above 45 solar masses.

The "Mimicry" Effect

Here is the magic trick: Even if the universe could make black holes heavier than 45 solar masses (if the "explosion" theory were wrong), this specific "Tug-of-War" dance ensures that the smaller black hole in the pair never gets that heavy.

• The Heavy One: Gets huge because it ate all its sibling's mass early on.
• The Light One: Stays light because it couldn't eat enough later.

So, when we look at the data, we see a sharp cutoff at 45 solar masses for the smaller black holes. It looks exactly like the "Pair-Instability Explosion" happened, but it actually just happened because of a messy meal between two stars.

How to Tell the Difference? (The Spin Test)

If the "Explosion Theory" is right, the black holes in that heavy zone might be "second-generation" monsters (black holes made from other black holes crashing together). These would spin wildly and chaotically.

If Olejak's "Tug-of-War" theory is right, these black holes were born from a stable pair of stars. They would likely be spinning in a neat, aligned way (like a well-organized dance).

The Analogy:

• Explosion Theory: Like a chaotic mosh pit where people bump into each other randomly (random spins).
• Binary Evolution Theory: Like a synchronized swimming team where everyone moves in perfect unison (aligned spins).

The Bottom Line

The paper argues that we might be misinterpreting the data. We think we are seeing a "forbidden zone" created by exploding stars, but we might actually just be seeing the natural result of stars trading mass unevenly.

Why does this matter?
It means we don't need to change the laws of physics regarding how massive stars explode. Instead, we just need to understand better how stars in pairs share their mass. Future gravitational wave detections will act as the final judge: if the heavy black holes are spinning neatly, Olejak's "Tug-of-War" theory wins. If they are spinning chaotically, the "Explosion" theory wins.

Technical Summary

1. Problem Statement

Recent gravitational wave (GW) data from the LIGO–Virgo–KAGRA (LVK) O4a run suggests a potential "pair-instability supernova (PSN) mass gap" in the black hole (BH) mass distribution. Specifically, analyses by Antonini et al. (2025) and Tong et al. (2025b) indicate:

• A sharp decline in the number of BHs with masses above $\sim 45 M_\odot$.
• A transition in effective spin ($\chi_{\text{eff}}$) distributions, where BHs above this mass threshold appear to have systematically higher spins.
• These features are currently interpreted as evidence that PSN mechanisms prevent the formation of BHs in the $\sim 45\text{--}130 M_\odot$ range, implying that massive BHs in this region are likely second-generation merger remnants.

The Core Question: Is this observed mass cutoff and spin transition truly caused by the PSN mechanism, or can it be reproduced by standard binary evolution physics without invoking a low-mass PSN limit?

2. Methodology

The author employs two complementary approaches to model the formation of merging Binary Black Hole (BBH) systems:

1. Population Synthesis: Using the StarTrack code (Belczynski et al.), the author simulates a large population of merging BBHs.
   • PSN Model: The default model assumes an extended PSN limit where disruption occurs only for helium cores between $90 M_\odot$ and $175 M_\odot$ (allowing BHs up to $\sim 90 M_\odot$). A comparative model with a strict $45 M_\odot$ PSN limit is also tested.
   • Mass Transfer Physics:
     • Phase 1 (Stable Mass Transfer): The initially more massive star transfers mass to the companion. The model assumes high efficiency ($\gtrsim 50\%$ of transferred mass is accreted), leading to a mass-ratio reversal.
     • Phase 2 (Mass Transfer onto BH): The secondary star (now the more massive component) expands and transfers mass onto the first-born BH. This phase is modeled as highly non-conservative, limited by the Eddington accretion rate, meaning the first-born BH gains negligible mass.
2. Semi-Analytical Framework: A simplified analytical model is used to verify that the results stem from fundamental binary physics rather than specific code details.

3. Key Contributions & Mechanism

The paper proposes a specific evolutionary pathway that mimics the PSN mass gap without requiring the PSN limit to be as low as $45 M_\odot$:

• Mass-Ratio Reversal: During the first Roche-lobe overflow, efficient mass transfer ($>50\%$) causes the initially less massive star to become the more massive component.
• Differential Mass Growth:
  • The accretor (originally the secondary) grows significantly, eventually collapsing into a massive BH (potentially up to the true PSN limit of $\sim 90 M_\odot$).
  • The donor (originally the primary) is stripped of its envelope and collapses into the first-born BH. Because it loses mass during the transfer, its final mass is capped at the stripped core mass.
• The Cutoff: The mass of the less massive BH in the final BBH system is determined by the stripped primary's core mass. The model shows that even if the PSN limit is high ($\sim 90 M_\odot$), the physics of stable mass transfer naturally limits the mass of the less massive component to below $\sim 45 M_\odot$.

4. Key Results

• Mass Distribution Mimicry: The simulations reproduce the observed mass distributions reported by Tong et al. (2025b).
  • The more massive BH component distribution extends up to the assumed PSN limit ($\sim 90 M_\odot$ in the default model).
  • The less massive BH component shows a sharp cutoff at $\sim 45 M_\odot$, regardless of whether the true PSN limit is $45 M_\odot$ or $90 M_\odot$.
• Statistical Rarity: In the default model (PSN limit $\sim 90 M_\odot$):
  • The intrinsic fraction of merging BBHs where the less massive BH exceeds $45 M_\odot$ is negligible ($< 10^{-5}$).
  • Even after applying detection weighting (scaling with chirp mass $M_{\text{chirp}}^{5/2}$), the fraction remains very low ($\sim 0.22\%$).
• Spin Implications: The proposed scenario naturally produces a correlation between mass and spin. The more massive BH (the accretor) can be spun up via tidal interactions in the post-mass-transfer phase, potentially explaining the observed trend of higher effective spins in massive systems.

5. Significance and Future Outlook

• Alternative Interpretation: The study challenges the necessity of a low-mass PSN limit ($\sim 45 M_\odot$) to explain current GW data. It suggests that binary interaction physics (specifically efficient mass transfer) can create an apparent mass gap in the lower-mass component distribution.
• Discriminating Observables: The paper proposes that future GW detections can distinguish between the PSN hypothesis and the binary evolution hypothesis by analyzing effective spins ($\chi_{\text{eff}}$):
  • PSN/Second-Generation Scenario: If the gap is due to PSN, massive BHs inside the gap might be second-generation mergers, which should exhibit a mix of positive and negative spins (dynamical origin) or specific high-spin signatures.
  • Binary Evolution Scenario: If the gap is due to binary evolution, the massive BHs should predominantly show positive effective spins (indicating spin-orbit alignment from isolated binary evolution).
• Conclusion: The observed features in GW data do not definitively prove the existence of a PSN mass gap at $45 M_\odot$. Instead, they may be a natural consequence of binary evolution, highlighting the need for precise spin measurements in future GW events to constrain stellar physics and formation channels.