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How Common Are Common Envelopes? Quantifying Their Role in Forming Gravitational-Wave Sources

By analyzing over 200 population-synthesis simulations, this study reveals that while common-envelope evolution is essential for binary neutron star formation, its role in binary black hole and black hole-neutron star formation is highly degenerate with non-common-envelope pathways, meaning merger rates alone cannot uniquely determine the underlying evolutionary mechanisms.

Original authors: Floor S. Broekgaarden, Ana Lam, Sasha Levina, Jakub Klencki, Kyle A. Rocha, Lieke van Son, Steffani M. Grondin, Monica Gallegos-Garcia, Brian D. Metzger, Enrico Ramirez-Ruiz, Angela Twum, Melanie Sant

Published 2026-06-05

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Floor S. Broekgaarden, Ana Lam, Sasha Levina, Jakub Klencki, Kyle A. Rocha, Lieke van Son, Steffani M. Grondin, Monica Gallegos-Garcia, Brian D. Metzger, Enrico Ramirez-Ruiz, Angela Twum, Melanie Santiago, Julia Haynes, Tyler B. Smith, Amedeo Romagnolo, Edo Berger, Lucas M. de Sá

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. On this floor, massive stars are born in pairs, holding hands as they spin around each other. Sometimes, these pairs stay together until they die, collapsing into dense, invisible objects like black holes or neutron stars. If they get close enough, they crash together, sending ripples through space-time called gravitational waves.

Scientists have been catching these ripples, but they are trying to solve a mystery: How did these star pairs get so close in the first place?

This paper is like a massive detective report that reviews over 200 different "theories" (computer simulations) about how these star pairs evolve. The authors are trying to figure out if there is one specific "move" the stars must do to get close enough to merge, or if there are many different ways to do it.

Here is the breakdown of their findings in simple terms:

The Big Mystery: The "Common Envelope" Dance

There is a specific, chaotic move in this cosmic dance called a Common Envelope (CE) phase.

The Analogy: Imagine two dancers spinning. One dancer suddenly gets too big (swells up like a giant balloon) and swallows the other dancer whole. They are now stuck inside a giant, shared cloud of gas (the "envelope").
The Result: Friction inside this cloud slows them down, causing them to spiral inward rapidly. If they can survive this and spit the cloud out, they end up very close together, ready to merge later.
The Question: For decades, scientists thought this "swallowing" move was required for any pair of stars to get close enough to merge. But recently, some scientists started saying, "Maybe not! Maybe they can just gently slow each other down without ever getting swallowed."

What the Paper Found: It Depends on Who You Are

The authors looked at three types of star pairs:

Black Hole + Black Hole (BBH)
Black Hole + Neutron Star (BHNS)
Neutron Star + Neutron Star (BNS)

Here is the twist: The answer is different for each group.

For Black Hole pairs (BBH) and Black Hole/Neutron Star pairs (BHNS):
The paper found that there is no single answer. Some computer models say these pairs must go through the "swallowing" (CE) phase. Other models say they can get close just by gently slowing each other down (Stable Mass Transfer) without ever getting swallowed.
- The Analogy: It's like asking, "How do you get to the top of a mountain?" Some people say, "You must take the steep, dangerous elevator (CE)." Others say, "No, you can just hike up the gentle slope (Stable Transfer)." The paper found that both groups of hikers exist in the simulations, and they both reach the top (the merger) at the same speed.
- The Problem: Because both methods produce the same number of mergers, just counting the mergers doesn't tell us which "hiking path" the stars actually took. This is called a degeneracy.
For Neutron Star pairs (BNS):
The story is very different. Almost every single model agrees that these pairs must go through the "swallowing" (CE) phase.
- The Analogy: For these specific dancers, there is no gentle slope. They must get swallowed by the giant cloud to get close enough to merge. If they don't, they stay too far apart.
- The Takeaway: This gives scientists a solid clue. If we see a Neutron Star merger, we know for sure the "swallowing" physics happened. This makes Neutron Star pairs a great "test case" to understand how that messy, chaotic envelope ejection works.

Why Do the Computer Models Disagree?

If the answer is so different for Black Holes vs. Neutron Stars, why do the computer models disagree so much? The paper found that the disagreement comes down to a few "knobs" the scientists turn in their simulations:

How stable is the mass transfer? (Does the star swell up gently or explode?)
How much energy is lost? (Does the system lose spin or keep it?)
How efficient is the "swallowing"? (Can the stars actually spit out the cloud, or do they crash and merge inside it?)

The paper shows that changing these knobs slightly can flip the result from "mostly swallowing" to "mostly no swallowing." It's like baking a cake: if you change the oven temperature just a little, you might get a perfect cake, or a burnt one, or a flat pancake. The models are sensitive to these details.

The Bottom Line

We can't just count the mergers. Knowing how many black holes merged doesn't tell us how they formed. We need to look at other clues, like how fast they are spinning or how heavy they are.
Neutron Stars are the key. Because they almost always require the "swallowing" phase, studying them helps us understand the messy physics of that phase.
We need better teamwork. The paper argues that scientists need to stop using different definitions for "formation channels" and start comparing their computer models using the same rules. They need to share their data openly so everyone can see exactly where the models agree and where they disagree.

In short: The universe is messy. For some star pairs, there are many ways to get close. For others, there is only one. To understand the story of the stars, we need to stop guessing and start comparing our maps carefully.

Technical Summary: How Common Are Common Envelopes? Quantifying Their Role in Forming Gravitational-Wave Sources

Problem Statement
A central objective of gravitational-wave (GW) astronomy is to use merging compact-object binaries (black hole–black hole [BBH], black hole–neutron star [BHNS], and binary neutron star [BNS]) as fossils to reconstruct the formation and evolution of massive stars. While population-synthesis models map massive stellar binaries to merging compact objects, there is a fundamental disagreement regarding the dominant orbital-hardening mechanisms within isolated binary evolution. Specifically, models diverge on whether common-envelope (CE) evolution is a required ingredient for forming merging systems or if stable mass transfer (SMT) pathways can suffice. Previous studies have typically focused on single compact-object classes, single population-synthesis codes, or limited parameter variations, making it difficult to disentangle physical uncertainties from framework-dependent differences.

Methodology
The authors compile and systematically compare formation-channel predictions from over 200 isolated-binary population-synthesis simulation results published within the last decade. The study restricts the sample to studies reporting intrinsic (astrophysical) merger rates rather than detection-weighted rates to ensure comparability across different detector sensitivities.

To organize the heterogeneous definitions found in the literature, the authors construct a unified hierarchical taxonomy:

Level 1: Systems are classified broadly into three categories: "without CE" (zero CE episodes), "with CE" (at least one CE episode), and "other" (unspecified).
Level 2: Sub-channels are defined based on interaction sequences relative to the first supernova (SN1). These include specific sequences such as SMT+SMT (stable mass transfer before and after SN1), NON+NON (no mass transfer), CHE (chemically homogeneous evolution), and various CE sequences (e.g., classic CE, single-core CE, double-core CE).

The authors analyze the fractional contributions of these pathways to the intrinsic merger rates ( $R_m$ ) for BBH, BHNS, and BNS populations. They examine parameter dependencies within specific codes (e.g., varying CE efficiency $\alpha$ , mass-transfer efficiency $\beta$ , angular-momentum loss $\gamma$ , and natal kick dispersion $\sigma$ ) and compare outcomes across different codes (e.g., COMPAS, StarTrack, POSYDON, SeBa, MOBSE).

Key Results

Degeneracy in BBH and BHNS Formation: The study finds that BBH and BHNS formation pathways span nearly the entire allowed range from CE-dominated (0% without CE) to without-CE-dominated (100% without CE). Crucially, models predicting vastly different formation-channel fractions often yield similar total merger rates. This reveals a fundamental degeneracy: merger-rate measurements alone do not uniquely constrain the underlying evolutionary pathways.
Robust CE Requirement for BNS: In stark contrast to BBH and BHNS, BNS formation proceeds almost exclusively through channels involving at least one CE phase ( $\gtrsim 90\text{--}100\%$ ). Only a small minority of models predict significant without-CE contributions, and these are often associated with fine-tuned parameter spaces (e.g., specific natal kicks or mass ratios). This suggests CE evolution plays a qualitatively different, essential role in BNS formation compared to other compact-object binaries.
Drivers of Disagreement: The relative contributions of with-CE and without-CE pathways are governed primarily by assumptions regarding:
- Mass-transfer stability: Criteria determining whether Roche-lobe overflow is stable or leads to a CE (e.g., critical mass ratio $q_c$ ).
- Angular-momentum loss: Efficiency of mass loss carrying away orbital angular momentum (parameterized by $\gamma$ ).
- CE efficiency: The efficiency of orbital energy used to eject the envelope ( $\alpha_{CE}$ ).
- Supernova physics: Remnant mass prescriptions and natal kick magnitudes ( $\sigma$ ).
  The authors demonstrate that these parameters often act non-linearly and in correlated fashions. Consequently, trends observed from "one-at-a-time" parameter variations within a single code do not generalize across different simulation frameworks.
Level 2 Complexity: The diversity in Level 1 fractions is not driven by a single dominant alternative sub-channel but by a redistribution across multiple evolutionary sequences (e.g., varying combinations of SMT, NON, and CE phases).

Significance and Claims
The paper claims that the central challenge in interpreting GW populations is not merely determining the value of a specific binary-evolution parameter, but disentangling fundamentally different physical pictures of how massive binaries shrink and survive interactions.

For BBH and BHNS: The results imply that the question of whether CE is "required" has no single answer; it depends heavily on the specific physical assumptions and the interplay of multiple uncertain parameters. The observed merger rates are insufficient to distinguish between CE-dominated and SMT-dominated universes.
For BNS: The robust requirement of CE evolution provides a critical anchor point. Since BNS formation is tightly coupled to CE physics, the observed BNS merger rate (and its ratio to BBH/BHNS rates) offers a more direct empirical constraint on CE efficiency and envelope ejection physics than rates for other systems.
Methodological Impact: The authors argue that robust interpretation of GW populations requires transparent formation-channel definitions, reproducible analysis pipelines, and systematic cross-code comparisons. They emphasize that future progress depends on moving beyond merger-rate comparisons to include other observables (masses, spins, delay times) and connecting GW sources to intermediate electromagnetic populations (e.g., stripped stars, X-ray binaries, luminous red novae) that probe the binary-interaction physics directly.

The work establishes a community benchmark for formation-channel predictions and highlights that the diversity in outcomes reflects the high-dimensional nature of binary evolution parameter space, where different physical assumptions can open, suppress, or reshape distinct routes to merger.

The Big Mystery: The "Common Envelope" Dance

What the Paper Found: It Depends on Who You Are

Why Do the Computer Models Disagree?

The Bottom Line

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